Axioms

23 pages, 463 KB

Open AccessArticle

The Existence and Uniqueness of Mild Solutions for Fuzzy Hilfer Fractional Evolution Equations with Non-Local Conditions

by Kholoud N. Alharbi and Sanaa Alotaibi

Axioms 2025, 14(11), 855; https://doi.org/10.3390/axioms14110855 - 20 Nov 2025

Viewed by 184

Abstract

In this paper, we investigate a fuzzy Hilfer fractional evolution equation of type

0 < β < 1

and order

1 < α < 2

subject to nonlocal conditions. Using the infinitesimal generator of a strongly continuous cosine family, we define a mild [...] Read more.

In this paper, we investigate a fuzzy Hilfer fractional evolution equation of type

0 < β < 1

and order

1 < α < 2

subject to nonlocal conditions. Using the infinitesimal generator of a strongly continuous cosine family, we define a mild solution for the proposed system. The existence and uniqueness of such mild solutions are established through Schauder’s fixed-point theorem and the Banach contraction principle. An illustrative application to a fuzzy fractional wave equation is presented to demonstrate the effectiveness of the developed approach. The main contribution of this study lies in the unified treatment of fuzzy Hilfer fractional evolution equations under nonlocal conditions, which generalizes and extends several existing results and provides a solid analytical foundation for modeling systems with memory and uncertainty. Full article

(This article belongs to the Special Issue Fractional Differentiation and Applied Mathematics: Recent Advances and Applications)

► Show Figures

Figure 1

16 pages, 255 KB

Open AccessArticle

On Generalized One-kZero Numbers

by Paula M. M. C. Catarino, Grieg A. Costa and Eudes A. Costa

Axioms 2025, 14(11), 854; https://doi.org/10.3390/axioms14110854 - 20 Nov 2025

Viewed by 187

Abstract

In this study is introduced a novel generalization of repunit and one-zero numbers through the formulation of the generalized One-kZero. This sequence extends the classical families of repunit and one-zero numbers by establishing a unified framework in which the parameter [...] Read more.

In this study is introduced a novel generalization of repunit and one-zero numbers through the formulation of the generalized One-kZero. This sequence extends the classical families of repunit and one-zero numbers by establishing a unified framework in which the parameter

(k \geq 0)

specifies the number of consecutive zeros separating two ones in the decimal representation. We introduce the new family of sequences, the generalized One-kZero numbers, and investigate some of their properties. The main purpose is to present a generalization for the recurrence relation of kind One-Zero numbers and determine some relations and properties. The reason that led us to this method is that the recurrence relation of One-Zero and Repunit numbers has a second-order difference equation as a specific case of the Horadam-type sequence. The Binet formula, generating function, sum formulas and many other relations will therefore be much easier to find. Also, some other identities that have not been found before in the particular case of One-Zero and Repunit sequences are also included in this study. Full article

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

53 pages, 473 KB

Open AccessArticle

Analysis of a k/n(G) Retrial System with Multiple Working Vacations

by Changjiang Lai, Rena Eskar and Ehmet Kasim

Axioms 2025, 14(11), 853; https://doi.org/10.3390/axioms14110853 - 20 Nov 2025

Viewed by 140

Abstract

In this paper, a

k / n (G)

retrial system with multiple working vacations is considered, and a mathematical model of the system is established by supplementary variable method, and a dynamic analysis of the system is carried out. Firstly, the [...] Read more.

In this paper, a

k / n (G)

retrial system with multiple working vacations is considered, and a mathematical model of the system is established by supplementary variable method, and a dynamic analysis of the system is carried out. Firstly, the model is transformed into an abstract Cauchy problem in Banach space by introducing the state space, main operator and its definition domain. Secondly, the

C_{0}

-semigroup theory in functional analysis and the spectral theory of linear operators are used to prove that the main operator of the model generates a positive contraction

C_{0}

-semigroup, which leads to the existence of a unique, non-negative time-dependent solution of the system that satisfies the probabilistic properties. Finally, Greiner’s boundary perturbation idea and the spectral properties of the corresponding operators are used to show that the time-dependent solution strongly converges to its steady-state solution. Full article

(This article belongs to the Special Issue Numerical and Analytical Methods for Partial Differential Equations with Integral Boundary Conditions)

12 pages, 262 KB

Open AccessArticle

Remarks on the Green’s Matrix of a General Incompressible Oldroyd-B System

by Yongtong Liu, Qiqing Li, Jinrui Huang and Bingyuan Huang

Axioms 2025, 14(11), 852; https://doi.org/10.3390/axioms14110852 - 20 Nov 2025

Viewed by 219

Abstract

In this manuscript, we study a general incompressible Oldroyd-B system and first establish a new interpretation for the Green’s matrix and then establish the pointwise estimates for the Green’s matrix, especially for the high-frequency part, where the dependence on the viscosity constants is [...] Read more.

