Axioms

7 pages, 528 KB

Open AccessArticle

by Shin-ya Matsushita and Hiromu Sasaki

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

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)

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12 pages, 263 KB

Open AccessArticle

Rigidity of Non-Steady Gradient Ricci Solitons

by Mohammed Guediri

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

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 (registering DOI) - 17 Nov 2025

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)

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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 (registering DOI) - 17 Nov 2025

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)

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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 (registering DOI) - 15 Nov 2025

Viewed by 38

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)

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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 (registering DOI) - 14 Nov 2025

Viewed by 152

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 65

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 174

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

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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 133

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, 417 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 (registering DOI) - 12 Nov 2025

Viewed by 96

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 172

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 132

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

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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 545

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)

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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 266

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)

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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 140

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

18 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 (registering DOI) - 8 Nov 2025

Viewed by 294

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)

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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

Viewed by 152

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 155

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)

17 pages, 295 KB

Open AccessArticle

On Distance Laplacian Energy of Unicyclic and Bicyclic Graphs

by Dan Li and Shiqi Zhou

Axioms 2025, 14(11), 825; https://doi.org/10.3390/axioms14110825 - 7 Nov 2025

Viewed by 203

Abstract

For a connected graph G, let

D^{L} (G)

be its distance Laplacian matrix and [...] Read more.

For a connected graph G, let

D^{L} (G)

be its distance Laplacian matrix and

λ_{1} (G) \geq λ_{2} (G) \geq \dots \geq λ_{n - 1} (G) > λ_{n} (G) = 0

be its

D^{L}

eigenvalues. The

D^{L}

energy of G is defined as

D L E (G) = \sum_{i = 1}^{n} |λ_{i} (G) - \frac{2 W (G)}{n}|

, where

W (G)

is the Wiener index of G. An important problem in graph energy studies is to determine exact formulations of the energy for specific graph classes and their complements. This paper gives the precise

D^{L}

energy formulations of a class of bicyclic graphs

C_{2} (p, q)

, a class of unicyclic graphs

C_{1} (p, q)

, and their complements. Moreover, we order the graphs

C_{2} (p, q)

on the basic of

λ_{1}

,

λ_{n - 1}

, and consider the same problems for their complements. And the ordering of the graphs

C_{1} (p, q)

on the basic of

λ_{n - 1}

and the ordering of their complements on the basics of

λ_{1}

,

λ_{n - 1}

and the

D^{L}

energy are obtained. Full article

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12 pages, 245 KB

Open AccessArticle

Weak Resolution Dimensions of Subcategories

by Juxiang Sun, Xinpeng Liu and Weimin Liu

Axioms 2025, 14(11), 824; https://doi.org/10.3390/axioms14110824 - 7 Nov 2025

Viewed by 128

Abstract

We investigate the relationships between the weak resolution dimensions of subcategories of module categories of Artinian algebras in the present paper. Let

Λ

be an Artinian algebra, and

A

,

B

and

X

subcategories of

Λ

-modules, such that each object X in [...] Read more.

We investigate the relationships between the weak resolution dimensions of subcategories of module categories of Artinian algebras in the present paper. Let

Λ

be an Artinian algebra, and

A

,

B

and

X

subcategories of

Λ

-modules, such that each object X in

X

is given by an exact sequence

0 \to A \to B \to X \to 0

with

A \in O b A

and

B \in O b B

. We prove that the weak resolution dimension of

X

is bounded above by the sum of the corresponding dimensions for

A

and

B

plus 1. As applications, we study weak resolution dimensions of Artinian algebras under left idealized extensions and conditions on special ideals. Full article

15 pages, 337 KB

Open AccessArticle

Fractional Error Bounds for Lobatto Quadrature: A Convexity Approach via Riemann–Liouville Integrals

by Li Liao, Abdelghani Lakhdari, Muhammad Uzair Awan, Hongyan Xu and Badreddine Meftah

Axioms 2025, 14(11), 823; https://doi.org/10.3390/axioms14110823 - 7 Nov 2025

Viewed by 185

Abstract

In this paper, we establish a new fractional integral identity linked to the 4-point Lobatto quadrature rule within the Riemann–Liouville fractional calculus framework. Building on this identity, we derive several Lobatto-type inequalities under convexity assumptions, yielding error bounds that involve only first-order derivatives, [...] Read more.

