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Axioms, Volume 13, Issue 11 (November 2024) – 81 articles

Cover Story (view full-size image): In this paper, we propose a global numerical method for approximating the Caputo fractional derivatives Dαf with m − 1 < αm, m ∈ N. We approximate f (m) by the m-th derivative of a Lagrange polynomial, interpolating f at Jacobi zeros and some additional nodes suitably chosen to have optimal Lebsegue constants. Error estimates in a uniform norm are provided, showing that the rate of convergence is related to the smoothness of the function f according to the best polynomial approximation error and depending on order α. As an application, we approximate the solution of a Volterra integral equation, equivalent in some sense to the Bagley–Torvik initial value problem, using a Nyström-type method. Finally, some numerical tests are presented to assess the performance of the procedure. View this paper
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15 pages, 310 KiB  
Article
Mathematical Optimization of Wind Turbine Maintenance Using Repair Rate Thresholds
by Nataša Kontrec, Stefan Panić, Jelena Vujaković, Dejan Stošović and Sergei Khotnenok
Axioms 2024, 13(11), 809; https://doi.org/10.3390/axioms13110809 - 20 Nov 2024
Viewed by 352
Abstract
As reliance on wind energy intensifies globally, optimizing the efficiency and reliability of wind turbines is becoming vital. This paper explores sophisticated maintenance strategies, crucial for enhancing the operational sustainability of wind turbines. It introduces an innovative approach to maintenance scheduling that utilizes [...] Read more.
As reliance on wind energy intensifies globally, optimizing the efficiency and reliability of wind turbines is becoming vital. This paper explores sophisticated maintenance strategies, crucial for enhancing the operational sustainability of wind turbines. It introduces an innovative approach to maintenance scheduling that utilizes a mathematical model incorporating an alternating renewal process for accurately determining repair rate thresholds. These thresholds are important for identifying optimal maintenance timings, thereby averting failures and minimizing downtime. Central to this study are the obtained generalized analytical expressions that can be used to predict the total repair time for an observed entity. Four key lemmas are developed to establish formal proofs for the probability density function (PDF) and cumulative distribution function (CDF) of repair rates, both above and below critical repair rate thresholds. The core innovation of this study lies in the methodological application of PDFs and CDFs to set repair time thresholds that refine maintenance schedules. The model’s effectiveness is illustrated using simulated data based on typical wind turbine components such as gearboxes, generators, and converters, validating its potential for improving system availability and operational readiness. By establishing measurable repair rate thresholds, the model effectively prioritizes maintenance tasks, extending the life of crucial turbine components and ensuring consistent energy output. Beyond enhancing theoretical understanding, this research provides practical insights that could inform broader maintenance strategies across various renewable energy systems, marking a significant advancement in the field of maintenance engineering Full article
(This article belongs to the Special Issue Stochastic Modeling and Optimization Techniques)
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27 pages, 383 KiB  
Article
Qualitative Analysis of Stochastic Caputo–Katugampola Fractional Differential Equations
by Zareen A. Khan, Muhammad Imran Liaqat, Ali Akgül and J. Alberto Conejero
Axioms 2024, 13(11), 808; https://doi.org/10.3390/axioms13110808 - 20 Nov 2024
Viewed by 384
Abstract
Stochastic pantograph fractional differential equations (SPFDEs) combine three intricate components: stochastic processes, fractional calculus, and pantograph terms. These equations are important because they allow us to model and analyze systems with complex behaviors that traditional differential equations cannot capture. In this study, we [...] Read more.
Stochastic pantograph fractional differential equations (SPFDEs) combine three intricate components: stochastic processes, fractional calculus, and pantograph terms. These equations are important because they allow us to model and analyze systems with complex behaviors that traditional differential equations cannot capture. In this study, we achieve significant results for these equations within the context of Caputo–Katugampola derivatives. First, we establish the existence and uniqueness of solutions by employing the contraction mapping principle with a suitably weighted norm and demonstrate that the solutions continuously depend on both the initial values and the fractional exponent. The second part examines the regularity concerning time. Third, we illustrate the results of the averaging principle using techniques involving inequalities and interval translations. We generalize these results in two ways: first, by establishing them in the sense of the Caputo–Katugampola derivative. Applying condition β=1, we derive the results within the framework of the Caputo derivative, while condition β0+ yields them in the context of the Caputo–Hadamard derivative. Second, we establish them in Lp space, thereby generalizing the case for p=2. Full article
(This article belongs to the Special Issue Advances in Mathematical Modeling and Related Topics)
14 pages, 300 KiB  
Article
On Warped Product Pointwise Pseudo-Slant Submanifolds of LCK-Manifolds and Their Applications
by Fatimah Alghamdi
Axioms 2024, 13(11), 807; https://doi.org/10.3390/axioms13110807 - 20 Nov 2024
Viewed by 326
Abstract
The concept of pointwise slant submanifolds of a Kähler manifold was presented by Chen and Garay. This research extends this notion to a more general setting, specifically in a locally conformal Kähler manifold. We study the pointwise pseudo-slant warped products of the form [...] Read more.