In this manuscript, we study a general incompressible Oldroyd-B system and first establish a new interpretation for the Green’s matrix and then establish the pointwise estimates for the Green’s matrix, especially for the high-frequency part, where the dependence on the viscosity constants is carefully analyzed. Full article

14 pages, 278 KB

Open AccessArticle

On Two-Dimensional Closed–Open Topological Field Theories

by Mohmmad Zailai

Axioms 2025, 14(11), 851; https://doi.org/10.3390/axioms14110851 - 20 Nov 2025

Viewed by 228

Abstract

Topological field theories (TFTs) have captured the attention of mathematicians due to their various applications. In categorical terms, an nTFT is defined as a monoidal functor that maps the category of n-dimensional cobordisms to the category of vector spaces. In this paper, we [...] Read more.

Topological field theories (TFTs) have captured the attention of mathematicians due to their various applications. In categorical terms, an nTFT is defined as a monoidal functor that maps the category of n-dimensional cobordisms to the category of vector spaces. In this paper, we introduce the category of two-dimensional closed–open cobordisms, denoted as

2 C o b_{C O}

. We demonstrate that the generating morphisms in this category total 35. Furthermore, we establish that the category

2 C o b_{C O}

is a monoidal category. We define a triple

(B, ε, ε^{'})

as a doubly Frobenius algebra if both

(B, ε)

and

(B, ε^{'})

are Frobenius algebras. We then introduce the category of doubly Frobenius algebras, wherein the objects are doubly Frobenius algebras and the morphisms are homomorphisms of Frobenius algebras that satisfy specific compatibility conditions. Additionally, we present a new type of 2TFT, which we refer to as the two-dimensional closed–open TFT (denoted as

2 T F T_{C O}

). We demonstrate that the category of all

2 T F T_{C O}

, referred to as

2 T F T_{C O}

, is equivalent to the category of all commutative doubly Frobenius algebras, denoted as

C F

. Full article

(This article belongs to the Section Geometry and Topology)

24 pages, 1811 KB

Open AccessArticle

Third-Order Nonlinear Neutral Delay Differential Equations with Several Deviating Arguments: Improved Oscillation Criteria

by Asma Al-Jaser, Stefano Serra-Capizzano, Eman Alluqmani and Belgees Qaraad

Axioms 2025, 14(11), 850; https://doi.org/10.3390/axioms14110850 - 18 Nov 2025

Viewed by 228

Abstract

In this paper, we initiate the study of the asymptotic and oscillatory properties of solutions to third-order functional differential equations. Using the Riccati transformation to eliminate the existence of non-oscillatory solutions, we derive various oscillation criteria that address different models of the studied [...] Read more.

In this paper, we initiate the study of the asymptotic and oscillatory properties of solutions to third-order functional differential equations. Using the Riccati transformation to eliminate the existence of non-oscillatory solutions, we derive various oscillation criteria that address different models of the studied equation. Our primary focus is on reducing the constraints imposed on oscillation criteria, thereby broadening their applicability. Our results improve, refine, and extend some of the known findings in previous studies. Several examples are presented to illustrate the significance of the main results. Full article

(This article belongs to the Special Issue Applied Mathematics and Numerical Analysis: Theory and Applications, 2nd Edition)

► Show Figures

Figure 1

25 pages, 395 KB

Open AccessArticle

Two-Stage Three-Dimensional Transportation Optimization Under Elliptic Intuitionistic Fuzzy Quadruples: An Index-Matrix Interpretation

by Velichka Traneva and Stoyan Tranev

Axioms 2025, 14(11), 849; https://doi.org/10.3390/axioms14110849 - 18 Nov 2025

Viewed by 202

Abstract

The transportation problem (TP) is a canonical linear programming model for minimizing the cost of distributing goods from multiple sources to multiple destinations. Classical TPs assume deterministic costs, supplies, and demands, whereas real supply chains are affected by volatility in fuel prices, inflation, [...] Read more.

The transportation problem (TP) is a canonical linear programming model for minimizing the cost of distributing goods from multiple sources to multiple destinations. Classical TPs assume deterministic costs, supplies, and demands, whereas real supply chains are affected by volatility in fuel prices, inflation, disruptions, and weather, making such parameters uncertain. Fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs) have been widely used to handle vagueness; however, while Atanassov’s IFSs incorporate hesitation in addition to membership and non-membership, they remain limited to isotropic representations of uncertainty. This paper introduces an index-matrix interpretation for a two-stage three-dimensional transportation problem (2-S 3-D TP) defined under Elliptic Intuitionistic Fuzzy Quadruples (E-IFQs). Within this framework, transportation costs, supplies, and demands are represented as E-IFQs, allowing the modeling of anisotropic and correlated uncertainty along the membership and non-membership axes. The two-stage formulation extends previous intuitionistic fuzzy approaches by adding a temporal dimension and incorporating practical constraints such as cost thresholds and feasibility checks. The objective is to determine optimal producer–hub–buyer allocations that minimize the total E-IFQ cost while preserving consistency across all stages and time periods. A detailed case study on EV battery module distribution demonstrates the effectiveness of the proposed model. Compared with conventional fuzzy and intuitionistic fuzzy formulations, the 2-S 3-D E-IFTP yields more robust and precise decisions under complex, multidimensional uncertainty, offering improved interpretability and policy integration over time. Full article

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

► Show Figures

Figure 1

43 pages, 403 KB

Open AccessArticle

On Quadraticity of Linear Combinations of Two Essentially Cubic Matrices That Commute

by Tuğba Demirkol and İrem Gamze Ünlütürk

Axioms 2025, 14(11), 848; https://doi.org/10.3390/axioms14110848 - 18 Nov 2025

Viewed by 175

Abstract

This work presents a complete and definitive characterization of all cases where every linear combination of two commuting essentially cubic matrices results in a quadratic matrix, thereby extending existing contributions in the literature. To facilitate a better understanding of the main results of [...] Read more.