In this paper, we establish a new fractional integral identity linked to the 4-point Lobatto quadrature rule within the Riemann–Liouville fractional calculus framework. Building on this identity, we derive several Lobatto-type inequalities under convexity assumptions, yielding error bounds that involve only first-order derivatives, thereby improving practical applicability. A numerical example with graphical illustration confirms the theoretical findings and demonstrates their accuracy. We also present applications to special means, highlighting the utility of the obtained inequalities. The integration of fractional analysis, quadrature theory, and numerical validation provides a robust methodology for refining and analyzing high-order integration rules. Full article

(This article belongs to the Special Issue Theory and Application of Integral Inequalities, 2nd Edition)

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29 pages, 10424 KB

Open AccessArticle

Fuzzy Edge Chromatic Number of the Join of Fuzzy Graphs and Its Applications

by Jing Qu, Qian Wang and Angmo Deji

Axioms 2025, 14(11), 822; https://doi.org/10.3390/axioms14110822 - 6 Nov 2025

Viewed by 167

Abstract

Fuzzy edge coloring has proven to be a powerful tool for modeling and optimizing complex network systems, owing to its ability to effectively represent and manage the uncertainty in relational strengths and conflicts. It focuses on defining the fuzzy edge chromatic number, optimizing [...] Read more.

Fuzzy edge coloring has proven to be a powerful tool for modeling and optimizing complex network systems, owing to its ability to effectively represent and manage the uncertainty in relational strengths and conflicts. It focuses on defining the fuzzy edge chromatic number, optimizing its computation, and exploring practical applications. For join graphs derived from fuzzy graphs, we propose an efficient fuzzy edge coloring algorithm and analyze the associated properties. Building on this, fuzzy edge coloring offers effective strategies for software promotion and traffic signal optimization. This work addresses fundamental theoretical challenges related to algorithm design, complexity analysis, and structural properties in fuzzy graph edge coloring, while also demonstrating its practical utility in complex scenarios such as software promotion and traffic signal optimization. Full article

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24 pages, 1707 KB

Open AccessArticle

Differential Game Analysis of Green Technology Investment in the Food Industry Under a Governmental Coordination Mechanism

by Enquan Luo, Shuwen Xiang and Yanlong Yang

Axioms 2025, 14(11), 821; https://doi.org/10.3390/axioms14110821 - 6 Nov 2025

Viewed by 133

Abstract

This study constructs a Stackelberg differential game model for green technology invest-ment in the food industry under a governmental coordination mechanism. The optimal dynamic strategies for local governments and enterprises are derived using Pontryagin’s maximum principle. The backward differential equation method is employed [...] Read more.

This study constructs a Stackelberg differential game model for green technology invest-ment in the food industry under a governmental coordination mechanism. The optimal dynamic strategies for local governments and enterprises are derived using Pontryagin’s maximum principle. The backward differential equation method is employed in this study. It is used to analyze the impact of shadow prices on the optimal decisions of both parties. Furthermore, the study examines how social welfare benefits influence the food quality levels within the jurisdiction of local governments. Based on these findings, optimal strategy pathways are proposed to achieve social welfare and enterprise profit maximization in the green transition process of both government and enterprises. The results indicate that a local government’s investment in food quality improvement significantly enhances the food quality levels within their jurisdictions—greater government investment leads to higher food quality. At the same time, food quality levels are positively correlated with the enterprises’ green technology capital investment. Additionally, consumer price sensitivity and sensitivity to price differences have a notable impact on product pricing. As consumers become more price-sensitive, product prices decrease accordingly, which, in turn, helps increase the market share of the enterprises’ products. Full article

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18 pages, 1005 KB

Open AccessArticle

An Online Generalized Multiscale Method for Embedded Discrete Fracture Model

by Zhengkang He and Bangmin Wu

Axioms 2025, 14(11), 820; https://doi.org/10.3390/axioms14110820 - 5 Nov 2025

Viewed by 290

Abstract

This study concerns an online generalized multiscale method for flow in fractured porous media that is based on an embedded discrete fracture model. We first convert a two-point flux-approximation scheme into an equivalent discrete weak formulation that results in the same linear algebraic [...] Read more.