The concept of pointwise slant submanifolds of a Kähler manifold was presented by Chen and Garay. This research extends this notion to a more general setting, specifically in a locally conformal Kähler manifold. We study the pointwise pseudo-slant warped products of the form Σθ×fΣ in a locally conformal Kähler manifold. Using the concept of pointwise pseudo-slant, we establish the necessary and sufficient condition for it to be characterized as a warped product submanifold. In addition, we derive several results on pointwise pseudo-slant warped products that expand previously proven main ones. Further, some examples of such submanifolds and their warped products are also given. Full article
(This article belongs to the Special Issue Advances in Differential Geometry and Singularity Theory, 2nd Edition)
17 pages, 611 KiB  
Article
Beta Autoregressive Moving Average Model with the Aranda-Ordaz Link Function
by Carlos E. F. Manchini, Diego Ramos Canterle, Guilherme Pumi and Fábio M. Bayer
Axioms 2024, 13(11), 806; https://doi.org/10.3390/axioms13110806 - 20 Nov 2024
Viewed by 381
Abstract
In this work, we introduce an extension of the so-called beta autoregressive moving average (βARMA) models. βARMA models consider a linear dynamic structure for the conditional mean of a beta distributed variable. The conditional mean is connected to the linear [...] Read more.
In this work, we introduce an extension of the so-called beta autoregressive moving average (βARMA) models. βARMA models consider a linear dynamic structure for the conditional mean of a beta distributed variable. The conditional mean is connected to the linear predictor via a suitable link function. We propose modeling the relationship between the conditional mean and the linear predictor by means of the asymmetric Aranda-Ordaz parametric link function. The link function contains a parameter estimated along with the other parameters via partial maximum likelihood. We derive the partial score vector and Fisher’s information matrix and consider hypothesis testing, diagnostic analysis, and forecasting for the proposed model. The finite sample performance of the partial maximum likelihood estimation is studied through a Monte Carlo simulation study. An application to the proportion of stocked hydroelectric energy in the south of Brazil is presented. Full article
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21 pages, 295 KiB  
Article
Applications of Common Fixed-Point Results in Complex-Valued Metric Spaces to Homotopy Theory
by Amnah Essa Shammaky and Jamshaid Ahmad
Axioms 2024, 13(11), 805; https://doi.org/10.3390/axioms13110805 - 19 Nov 2024
Viewed by 408
Abstract
The aim of this research article is to introduce generalized rational contractions in the context of complex-valued metric spaces and to establish novel common fixed-point theorems. Our findings generalize several well-known fixed-point theorems and contribute to the advancement of fixed-point theory. A non-trivial [...] Read more.
The aim of this research article is to introduce generalized rational contractions in the context of complex-valued metric spaces and to establish novel common fixed-point theorems. Our findings generalize several well-known fixed-point theorems and contribute to the advancement of fixed-point theory. A non-trivial example is provided to demonstrate the efficacy of the obtained results. Additionally, we demonstrate the practical significance of our findings through a homotopy result. Full article
14 pages, 283 KiB  
Article
Bounds for the Energy of Hypergraphs
by Liya Jess Kurian and Chithra Velu
Axioms 2024, 13(11), 804; https://doi.org/10.3390/axioms13110804 - 19 Nov 2024
Viewed by 293
Abstract
The concept of the energy of a graph has been widely explored in the field of mathematical chemistry and is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. The energy of a hypergraph is the trace [...] Read more.
The concept of the energy of a graph has been widely explored in the field of mathematical chemistry and is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. The energy of a hypergraph is the trace norm of its connectivity matrices, which generalize the concept of graph energy. In this paper, we establish bounds for the adjacency energy of hypergraphs in terms of the number of vertices, maximum degree, eigenvalues, and the norm of the adjacency matrix. Additionally, we compute the sum of squares of adjacency eigenvalues of linear k-hypergraphs and derive its bounds for k-hypergraph in terms of number of vertices and uniformity of the k-hypergraph. Moreover, we determine the Nordhaus–Gaddum type bounds for the adjacency energy of k-hypergraphs. Full article
(This article belongs to the Special Issue Recent Developments in Graph Theory)
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16 pages, 7742 KiB  
Article
Response Analysis and Vibration Suppression of Fractional Viscoelastic Shape Memory Alloy Spring Oscillator Under Harmonic Excitation
by Rong Guo, Na Meng, Jinling Wang, Junlin Li and Jinbin Wang
Axioms 2024, 13(11), 803; https://doi.org/10.3390/axioms13110803 - 19 Nov 2024
Viewed by 344
Abstract
This study investigates the dynamic behavior and vibration mitigation of a fractional single-degree-of-freedom (SDOF) viscoelastic shape memory alloy spring oscillator system subjected to harmonic external forces. A fractional derivative approach is employed to characterize the viscoelastic properties of shape memory alloy materials, leading [...] Read more.