This work presents a complete and definitive characterization of all cases where every linear combination of two commuting essentially cubic matrices results in a quadratic matrix, thereby extending existing contributions in the literature. To facilitate a better understanding of the main results of this study, several numerical examples are provided at the end of the paper, and connections with the results in the literature are established. Full article

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

► Show Figures

Figure 1

19 pages, 311 KB

Open AccessArticle

On the Application of a Hypergeometric Identity to Generate Generalized Hypergeometric Reduction Formulas

by Juan Luis González-Santander

Axioms 2025, 14(11), 847; https://doi.org/10.3390/axioms14110847 - 18 Nov 2025

Viewed by 141

Abstract

We systematically exploit a new generalized hypergeometric identity to obtain new hypergeometric summation formulas. As a consistency test, alternative proofs for some special cases are also provided. As a byproduct, new summation formulas with finite sums involving the psi function and a recursive [...] Read more.

We systematically exploit a new generalized hypergeometric identity to obtain new hypergeometric summation formulas. As a consistency test, alternative proofs for some special cases are also provided. As a byproduct, new summation formulas with finite sums involving the psi function and a recursive formula for Bateman’s G function are derived. Finally, all the results have been numerically checked with MATHEMATICA. Full article

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

41 pages, 18402 KB

Open AccessArticle

Trapped Modes Along Periodic Structures Submerged in a Two-Layer Fluid with Free Surface and a Background Steady Flow

by Gonçalo Dias and Bruno Pereira

Axioms 2025, 14(11), 846; https://doi.org/10.3390/axioms14110846 - 18 Nov 2025

Viewed by 131

Abstract

This study examines the trapping of linear water waves by an endless structure of stationary, three-dimensional periodic obstacles within a two-layer fluid system. The setup features a lower layer of either limited or unlimited depth, overlaid by an upper layer of finite thickness [...] Read more.

This study examines the trapping of linear water waves by an endless structure of stationary, three-dimensional periodic obstacles within a two-layer fluid system. The setup features a lower layer of either limited or unlimited depth, overlaid by an upper layer of finite thickness bounded by a free surface, with each layer exhibiting its own constant background speed relative to the fixed reference frame. For real roots to emerge in the dispersion relation, an additional stability condition on the layer velocities is necessary. By selecting adequate choices for the background flow, a non-linear eigenvalue problem is derived from the variational formulation; its reasonable approximation yields a geometric criterion that guarantees the presence of trapped modes (subject to the aforementioned stability bounds). The selection of the eigenvalue is influenced by velocity owing to the presence of an interface and free surface. Due to inherent symmetries, the overall analysis can be confined to the positive quadrant of the velocity domain. Illustrations are provided for various obstacle setups that produce trapped modes in diverse ways. Full article

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

► Show Figures

Figure 1

17 pages, 459 KB

Open AccessArticle

The Conservative Field of Coupled Newton–Coulomb Sources: Component Coupling Constants, Mass ⇌ Charge Cross-Forces, and Radiation from Reissner–Nordström Black Hole Mergers

by Dimitris M. Christodoulou, Demosthenes Kazanas and Silas G. T. Laycock

Axioms 2025, 14(11), 845; https://doi.org/10.3390/axioms14110845 - 18 Nov 2025

Viewed by 272

Abstract

We investigate a combined conservative field, in which classical gravitational and electrostatic sources also exhibit mutual interactions. Hitherto neglected, the coupling between mass and charge may be necessary for constructing a unified conservative force field generated by a single underlying source. We determine [...] Read more.

We investigate a combined conservative field, in which classical gravitational and electrostatic sources also exhibit mutual interactions. Hitherto neglected, the coupling between mass and charge may be necessary for constructing a unified conservative force field generated by a single underlying source. We determine the coupling constant of the cross-field components as the geometric mean (G-M) of Newton’s G and Coulomb’s K constants, in both SI units and dimensionless form. Consequently, for two identical objects, the cross-force (

F_{\times}

) is the G-M of the familiar Newton (

F_{g}

) and Coulomb (

F_{e}

) forces, so that

F_{\times} = \sqrt{F_{g} F_{e}}

, where

F_{g} ≪ F_{\times} ≪ F_{e}

. Remarkably, such cross-forces should be measurable in torsion balance experiments involving a suspended neutral mass interacting with a partially ionized gas. Furthermore, we apply our new formulation to estimate the dimensionless amplitude

∥ h_{α β}^{TT} ∥

of gravitational waves that are emitted by inspiraling Reissner–Nordström (RN) black hole binaries, expressed in terms of ratios of the four fundamental lengths of the problem: the distance to the binary D, the binary separation R, the Schwarzschild radius