This study concerns an online generalized multiscale method for flow in fractured porous media that is based on an embedded discrete fracture model. We first convert a two-point flux-approximation scheme into an equivalent discrete weak formulation that results in the same linear algebraic system for the unknown pressure. Then, by the use of a suitable local snapshot space and a well-designed spectral decomposition, we compute offline basis functions to capture local heterogeneity information on account of the presence of various fractures in each coarse cell. After that, we compute residual-based online basis functions that contain global multiscale information to enrich the multiscale space and thus achieve higher accuracy of the multiscale solution. Meanwhile, theoretical analyses are conducted to show the convergence behavior, and a number of numerical tests with different fracture configurations are performed to investigate the performance of online enrichment. Full article

(This article belongs to the Section Mathematical Analysis)

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11 pages, 237 KB

Open AccessArticle

A Grammatical Interpretation of Horadam Sequences

by Jun-Ying Liu, Hai-Ling Li and Zhi-Hong Zhang

Axioms 2025, 14(11), 819; https://doi.org/10.3390/axioms14110819 - 3 Nov 2025

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Abstract

The Horadam sequence

{H_{n} (a, b; p, q)}_{n ⩾ 0}

has been widely studied in combinatorics and number theory. In this paper, we find that the context-free grammar [...] Read more.

The Horadam sequence

{H_{n} (a, b; p, q)}_{n ⩾ 0}

has been widely studied in combinatorics and number theory. In this paper, we find that the context-free grammar

G = {x \to p x + y, y \to q x}

can be used to generate Horadam sequences. Using this grammar, we deduce several identities, including Cassini-like identities. Moreover, we investigate the relationship between two distinct Horadam sequences

H_{n} (a, b; p, q)

and

H_{n} (c, d; p, q)

with

(a, b) \neq (c, d)

and provide an approach to derive identities, which can be illustrated by the Fibonacci and Lucas sequences as well as the two kinds of Chebyshev polynomials. Full article

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

14 pages, 294 KB

Open AccessArticle

One Optimization Problem with Convex Set-Valued Mapping and Duality

by Elimhan N. Mahmudov and Uğur Yıldırım

Axioms 2025, 14(11), 818; https://doi.org/10.3390/axioms14110818 - 2 Nov 2025

Viewed by 348

Abstract

This study focuses on the formulation and analysis of problems that are dual to those defined by convex set-valued mappings. Various important classes of optimization problems—such as the classical problems of mathematical and linear programming, as well as extremal problems arising in economic [...] Read more.

This study focuses on the formulation and analysis of problems that are dual to those defined by convex set-valued mappings. Various important classes of optimization problems—such as the classical problems of mathematical and linear programming, as well as extremal problems arising in economic dynamics models—can be reduced to problems of this type. The dual problem proposed in this work is constructed on the basis of the duality theorem connecting the operations of addition and infimal convolution of convex functions, a result that has been previously applied to compact-valued mappings. It appears that, under the so-called nondegeneracy condition, this construction serves as a fundamental approach for deriving duality theorems and establishing both necessary and sufficient optimality conditions. Furthermore, alternative conditions that partially replace the nondegeneracy assumption may also prove valuable for addressing other issues within convex analysis. Full article

(This article belongs to the Section Mathematical Analysis)

15 pages, 279 KB

Open AccessArticle

Fractional-Order Delay Differential Equations: Existence, Uniqueness, and Ulam–Hyers Stability

by Farva Hafeez, Mdi Begum Jeelani and Ghaliah Alhamzi

Axioms 2025, 14(11), 817; https://doi.org/10.3390/axioms14110817 - 31 Oct 2025

Viewed by 267

Abstract

This article presents several key findings for fractional-order delay differential equations. First, we establish the existence and uniqueness of solutions using two distinct approaches, the Chebyshev norm and the Bielecki norm, thereby providing a comprehensive understanding of the solution space. Notably, the uniqueness [...] Read more.

This article presents several key findings for fractional-order delay differential equations. First, we establish the existence and uniqueness of solutions using two distinct approaches, the Chebyshev norm and the Bielecki norm, thereby providing a comprehensive understanding of the solution space. Notably, the uniqueness of the solution is rigorously demonstrated using the Lipschitz condition, ensuring a single solution under specific constraints. Additionally, we examine a specific form of constant delay and apply Burton’s method to further confirm the uniqueness of the solution. Furthermore, we conduct an in-depth investigation into the Hyers–Ulam stability of the problem, providing valuable insights into the behavior of solutions under perturbations. Notably, our results eliminate the need for contraction constant conditions that are commonly imposed in the existing literature. Finally, numerical simulations are performed to illustrate and validate the theoretical results obtained in this study. Fractional-order delay differential equations play a crucial role in real-life applications in systems where memory and delayed effects are essential. In biology and epidemiology, they model disease spread with incubation delays and immune memory. In control systems and robotics, they help design stable controllers by accounting for time-lagged responses and past behavior. Full article