This study investigates the dynamic behavior and vibration mitigation of a fractional single-degree-of-freedom (SDOF) viscoelastic shape memory alloy spring oscillator system subjected to harmonic external forces. A fractional derivative approach is employed to characterize the viscoelastic properties of shape memory alloy materials, leading to the development of a novel fractional viscoelastic model. The model is then theoretically examined using the averaging method, with its effectiveness being confirmed through numerical simulations. Furthermore, the impact of various parameters on the system’s low- and high-amplitude vibrations is explored through a visual response analysis. These findings offer valuable insights for applying fractional sliding mode control (SMC) theory to address the system’s vibration control challenges. Despite the high-amplitude vibrations induced by the fractional order, SMC effectively suppresses these vibrations in the shape memory alloy spring system, thereby minimizing the risk of catastrophic events. Full article
(This article belongs to the Special Issue Fractional Differential Equation and Its Applications)
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17 pages, 341 KiB  
Article
Extension of an Eighth-Order Iterative Technique to Address Non-Linear Problems
by Higinio Ramos, Ioannis K. Argyros, Ramandeep Behl and Hashim Alshehri
Axioms 2024, 13(11), 802; https://doi.org/10.3390/axioms13110802 - 18 Nov 2024
Viewed by 353
Abstract
The convergence order of an iterative method used to solve equations is usually determined by using Taylor series expansions, which in turn require high-order derivatives, which are not necessarily present in the method. Therefore, such convergence analysis cannot guarantee the theoretical convergence of [...] Read more.
The convergence order of an iterative method used to solve equations is usually determined by using Taylor series expansions, which in turn require high-order derivatives, which are not necessarily present in the method. Therefore, such convergence analysis cannot guarantee the theoretical convergence of the method to a solution if these derivatives do not exist. However, the method can converge. This indicates that the most sufficient convergence conditions required by the Taylor approach can be replaced by weaker ones. Other drawbacks exist, such as information on the isolation of simple solutions or the number of iterations that must be performed to achieve the desired error tolerance. This paper positively addresses all these issues by considering a technique that uses only the operators on the method and Ω-generalized continuity to control the derivative. Moreover, both local and semi-local convergence analyses are presented for Banach space-valued operators. The technique can be used to extend the applicability of other methods along the same lines. A large number of concrete examples are shown in which the convergence conditions are fulfilled. Full article
(This article belongs to the Section Mathematical Analysis)
36 pages, 2057 KiB  
Article
One Class of Stackelberg Linear–Quadratic Differential Games with Cheap Control of a Leader: Asymptotic Analysis of an Open-Loop Solution
by Valery Y. Glizer and Vladimir Turetsky
Axioms 2024, 13(11), 801; https://doi.org/10.3390/axioms13110801 - 18 Nov 2024
Viewed by 329
Abstract
We consider a two-player finite horizon linear–quadratic Stackelberg differential game. For this game, we study the case where the control cost of a leader in the cost functionals of both players is small, which means that the game under consideration is a cheap [...] Read more.
We consider a two-player finite horizon linear–quadratic Stackelberg differential game. For this game, we study the case where the control cost of a leader in the cost functionals of both players is small, which means that the game under consideration is a cheap control game. We look for open-loop optimal players’ controls of this game. Using the game’s solvability conditions, the obtaining such controls is reduced to the solution to a proper boundary-value problem. Due to the smallness of the leader’s control cost, this boundary-value problem is singularly perturbed. Asymptotic behavior of the solution to this problem is analyzed. Based on this analysis, the asymptotic behavior of the open-loop optimal players’ controls and the optimal values of the cost functionals is studied. Using these results, asymptotically suboptimal players’ controls are designed. An illustrative example is presented. Full article
(This article belongs to the Special Issue Advances in Mathematical Methods in Optimal Control and Applications)
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15 pages, 545 KiB  
Article
Modified Sweeping Surfaces in Euclidean 3-Space
by Yanlin Li, Kemal Eren, Soley Ersoy and Ana Savić
Axioms 2024, 13(11), 800; https://doi.org/10.3390/axioms13110800 - 18 Nov 2024
Viewed by 385
Abstract
In this study, we explore the sweeping surfaces in Euclidean 3-space, utilizing the modified orthogonal frames with non-zero curvature and torsion, which allows us to consider the spine curves even if their second differentiations vanish. If the curvature of the spine curve of [...] Read more.