R_{S} \propto 2 M

of mass M, and the RN charge (Q) length scale

L_{Q} \propto 2 Q

. In this classical setting with speeds much lower than the speed of light c in vacuum, the surprising appearance of the maximum relativistic tension force

F_{\max} = c^{4} / (4 G)

is duly noted. Full article

(This article belongs to the Special Issue Mathematical Aspects of Black Holes in General Relativity and Beyond)

► Show Figures

Figure 1

15 pages, 4502 KB

Open AccessArticle

Quantum Fisher Information Dynamics in Squeezed Reservoirs: Mathematical Insights and Quantum Applications

by Kamal Barrada

Axioms 2025, 14(11), 844; https://doi.org/10.3390/axioms14110844 - 18 Nov 2025

Viewed by 308

Abstract

This work explores the dynamics of quantum Fisher information (QFI) in open quantum systems coupled to squeezed reservoirs, providing a mathematical framework for analyzing parameter estimation precision under decoherence. We analyze QFI in two-qubit systems undergoing pure dephasing, considering the effects of squeezing [...] Read more.

This work explores the dynamics of quantum Fisher information (QFI) in open quantum systems coupled to squeezed reservoirs, providing a mathematical framework for analyzing parameter estimation precision under decoherence. We analyze QFI in two-qubit systems undergoing pure dephasing, considering the effects of squeezing parameter, phase difference, and coupling strength within an Ohmic spectral density model. The decoherence factor shows how reservoir engineering influences coherence loss. Numerical results demonstrate that optimal squeezing and local bath configurations enhance QFI preservation, while collective couplings accelerate decay. We also examine the interplay with von Neumann entropy, highlighting their inverse correlation, where increased mixedness reduces metrological sensitivity. Full article

(This article belongs to the Special Issue A Century of Quantum Mechanics: Mathematical Foundations and Computational Applications)

► Show Figures

Figure 1

7 pages, 528 KB

Open AccessArticle

Structural Results on the HMLasso

by Shin-ya Matsushita and Hiromu Sasaki

Axioms 2025, 14(11), 843; https://doi.org/10.3390/axioms14110843 - 17 Nov 2025

Viewed by 143

Abstract

HMLasso (Lasso with High Missing Rate) is a useful technique for sparse regression when a high-dimensional design matrix contains a large number of missing data. To solve HMLasso, an appropriate positive semidefinite symmetric matrix must be obtained. In this paper, we present two [...] Read more.

HMLasso (Lasso with High Missing Rate) is a useful technique for sparse regression when a high-dimensional design matrix contains a large number of missing data. To solve HMLasso, an appropriate positive semidefinite symmetric matrix must be obtained. In this paper, we present two structural results on the HMLasso problem. These results allow existing acceleration algorithms for strongly convex functions to be applied to solve the HMLasso problem. Full article

(This article belongs to the Special Issue New Theory and Applications of Nonlinear Analysis, Fractional Calculus and Optimization, 2nd Edition)

► Show Figures

Figure 1

12 pages, 266 KB

Open AccessArticle

Rigidity of Non-Steady Gradient Ricci Solitons

by Mohammed Guediri

Axioms 2025, 14(11), 842; https://doi.org/10.3390/axioms14110842 - 17 Nov 2025

Viewed by 149

Abstract

Let

(M, g)

be a connected, compact Riemannian manifold of dimensionan n. We demonstrate that, after a suitable normalization, a shrinking gradient Ricci soliton

(M, g, f, λ)

is trivial exactly when the mean [...] Read more.

Let

(M, g)

be a connected, compact Riemannian manifold of dimensionan n. We demonstrate that, after a suitable normalization, a shrinking gradient Ricci soliton

(M, g, f, λ)

is trivial exactly when the mean value of f is less than or equal to

\frac{n}{2}

. Moreover, we prove that a normalized non-steady gradient Ricci soliton

(M, g, f, λ)

is trivial if and only if its scalar curvature S satisfies the relation

S = λ (f + \frac{n}{2}) .

In addition, we establish that if

(M, g, f, λ)

admits an isometric immersion as a hypersurface in the Euclidean space, then the soliton must necessarily be of a shrinking type. In such a case, the constant

λ

and the mean curvature of M satisfy a certain inequality, with equality occurring precisely when M is isometric to a round sphere. Full article

(This article belongs to the Special Issue Differential Geometry and Its Application, 3rd Edition)

9 pages, 382 KB

Open AccessArticle

The Fine-Structure Constant in the Bivector Standard Model

by Bryan Sanctuary

Axioms 2025, 14(11), 841; https://doi.org/10.3390/axioms14110841 - 17 Nov 2025

Viewed by 315

Abstract

The geometrical view of the electron as a spinning bivector leads to the partitioning of the electron’s energy into internal and external. The reduced Compton wavelength,

{\bar{λ}}_{C}

, is taken as the radius of the inertial ring (a disc), while [...] Read more.