(This article belongs to the Special Issue Fractional Calculus and Applied Analysis, 2nd Edition)

17 pages, 363 KB

Open AccessArticle

Inequalities Including Fractional Integral Operators of General Riemann–Liouville for an Abstract Convex Function and Their Applications

by Ilknur Yesilce Isik

Axioms 2025, 14(11), 816; https://doi.org/10.3390/axioms14110816 - 31 Oct 2025

Viewed by 250

Abstract

An abstract convexity type is

B^{- 1}

–convexity. For

B^{- 1}

–convex functions, the Hermite–Hadamard inequality was previously found. Recently, however, new and more popular types of fractional integral operators have been developed. This paper’s goal is to demonstrate the Hermite–Hadamard [...] Read more.

An abstract convexity type is

B^{- 1}

–convexity. For

B^{- 1}

–convex functions, the Hermite–Hadamard inequality was previously found. Recently, however, new and more popular types of fractional integral operators have been developed. This paper’s goal is to demonstrate the Hermite–Hadamard inequality using additional, more general kinds of fractional integral operators. The generalization of the results are proven with the additional theorems. It is shown that the old fractional Hermite–Hadamard inequalities for

B^{- 1}

–convex functions can be obtained from the new inequalities given in this paper. Additionally, applications for each results are presented with tables and graphs. The inequalities for incomplete gamma function are proved and presented with graphs. Full article

(This article belongs to the Section Mathematical Analysis)

22 pages, 547 KB

Open AccessArticle

Data-Driven Modeling of Web Traffic Flow Using Functional Modal Regression

by Zoulikha Kaid and Mohammed B. Alamari

Axioms 2025, 14(11), 815; https://doi.org/10.3390/axioms14110815 - 31 Oct 2025

Viewed by 269

Abstract

Real-time control of web traffic is a critical issue for network operators and service providers. It helps ensure robust service and avoid service interruptions, which has an important financial impact. However, due to the high speed and volume of actual internet traffic, standard [...] Read more.

Real-time control of web traffic is a critical issue for network operators and service providers. It helps ensure robust service and avoid service interruptions, which has an important financial impact. However, due to the high speed and volume of actual internet traffic, standard multivariate time series models are inadequate for ensuring efficient real-time traffic management. In this paper we introduce a new model for functional time series analysis, developed by combining a local linear smoothing approach with an

L^{1}

-robust estimator of the quantile’s derivative. It constitutes an alternative, robust estimator for functional modal regression that is adequate to handle the stochastic volatility of high-frequency of web traffic data. The mathematical support of the new model is established under functional dependent case. The asymptotic analysis emphasizes the functional structure of the data, the functional feature of the model, and the stochastic characteristics of the underlying time-varying process. We evaluate the effectiveness of our proposed model using comprehensive simulations and real-data application. The computational results illustrate the superiority of the nonparametric functional model over the existing conventional methods in web traffic modeling. Full article

(This article belongs to the Special Issue Functional Data Analysis and Its Application)

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10 pages, 259 KB

Open AccessArticle

Some New Applications of the Mellin Transform Involving the Lambert Transforms and Implications for the Riemann Hypothesis

by Hari M. Srivastava, Jeetendrasingh Maan and Emilio R. Negrín

Axioms 2025, 14(11), 814; https://doi.org/10.3390/axioms14110814 - 31 Oct 2025

Viewed by 274

Abstract

This work investigates the interplay between the Mellin transform and Lambert transforms to derive several novel results. In particular, we establish new inversion formulae for the Lambert transforms along with a Plancherel-type identity. Additionally, we explore the implications of these findings, highlighting their [...] Read more.

This work investigates the interplay between the Mellin transform and Lambert transforms to derive several novel results. In particular, we establish new inversion formulae for the Lambert transforms along with a Plancherel-type identity. Additionally, we explore the implications of these findings, highlighting their relevance to Salem’s equivalence and potential connections with the Riemann hypothesis. Full article

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

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Axioms, Volume 14, Issue 11 (November 2025) – 69 articles

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