In this study, we explore the sweeping surfaces in Euclidean 3-space, utilizing the modified orthogonal frames with non-zero curvature and torsion, which allows us to consider the spine curves even if their second differentiations vanish. If the curvature of the spine curve of a sweeping surface has discrete zero points, the Frenet frame might undergo a discontinuous change in orientation. Therefore, the conventional parametrization with the Frenet frame of such a surface cannot be given. Thus, we introduce two types of modified sweeping surfaces by considering two types of spine curves; the first one’s curvature is not identically zero and the second one’s torsion is not identically zero. Then, we determine the criteria for classifying the coordinate curves of these two types of modified sweeping surfaces as geodesic, asymptotic, or curvature lines. Additionally, we delve into determining criteria for the modified sweeping surfaces to be minimal, developable, or Weingarten. Through our analysis, we aim to clarify the characteristics defining these surfaces. We present graphical representations of sample modified sweeping surfaces to enhance understanding and provide concrete examples that showcase their properties. Full article
(This article belongs to the Special Issue Advances in Classical and Applied Mathematics)
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23 pages, 3820 KiB  
Article
Semi-Overlap Functions on Complete Lattices, Semi-Θ-Ξ Functions, and Inflationary MTL Algebras
by Xingna Zhang, Eunsuk Yang and Xiaohong Zhang
Axioms 2024, 13(11), 799; https://doi.org/10.3390/axioms13110799 - 18 Nov 2024
Viewed by 373
Abstract
As new kinds of aggregation functions, overlap functions and semi overlap functions are widely applied to information fusion, approximation reasoning, data classification, decision science, etc. This paper extends the semi-overlap function on [0, 1] to the function on complete lattices and investigates the [...] Read more.
As new kinds of aggregation functions, overlap functions and semi overlap functions are widely applied to information fusion, approximation reasoning, data classification, decision science, etc. This paper extends the semi-overlap function on [0, 1] to the function on complete lattices and investigates the residual implication derived from it; then it explores the construction of a semi-overlap function on complete lattices and some fundamental properties. Especially, this paper introduces a more generalized concept of the ‘semi-Θ-Ξ function’, which innovatively unifies the semi-overlap function and semi-grouping function. Additionally, it provides methods for constructing and characterizing the semi-Θ-Ξ function. Furthermore, this paper characterizes the semi-overlap function on complete lattices and the semi-Θ-Ξ function on [0, 1] from an algebraic point of view and proves that the algebraic structures corresponding to the inflationary semi-overlap function, the inflationary semi-Θ-Ξ function, and residual implications derived by each of them are inflationary MTL algebras. This paper further discusses the properties of inflationary MTL algebra and its relationship with non-associative MTL algebra, and it explores the connections between some related algebraic structures. Full article
(This article belongs to the Special Issue Fuzzy Systems, Fuzzy Decision Making, and Fuzzy Mathematics)
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13 pages, 1489 KiB  
Article
Stability and Bifurcation Analysis for the Transmission Dynamics of Skin Sores with Time Delay
by Yanan Wang and Tiansi Zhang
Axioms 2024, 13(11), 798; https://doi.org/10.3390/axioms13110798 - 18 Nov 2024
Viewed by 295
Abstract
Impetigo is a highly contagious skin infection that primarily affects children and communities in low-income regions and has become a significant public health issue impacting both individuals and healthcare systems. A nonlinear deterministic model based on the transmission dynamics of skin sores (impetigo) [...] Read more.
Impetigo is a highly contagious skin infection that primarily affects children and communities in low-income regions and has become a significant public health issue impacting both individuals and healthcare systems. A nonlinear deterministic model based on the transmission dynamics of skin sores (impetigo) is developed with a specific emphasis on the time delay effects in the infection and recovery processes. To address this complexity, we introduce a delay differential equation (DDE) to describe the dynamic process. We analyzed the existence of Hopf bifurcations associated with the two equilibrium points and examined the mechanisms underlying the occurrence of these bifurcations as delays exceeded certain critical values. To obtain more comprehensive insights into this phenomenon, we applied the center manifold theory and the normal form method to determine the direction and stability of Hopf bifurcations near bifurcation curves. This research not only offers a novel theoretical perspective on the transmission of impetigo but also lays a significant mathematical foundation for developing clinical intervention strategies. Specifically, it suggests that an increased time delay between infection and isolation could lead to more severe outbreaks, further supporting the development of more effective intervention approaches. Full article
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12 pages, 259 KiB  
Article
Some Theorems of Uncertain Multiple-Delay Differential Equations
by Yin Gao and Han Tang
Axioms 2024, 13(11), 797; https://doi.org/10.3390/axioms13110797 - 18 Nov 2024
Viewed by 355
Abstract
Uncertain differential equations with a time delay, called uncertain-delay differential equations, have been successfully applied in feedback control systems. In fact, many systems have multiple delays, which can be described by uncertain differential equations with multiple delays. This paper defines uncertain differential equations [...] Read more.