The geometrical view of the electron as a spinning bivector leads to the partitioning of the electron’s energy into internal and external. The reduced Compton wavelength,

{\bar{λ}}_{C}

, is taken as the radius of the inertial ring (a disc), while

r_{e}

characterizes the EM coupling scale. Within this picture, the fine-structure constant emerges as the structural ratio

α = r_{e} / {\bar{λ}}_{C}

. We make the partitioning explicit, derive simple ratios among moments of inertia and stored energies, and compare the Bivector Standard Model with the Standard model. Full article

(This article belongs to the Special Issue Mathematical Aspects of Quantum Field Theory and Quantization)

► Show Figures

Figure 1

28 pages, 1053 KB

Open AccessArticle

Optimal Boundary-Flux Control of a Sharp Moving Interface in the Classical Two-Phase Stefan Problem

by Khalid Ali Alanezy and Jihad Souissi

Axioms 2025, 14(11), 840; https://doi.org/10.3390/axioms14110840 - 17 Nov 2025

Viewed by 310

Abstract

In this paper, we study the optimal boundary control of solidification governed by the classical two-phase Stefan problem with a sharp moving interface. The main objective is to formulate an optimal control problem for interface motion using boundary heat-flux control. The control acts [...] Read more.

In this paper, we study the optimal boundary control of solidification governed by the classical two-phase Stefan problem with a sharp moving interface. The main objective is to formulate an optimal control problem for interface motion using boundary heat-flux control. The control acts as a Neumann heat flux on a designated boundary segment and steers the interface through the Stefan condition. Using an enthalpy formulation, we prove well-posedness under boundary control and establish Lipschitz continuity of the control-to-state map and continuous dependence on the initial data. We then derive first-order necessary optimality conditions using a Lagrangian approach and propose a practical algorithm that couples a semismooth Newton method with Sequential Quadratic Programming (SQP) to compute the optimal boundary flux. Full article

(This article belongs to the Special Issue Nonlinear Analysis and Boundary Value Problems)

► Show Figures

Figure 1

15 pages, 2144 KB

Open AccessArticle

Mathematical Modeling of the Influence of Equilibrium Coefficient Variation on the Steady-State Transport of a Binary Electrolyte in the Cross-Section of a Desalination Channel

by Evgenia Kirillova, Natalia Chubyr, Roman Nazarov, Anna Kovalenko and Makhamet Urtenov

Axioms 2025, 14(11), 839; https://doi.org/10.3390/axioms14110839 - 15 Nov 2025

Viewed by 238

Abstract

This paper presents the first theoretical investigation of the effect of a variable equilibrium coefficient on the steady-state transport of a binary electrolyte in a desalination channel cross-section of the electrodialyzer. To address this problem, we developed a new mathematical model in the [...] Read more.

This paper presents the first theoretical investigation of the effect of a variable equilibrium coefficient on the steady-state transport of a binary electrolyte in a desalination channel cross-section of the electrodialyzer. To address this problem, we developed a new mathematical model in the form of a boundary value problem for an extended system of stationary Nernst–Planck–Poisson equations. We obtained a numerical solution to this problem using the finite element method. Analysis of this solution revealed that the channel cross-section has a complex structure: it is divided into seven regions dominated by different processes, and, consequently, the solution to the boundary value problem behaves differently in each of them. Existing models of the diffusion layer or channel cross-section typically assume a constant equilibrium coefficient. In this paper, we demonstrated that in the channel cross-section, the velocity change corresponding to the equilibrium constant is related not only to the field strength but also to the magnitude of the space charge. In the space-charge region, in the boundary layers near the ion-exchange membranes, intense dissociation of water molecules occurs, and the higher the equilibrium coefficient, the more intense this dissociation is. We have shown that an internal boundary layer (recombination region) arises deep within the solution, associated with the recombination reaction of H+ and OH− ions. In this study, we found that with increasing equilibrium coefficient, fluxes increase, while with increasing fluxes, the electric field strength decreases proportionally, and equilibrium is reached. We demonstrate that by calibrating a single fitting parameter in the model, the simulation results can be matched to experimental data with high accuracy. Thus, our proposed model and its numerical solution provide a completely new understanding of the ion transport process in electromembrane systems, taking into account the influence of the dissociation/recombination reaction of water molecules. Full article

(This article belongs to the Special Issue Advances in Nonlinear Analysis and Numerical Modeling)

► Show Figures

Figure 1

12 pages, 264 KB

Open AccessArticle

An Algorithm for Determining Whether the Quotient Ring Modulo an Ideal Has a Cyclic Basis

by Hengjia Cao and Chang Tan

Axioms 2025, 14(11), 838; https://doi.org/10.3390/axioms14110838 - 14 Nov 2025

Viewed by 273

Abstract

This paper focuses on the research of the existence of cyclic bases for the quotient ring modulo, a zero-dimensional ideal. Based on the necessary and sufficient condition for the existence of cyclic bases, it further deduces an equivalent condition for the existence of [...] Read more.