Uncertain differential equations with a time delay, called uncertain-delay differential equations, have been successfully applied in feedback control systems. In fact, many systems have multiple delays, which can be described by uncertain differential equations with multiple delays. This paper defines uncertain differential equations with multiple delays, which are called uncertain multiple-delay differential equations (UMDDEs). Based on the linear growth condition and the Lipschitz condition, the existence and uniqueness theorem of the solutions to the UMDDEs is proven. In order to judge the stability of the solutions to the UMDDEs, the concept of the stability in measure for UMDDEs is presented. Moreover, two theorems sufficient for use as tools to identify the stability in measure for UMDDEs are proved, and some examples are also discussed in this paper. Full article
(This article belongs to the Special Issue Differential Equations and Related Topics, 2nd Edition)
20 pages, 3039 KiB  
Article
Bayesian and Non-Bayesian Inference to Bivariate Alpha Power Burr-XII Distribution with Engineering Application
by Dina A. Ramadan, Mustafa M. Hasaballah, Nada K. Abd-Elwaha, Arwa M. Alshangiti, Mahmoud I. Kamel, Oluwafemi Samson Balogun and Mahmoud M. El-Awady
Axioms 2024, 13(11), 796; https://doi.org/10.3390/axioms13110796 - 17 Nov 2024
Viewed by 378
Abstract
In this research, we present a new distribution, which is the bivariate alpha power Burr-XII distribution, based on the alpha power Burr-XII distribution. We thoroughly examine the key features of our newly developed bivariate model. We introduce a new class of bivariate models, [...] Read more.
In this research, we present a new distribution, which is the bivariate alpha power Burr-XII distribution, based on the alpha power Burr-XII distribution. We thoroughly examine the key features of our newly developed bivariate model. We introduce a new class of bivariate models, which are built with the copula function. The statistical properties of the proposed distribution, such as conditional distributions, conditional expectations, marginal distributions, moment-generating functions, and product moments were studied. This was accomplished with two datasets of real data that came from two distinct devices. We employed Bayesian, maximum likelihood estimation, and least squares estimation strategies to obtain estimated points and intervals. Additionally, we generated bootstrap confidence intervals and conducted numerical analyses using the Markov chain Monte Carlo method. Lastly, we compared this novel bivariate distribution’s performance to earlier bivariate models, to determine how well it fit the real data. Full article
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20 pages, 2178 KiB  
Article
Intrinsic Functional Partially Linear Poisson Regression Model for Count Data
by Jiaqi Xu, Yu Lu, Yuanshen Su, Tao Liu, Yunfei Qi and Wu Xie
Axioms 2024, 13(11), 795; https://doi.org/10.3390/axioms13110795 - 16 Nov 2024
Viewed by 623
Abstract
Poisson regression is a statistical method specifically designed for analyzing count data. Considering the case where the functional and vector-valued covariates exhibit a linear relationship with the log-transformed Poisson mean, while the covariates in complex domains act as nonlinear random effects, an intrinsic [...] Read more.
Poisson regression is a statistical method specifically designed for analyzing count data. Considering the case where the functional and vector-valued covariates exhibit a linear relationship with the log-transformed Poisson mean, while the covariates in complex domains act as nonlinear random effects, an intrinsic functional partially linear Poisson regression model is proposed. This model flexibly integrates predictors from different spaces, including functional covariates, vector-valued covariates, and other non-Euclidean covariates taking values in complex domains. A truncation scheme is applied to approximate the functional covariates, and the random effects related to non-Euclidean covariates are modeled based on the reproducing kernel method. A quasi-Newton iterative algorithm is employed to optimize the parameters of the proposed model. Furthermore, to capture the intrinsic geometric structure of the covariates in complex domains, the heat kernel is employed as the kernel function, estimated via Brownian motion simulations. Both simulation studies and real data analysis demonstrate that the proposed method offers significant advantages over the classical Poisson regression model. Full article
(This article belongs to the Special Issue Computational Statistics and Its Applications)
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10 pages, 251 KiB  
Article
Spectral Properties of the Laplace Operator with Variable Dependent Boundary Conditions in a Disk
by Aishabibi Dukenbayeva and Makhmud Sadybekov
Axioms 2024, 13(11), 794; https://doi.org/10.3390/axioms13110794 - 16 Nov 2024
Viewed by 455
Abstract
In this work, we study the spectral properties of the Laplace operator with variable dependent boundary conditions in a disk. The boundary conditions include periodic and antiperiodic boundary conditions as well as the generalized Samarskii–Ionkin-type boundary conditions. We show eigenfunctions and eigenvalues of [...] Read more.
In this work, we study the spectral properties of the Laplace operator with variable dependent boundary conditions in a disk. The boundary conditions include periodic and antiperiodic boundary conditions as well as the generalized Samarskii–Ionkin-type boundary conditions. We show eigenfunctions and eigenvalues of these problems in an explicit form. Moreover, the completeness of their eigenfunctions is investigated. Full article
(This article belongs to the Special Issue Difference, Functional, and Related Equations)
14 pages, 777 KiB  
Article
Exploring Nonlinear Dynamics in Intertidal Water Waves: Insights from Fourth-Order Boussinesq Equations
by Hassan Almusawa, Musawa Yahya Almusawa, Adil Jhangeer and Zamir Hussain
Axioms 2024, 13(11), 793; https://doi.org/10.3390/axioms13110793 - 16 Nov 2024
Viewed by 495
Abstract
The fourth-order nonlinear Boussinesq water wave equation, which describes the propagation of long waves in the intertidal zone, is investigated in this study. The exact wave patterns of the equation were computed using the tanh method. As stability decreased, soliton [...] Read more.
The fourth-order nonlinear Boussinesq water wave equation, which describes the propagation of long waves in the intertidal zone, is investigated in this study. The exact wave patterns of the equation were computed using the tanh method. As stability decreased, soliton wave structures were derived using similarity transformations. Numerical simulations supported these findings. The tanh method introduced a Galilean modification, leading to the discovery of several new exact solutions. Subsequently, the fourth-order nonlinear Boussinesq wave equation was transformed into a planar dynamical system using the travelling wave transformation. The quasi-periodic, cyclical, and nonlinear behaviors of the analyzed equation were particularly examined. Numerical simulations revealed that varying the physical parameters impacts the system’s nonlinear behavior. Graphs represent all possible examples of phase portraits in terms of these parameters. Furthermore, the study was proven to be highly beneficial for addressing issues such as shock waves and highly active travelling wave processes. Sensitivity analysis theory and the Lyapunov exponent were employed, offering a wide variety of linear periodic and first-frequency periodic characteristics. Sensitivity analysis and multistability analysis of the Boussinesq water wave equation were thoroughly investigated. Full article
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10 pages, 663 KiB  
Article
Total and Double Total Domination on Octagonal Grid
by Antoaneta Klobučar and Ana Klobučar Barišić
Axioms 2024, 13(11), 792; https://doi.org/10.3390/axioms13110792 - 16 Nov 2024
Viewed by 438
Abstract
A k-total dominating set is a set of vertices such that all vertices in the graph, including the vertices in the dominating set themselves, have at least k neighbors in the dominating set. The k-total domination number [...] Read more.
A k-total dominating set is a set of vertices such that all vertices in the graph, including the vertices in the dominating set themselves, have at least k neighbors in the dominating set. The k-total domination number γkt(G) is the cardinality of the smallest k-total dominating set. For k=1,2, the k-total dominating number is called the total and the double total dominating number, respectively. In this paper, we determine the exact values for the total domination number on a linear and on a double octagonal chain and an upper bound for the total domination number on a triple octagonal chain. Furthermore, we determine the exact values for the double total domination number on a linear and on a double octagonal chain and an upper bound for the double total domination number on a triple octagonal chain and on an octagonal grid Om,n,m3,n3. As each vertex in the octagonal system is either of degree two or of degree three, there is no k-total domination for k3. Full article
(This article belongs to the Special Issue Recent Developments in Graph Theory)
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14 pages, 4897 KiB  
Article
Novel Dynamic Behaviors in Fractional Chaotic Systems: Numerical Simulations with Caputo Derivatives
by Mohamed A. Abdoon, Diaa Eldin Elgezouli, Borhen Halouani, Amr M. Y. Abdelaty, Ibrahim S. Elshazly, Praveen Ailawalia and Alaa H. El-Qadeem
Axioms 2024, 13(11), 791; https://doi.org/10.3390/axioms13110791 - 16 Nov 2024
Viewed by 586
Abstract
Over the last several years, there has been a considerable improvement in the possible methods for solving fractional-order chaotic systems; however, achieving high accuracy remains a challenge. This work proposes a new precise numerical technique for fractional-order chaotic systems. Through simulations, we obtain [...] Read more.
Over the last several years, there has been a considerable improvement in the possible methods for solving fractional-order chaotic systems; however, achieving high accuracy remains a challenge. This work proposes a new precise numerical technique for fractional-order chaotic systems. Through simulations, we obtain new types of complex and previously undiscussed dynamic behaviors.These phenomena, not recognized in prior numerical results or theoretical estimations, underscore the unique dynamics present in fractional systems. We also study the effects of the fractional parameters β1, β2, and β3 on the system’s behavior, comparing them to integer-order derivatives. It has been demonstrated via the findings that the suggested technique is consistent with conventional numerical methods for integer-order systems while simultaneously providing an even higher level of precision. It is possible to demonstrate the efficacy and precision of this technique through simulations, which demonstrates that this method is useful for the investigation of complicated chaotic models. Full article
(This article belongs to the Special Issue Fractional Calculus and the Applied Analysis)
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20 pages, 306 KiB  
Article
Cubic-like Features of I–V Relations via Classical Poisson–Nernst–Planck Systems Under Relaxed Electroneutrality Boundary Conditions
by Hong Li, Zhantao Li, Chaohong Pan, Jie Song and Mingji Zhang
Axioms 2024, 13(11), 790; https://doi.org/10.3390/axioms13110790 - 15 Nov 2024
Viewed by 405
Abstract
We focus on higher-order matched asymptotic expansions of a one-dimensional classical Poisson–Nernst–Planck system for ionic flow through membrane channels with two oppositely charged ion species under relaxed electroneutrality boundary conditions. Of particular interest are the current–voltage (I–V) relations, which are used to characterize [...] Read more.