This paper focuses on the research of the existence of cyclic bases for the quotient ring modulo, a zero-dimensional ideal. Based on the necessary and sufficient condition for the existence of cyclic bases, it further deduces an equivalent condition for the existence of cyclic bases. In accordance with this condition, a new algorithm is proposed. The existence of a cyclic is determined by constructing a matrix and calculating its determinant in the algorithm. Compared with the original algorithm, it narrows the scope of the candidate element set and improves the computational efficiency of the algorithm. Full article

(This article belongs to the Special Issue Computational Algebra, Coding Theory and Cryptography: Theory and Applications, 2nd Edition)

11 pages, 377 KB

Open AccessArticle

Geometric Families Define Differential K-Theory

by Jae Min Lee and Byungdo Park

Axioms 2025, 14(11), 837; https://doi.org/10.3390/axioms14110837 - 14 Nov 2025

Viewed by 196

Abstract

The index-theoretic construction of differential K-theory by Bunke and Schick uses both a geometric family and a differential form as a cocycle data. We prove that geometric families alone can codify the differential K-theory. Full article

(This article belongs to the Special Issue Trends in Differential Geometry and Algebraic Topology)

23 pages, 497 KB

Open AccessArticle

Quasi-Optimal Convergence of a Family of Adaptive Nonconforming Finite Element Methods

by Xuying Zhao

Axioms 2025, 14(11), 836; https://doi.org/10.3390/axioms14110836 - 13 Nov 2025

Viewed by 300

Abstract

This study is devoted to the quasi-optimal convergence analysis of a family of adaptive nonconforming elements with high-order terms, which preserve weak continuities. In contrast with the nonconforming

P_{1}

element (Crouzeix–Raviart element) the gradient of the discrete solution considered in this paper [...] Read more.

This study is devoted to the quasi-optimal convergence analysis of a family of adaptive nonconforming elements with high-order terms, which preserve weak continuities. In contrast with the nonconforming

P_{1}

element (Crouzeix–Raviart element) the gradient of the discrete solution considered in this paper is not a piecewise constant vector. New quasi-orthogonality and a new discrete upper bound are established for the first time, based on which the convergence of the adaptive algorithm with a standard Dörfler collective marking strategy and quasi-optimality results are eventually established. Some other properties are also investigated, for example, the discrete Helmholtz decomposition for this family of nonconforming elements. Numerical experiments confirm the theoretical results. Full article

► Show Figures

Figure 1

7 pages, 234 KB

Open AccessArticle

Polyadic Encryption

by Steven Duplij and Qiang Guo

Axioms 2025, 14(11), 835; https://doi.org/10.3390/axioms14110835 - 13 Nov 2025

Viewed by 194

Abstract

A novel original procedure of encryption/decryption based on the polyadic algebraic structures and on signal processing methods is proposed. First, we use signals with integer amplitudes to send information. Then, we use polyadic techniques to transfer the plaintext into series of special integers. [...] Read more.

A novel original procedure of encryption/decryption based on the polyadic algebraic structures and on signal processing methods is proposed. First, we use signals with integer amplitudes to send information. Then, we use polyadic techniques to transfer the plaintext into series of special integers. The receiver restores the plaintext using special rules and systems of equations. Full article

(This article belongs to the Special Issue Computational Algebra, Coding Theory and Cryptography: Theory and Applications, 2nd Edition)

50 pages, 422 KB

Open AccessArticle

Asymptotic Behavior of the Time-Dependent Solution of the M^[X]/G/1 Queuing Model with Feedback and Optional Server Vacations Based on a Single Vacation Policy

by Nuraya Nurahmat and Geni Gupur

Axioms 2025, 14(11), 834; https://doi.org/10.3390/axioms14110834 - 12 Nov 2025

Viewed by 173

Abstract

By using the

C_{0}

-semigroup theory, we study the asymptotic behavior of the time-dependent solution and the time-dependent indices of the

M^{[X]} / G / 1

queuing model with feedback and optional server vacations based on a single vacation [...] Read more.

By using the

C_{0}

-semigroup theory, we study the asymptotic behavior of the time-dependent solution and the time-dependent indices of the

M^{[X]} / G / 1

queuing model with feedback and optional server vacations based on a single vacation policy. This queuing model is described by infinitely many partial differential equations with integral boundary conditions in an unbounded interval. Under certain conditions, by studying spectrum of the underlying operator of this queuing model on the imaginary axis, we prove that the time-dependent solution of this queuing model strongly converges to its steady-state solution. Next, we prove that the time-dependent queuing length of this queuing system converges to its steady-state queuing length and the time-dependent waiting time of this queuing system converges to its steady-state waiting time as time tends to infinity. Our results extend the steady-state results of this queuing system. Full article

(This article belongs to the Special Issue Numerical and Analytical Methods for Partial Differential Equations with Integral Boundary Conditions)

14 pages, 267 KB

Open AccessArticle

A Quasi-Boundary Value Method for Solving a Backward Problem of the Fractional Rayleigh–Stokes Equation

by Xiaomin Wang and Aimin Yang

Axioms 2025, 14(11), 833; https://doi.org/10.3390/axioms14110833 - 12 Nov 2025

Viewed by 261

Abstract

In this paper, we study a backward problem for a fractional Rayleigh–Stokes equation by using a quasi-boundary value method. This problem is ill-posed; i.e., the solution (if it exists) does not depend continuously on the data. To overcome its instability, a regularization method [...] Read more.