We focus on higher-order matched asymptotic expansions of a one-dimensional classical Poisson–Nernst–Planck system for ionic flow through membrane channels with two oppositely charged ion species under relaxed electroneutrality boundary conditions. Of particular interest are the current–voltage (I–V) relations, which are used to characterize the two most relevant biological properties of ion channels—permeation and selectivity—experimentally. Our result shows that, up to the second order in ε=λ/r, where λ is the Debye length and r is the characteristic radius of the channel, the cubic I–V relation has either three distinct real roots or a unique real root with a multiplicity of three, which sensitively depends on the boundary layers because of the relaxation of the electroneutrality boundary conditions. This indicates more rich dynamics of ionic flows under our more realistic setups and provides a better understanding of the mechanism of ionic flows through membrane channels. Full article
18 pages, 391 KiB  
Article
Statistical Inference of Uncertain Autoregressive Model via the Principle of Least Squares
by Han Wang, Yang Liu and Haiyan Shi
Axioms 2024, 13(11), 789; https://doi.org/10.3390/axioms13110789 - 15 Nov 2024
Viewed by 332
Abstract
In the study of uncertain autoregressive models, how to estimate the unknown parameters and uncertain disturbance term in the models is always a key problem. In view of this, this paper proposes a statistical inference method based on the principle of least squares [...] Read more.
In the study of uncertain autoregressive models, how to estimate the unknown parameters and uncertain disturbance term in the models is always a key problem. In view of this, this paper proposes a statistical inference method based on the principle of least squares to determine the unknown parameters and uncertain disturbance term in an uncertain autoregressive model, and designs a numerical algorithm to calculate the numerical solutions of the corresponding estimators. Then, the uncertain hypothesis test is used to verify the applicability of the estimated uncertain autoregressive model, and point forecast and interval forecast are also made for the time series of future moments. Finally, a case study of the Consumer Price Index for all items in U.S. cities is provided to illustrate the effectiveness of the approach proposed in this paper. Full article
(This article belongs to the Section Mathematical Analysis)
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16 pages, 586 KiB  
Article
Autonomous Second-Order ODEs: A Geometric Approach
by Antonio J. Pan-Collantes and José Antonio Álvarez-García
Axioms 2024, 13(11), 788; https://doi.org/10.3390/axioms13110788 - 14 Nov 2024
Viewed by 376
Abstract
Given an autonomous second-order ordinary differential equation (ODE), we define a Riemannian metric on an open subset of the first-order jet bundle. A relationship is established between the solutions of the ODE and the geodesic curves with respect to the defined metric. We [...] Read more.
Given an autonomous second-order ordinary differential equation (ODE), we define a Riemannian metric on an open subset of the first-order jet bundle. A relationship is established between the solutions of the ODE and the geodesic curves with respect to the defined metric. We introduce the notion of energy foliation for autonomous ODEs and highlight its connection to the classical energy concept. Additionally, we explore the geometry of the leaves of the foliation. Finally, the results are applied to the analysis of Lagrangian mechanical systems. In particular, we provide an autonomous Lagrangian for a damped harmonic oscillator. Full article
(This article belongs to the Section Mathematical Analysis)
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26 pages, 336 KiB  
Article
On Generalizations of Jacobi–Jordan Algebras
by Hani Abdelwahab, Naglaa Fathi Abdo, Elisabete Barreiro and José María Sánchez
Axioms 2024, 13(11), 787; https://doi.org/10.3390/axioms13110787 - 14 Nov 2024
Viewed by 310
Abstract
In this paper, we present some generalizations of Jacobi–Jordan algebras. More concretely, we will focus on noncommutative Jacobi–Jordan algebras, Malcev–Jordan algebras, and general Jacobi–Jordan algebras. We adapt a method, used to classify Poisson algebras, in order to classify all general Jacobi–Jordan algebras up [...] Read more.