In this paper, we study a backward problem for a fractional Rayleigh–Stokes equation by using a quasi-boundary value method. This problem is ill-posed; i.e., the solution (if it exists) does not depend continuously on the data. To overcome its instability, a regularization method is employed, and convergence rate estimates are derived under both a priori and a posteriori criteria for selecting the regularization parameter. The theoretical results demonstrate the effectiveness of the proposed method in deriving stable and accurate solutions. Full article

(This article belongs to the Special Issue Differential Equations and Inverse Problems, 2nd Edition)

23 pages, 7293 KB

Open AccessArticle

The Influence of Generalist Predator and Michaelis–Menten Harvesting in a Holling–Tanner Model

by Tanglei Huang, Huiling Wu and Zhong Li

Axioms 2025, 14(11), 832; https://doi.org/10.3390/axioms14110832 - 12 Nov 2025

Viewed by 226

Abstract

In this paper, a Holling–Tanner predator–prey model with generalist predators and Michaelis–Menten-type prey harvesting is investigated. We analyze the existence and stability of equilibria and find the system has at most three positive equilibria. The double positive equilibrium belongs to the cusp type, [...] Read more.

In this paper, a Holling–Tanner predator–prey model with generalist predators and Michaelis–Menten-type prey harvesting is investigated. We analyze the existence and stability of equilibria and find the system has at most three positive equilibria. The double positive equilibrium belongs to the cusp type, with its codimension being at least 5. We then prove that the triple positive equilibrium is either a nilpotent focus (or elliptic point) of codimension 3, or a nilpotent elliptic equilibrium with codimension no less than 4. Additionally, the system undergoes two types of bifurcations: a cusp-type degenerate Bogdanov–Takens bifurcation (codimension 3) and a Hopf bifurcation. Using numerical simulations, the system has two limit cycles, which indicates that Michaelis–Menten-type prey harvesting makes the system’s dynamics more complex. Full article

► Show Figures

Figure 1

20 pages, 36430 KB

Open AccessArticle

A Brief Review of Wormhole Cosmic Censorship

by Leonel Bixano, I. A. Sarmiento-Alvarado and Tonatiuh Matos

Axioms 2025, 14(11), 831; https://doi.org/10.3390/axioms14110831 - 11 Nov 2025

Viewed by 825

Abstract

Spacetime singularities, in the sense that curvature invariants are infinite at some point or region, are thought to be impossible to observe, and must be hidden within an event horizon. This conjecture is called Cosmic Censorship (CC), and was formulated by Penrose. Here [...] Read more.

Spacetime singularities, in the sense that curvature invariants are infinite at some point or region, are thought to be impossible to observe, and must be hidden within an event horizon. This conjecture is called Cosmic Censorship (CC), and was formulated by Penrose. Here we review another type of CC where spacetime singularities are causally disconnected from the universe, because the throat of a wormhole “sucks in” the geodesics and prevents them from making contact with the singularity. In this work, we present a series of exact solutions to the Einstein–Maxwell–Dilaton equations that feature a ring singularity; that is, the curvature invariants are singular in this ring, but the ring is causally disconnected from the universe so that no geodesics can touch it. This extension of CC is called Wormhole Cosmic Censorship. Full article

(This article belongs to the Special Issue Mathematical Aspects of Black Holes in General Relativity and Beyond)

► Show Figures

Figure 1

21 pages, 395 KB

Open AccessArticle

An Efficient Iteration Method for Fixed-Point Approximation and Its Application to Fractional Volterra–Fredholm Integro–Differential Equations

by Ekta Sharma, Shubham Kumar Mittal, Sunil Panday and Lorentz Jäntschi

Axioms 2025, 14(11), 830; https://doi.org/10.3390/axioms14110830 - 11 Nov 2025

Viewed by 395

Abstract

This paper proposes an efficient iteration method for fixed-point approximation in Banach spaces. The method accelerates convergence by incorporating a squared operator term within the iteration process. Analytical proofs verify its convergence and stability. Comparative numerical tests show that it converges faster and [...] Read more.

This paper proposes an efficient iteration method for fixed-point approximation in Banach spaces. The method accelerates convergence by incorporating a squared operator term within the iteration process. Analytical proofs verify its convergence and stability. Comparative numerical tests show that it converges faster and more reliably than established Picard-type methods. Its application to fractional models involving the Gamma function highlights the method’s efficiency and potential for broader use in nonlinear and fractional systems. Full article

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

► Show Figures

Figure 1

23 pages, 356 KB

Open AccessArticle

Foundations of the Preisach Operator in Real Options Problems with Subscription Cost and Heterogeneous Population of Consumers

by Dmitrii Rachinskii, Lev Rachinskiy and Alejandro Rivera

Axioms 2025, 14(11), 829; https://doi.org/10.3390/axioms14110829 - 10 Nov 2025

Viewed by 191

Abstract

This paper considers the pricing of a subscription service in a heterogeneous market with consumers having different discount rates. We show that in the case of a non-zero enrollment/cancellation cost, solutions of the Hamilton–Jacobi–Bellman equation naturally contain an equivalent of the well-known Preisach [...] Read more.

This paper considers the pricing of a subscription service in a heterogeneous market with consumers having different discount rates. We show that in the case of a non-zero enrollment/cancellation cost, solutions of the Hamilton–Jacobi–Bellman equation naturally contain an equivalent of the well-known Preisach operator, a fundamental model of hysteresis in engineering applications. Singular perturbation expansions are used to approximate the optimal solution, assuming that enrollment/cancellation costs are small, relative to the total subscription cost. As a case study, we consider and compare markets with one and two consumers. Full article

17 pages, 916 KB

Open AccessArticle

Comparative Study of Dragonfly and Cuckoo Search Algorithms Applying Type-2 Fuzzy Logic Parameter Adaptation

by Hector M. Guajardo, Fevrier Valdez, Patricia Melin, Oscar Castillo and Prometeo Cortes-Antonio

Axioms 2025, 14(11), 828; https://doi.org/10.3390/axioms14110828 - 8 Nov 2025

Viewed by 388

Abstract

This study presents a comparative analysis of two bio-inspired optimization techniques: the Dragonfly Algorithm (DA) and Cuckoo Search (CS). The DA models the collective behavior of dragonflies, replicating dynamic processes such as foraging, evasion, and synchronized movement to effectively explore and exploit the [...] Read more.

This study presents a comparative analysis of two bio-inspired optimization techniques: the Dragonfly Algorithm (DA) and Cuckoo Search (CS). The DA models the collective behavior of dragonflies, replicating dynamic processes such as foraging, evasion, and synchronized movement to effectively explore and exploit the solution space. In contrast, the CS algorithm draws inspiration from the brood parasitism strategy observed in certain Cuckoo species, where eggs are laid in the nests of other birds, thereby leveraging randomization and selection mechanisms for optimization. To enhance the performance of both algorithms, Type-2 fuzzy logic systems were integrated into their structures. Specifically, the DA was fine-tuned through the adjustment of its inertia weight (W) and attraction coefficient (Beta), while the CS algorithm was optimized by calibrating the Lévy flight distribution parameter. A comprehensive set of benchmark functions, F1 through F10, was employed to evaluate and compare the effectiveness and convergence behavior of each method under fuzzy-enhanced configurations. Results indicate that the fuzzy-based adaptations consistently improved convergence stability and accuracy, demonstrating the advantage of integrating Type-2 fuzzy parameter control into swarm-based optimization frameworks. Full article

(This article belongs to the Special Issue Advances in Mathematical Optimization Algorithms and Its Applications)

► Show Figures

Figure 1

20 pages, 328 KB

Open AccessArticle

Resource Allocation and Minmax Scheduling Under Group Technology and Different Due-Window Assignments

by Li-Han Zhang and Ji-Bo Wang

Axioms 2025, 14(11), 827; https://doi.org/10.3390/axioms14110827 - 7 Nov 2025

Cited by 1 | Viewed by 207

Abstract

This article investigates single-machine group scheduling integrated with resource allocation under different due-window (

D I F D W

) assignment. Three distinct scenarios are examined: one with constant processing times, one with a linear resource consumption function, and one with a convex [...] Read more.

This article investigates single-machine group scheduling integrated with resource allocation under different due-window (

D I F D W

) assignment. Three distinct scenarios are examined: one with constant processing times, one with a linear resource consumption function, and one with a convex resource consumption function. The objective is to minimize the total cost comprising the maximum earliness/tardiness penalties, the due-window starting time cost, the due-window size cost, and the resource consumption cost. For each problem variant, we analyze the structural properties of optimal solutions and develop corresponding solution algorithms: a polynomial-time optimal algorithm for the case with constant processing times, heuristic algorithms for problems involving linear and convex resource allocation, and the branch-and-bound algorithm for obtaining exact solutions. Numerical experiments are conducted to evaluate the performance of the proposed algorithms. Full article

(This article belongs to the Special Issue Advances in Mathematical Optimization Algorithms and Its Applications)

13 pages, 300 KB

Open AccessArticle

Equivalence of Common Metrics on Trapezoidal Fuzzy Numbers

by Qingsong Mao and Huan Huang

Axioms 2025, 14(11), 826; https://doi.org/10.3390/axioms14110826 - 7 Nov 2025

Viewed by 202

Abstract

From both theoretical and applied perspectives, the trapezoidal fuzzy numbers are widely relevant fuzzy sets. In this paper, we show that the four kinds of common metrics—the supremum metric, the

L_{p}

-type

d_{p}

metrics, the sendograph metric, and the endograph metric—are [...] Read more.

From both theoretical and applied perspectives, the trapezoidal fuzzy numbers are widely relevant fuzzy sets. In this paper, we show that the four kinds of common metrics—the supremum metric, the

L_{p}

-type

d_{p}

metrics, the sendograph metric, and the endograph metric—are equivalent on the trapezoidal fuzzy numbers. In fact, we obtain a stronger result: the convergence induced by these four kinds of metrics on the trapezoidal fuzzy numbers is equivalent to the convergence of the corresponding representation quadruples of the trapezoidal fuzzy numbers in

R^{4}

. The latter convergence is very easy to verify. Our results give a fundamental understanding of these four kinds of common metrics on the trapezoidal fuzzy numbers and provide a quick judgment condition for the convergence induced by them. Full article

(This article belongs to the Special Issue Recent Advances in Fuzzy Sets and Related Topics, 2nd Edition)

Journal Menu

Journal Browser

Axioms, Volume 14, Issue 11 (November 2025) – 81 articles

Further Information

Guidelines

MDPI Initiatives

Follow MDPI