In this paper, we present some generalizations of Jacobi–Jordan algebras. More concretely, we will focus on noncommutative Jacobi–Jordan algebras, Malcev–Jordan algebras, and general Jacobi–Jordan algebras. We adapt a method, used to classify Poisson algebras, in order to classify all general Jacobi–Jordan algebras up to dimension 4, and, in particular, all noncommutative Jacobi–Jordan algebras up to dimension 4. We present the classification of Malcev–Jordan algebras up to dimension 5. As the class of Jacobi–Jordan algebras (commutative algebras that satisfy the Jacobi identity), we find that Malcev–Jordan algebras are Jordan algebras but not necessarily nilpotent. However, we show that the classification of nilpotent Malcev–Jordan algebras is sufficient to obtain the classification of the whole class. Full article
(This article belongs to the Section Algebra and Number Theory)
20 pages, 459 KiB  
Article
Fractal Differential Equations of 2α-Order
by Alireza Khalili Golmankhaneh and Donatella Bongiorno
Axioms 2024, 13(11), 786; https://doi.org/10.3390/axioms13110786 - 14 Nov 2024
Viewed by 405
Abstract
In this research paper, we provide a concise overview of fractal calculus applied to fractal sets. We introduce and solve a 2α-order fractal differential equation with constant coefficients across different scenarios. We propose a uniqueness theorem for 2α-order fractal [...] Read more.
In this research paper, we provide a concise overview of fractal calculus applied to fractal sets. We introduce and solve a 2α-order fractal differential equation with constant coefficients across different scenarios. We propose a uniqueness theorem for 2α-order fractal linear differential equations. We define the solution space as a vector space with non-integer orders. We establish precise conditions for 2α-order fractal linear differential equations and derive the corresponding fractal adjoint differential equation. Full article
(This article belongs to the Special Issue Fractal Analysis and Mathematical Integration)
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15 pages, 292 KiB  
Article
Modeling Directional Monotonicity in Sequence with Copulas
by José Juan Quesada-Molina and Manuel Úbeda-Flores
Axioms 2024, 13(11), 785; https://doi.org/10.3390/axioms13110785 - 14 Nov 2024
Viewed by 294
Abstract
In this paper, we present the concept of being monotonic in sequence according to a specific direction for a collection of random variables. This concept broadens the existing notions of multivariate dependence, such as sequential left-tail and right-tail dependence. Furthermore, we explore connections [...] Read more.
In this paper, we present the concept of being monotonic in sequence according to a specific direction for a collection of random variables. This concept broadens the existing notions of multivariate dependence, such as sequential left-tail and right-tail dependence. Furthermore, we explore connections with other multivariate dependence concepts, highlight key properties, and analyze the new concept within the framework of copulas. Several examples are provided to demonstrate our findings. Full article
(This article belongs to the Special Issue New Perspectives in Fuzzy Sets and Their Applications)
2 pages, 160 KiB  
Editorial
Computational Algebra, Coding Theory, and Cryptography: Theory and Applications
by Hashem Bordbar
Axioms 2024, 13(11), 784; https://doi.org/10.3390/axioms13110784 - 14 Nov 2024
Viewed by 338
Abstract
The primary aim of this Special Issue is to explore innovative encoding and decoding procedures that leverage various algebraic structures to enhance error-control coding techniques [...] Full article
14 pages, 375 KiB  
Article
The Stability of a Predator–Prey Model with Cross-Dispersal in a Multi-Patch Environment
by Keyao Xu, Keyu Peng and Shang Gao
Axioms 2024, 13(11), 783; https://doi.org/10.3390/axioms13110783 - 13 Nov 2024
Viewed by 341
Abstract
This paper investigates the stability of predator–prey models within multi-patch environments, with a particular focus on the influence of cross-dispersion across patches. We apply Kirchhoff’s matrix tree theorem and Liapunov’s method to derive criteria related to the cross-dispersion topology, thus solving the challenge [...] Read more.
This paper investigates the stability of predator–prey models within multi-patch environments, with a particular focus on the influence of cross-dispersion across patches. We apply Kirchhoff’s matrix tree theorem and Liapunov’s method to derive criteria related to the cross-dispersion topology, thus solving the challenge of determining global asymptotic stability conditions. The method incorporates realistic ecological interactions and spatial heterogeneity, offering a framework for stability analysis. Our findings demonstrate that an appropriate level of cross-dispersion can effectively mitigate oscillations and foster convergence toward equilibrium. Two numerical examples validate these theoretical results and demonstrate the feasibility and effectiveness of the model across multiple patches. Full article
(This article belongs to the Special Issue Complex Networks and Dynamical Systems)
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14 pages, 455 KiB  
Article
Skew-Symmetric Generalized Normal and Generalized t Distributions
by Najmeh Nakhaei Rad, Mahdi Salehi, Yaser Mehrali and Ding-Geng Chen
Axioms 2024, 13(11), 782; https://doi.org/10.3390/axioms13110782 - 13 Nov 2024
Viewed by 331
Abstract
In this paper, we introduce the skew-symmetric generalized normal and the skew-symmetric generalized t distributions, which are skewed extensions of symmetric special cases of generalized skew-normal and generalized skew-t distributions, respectively. We derive key distributional properties for these new distributions, including a [...] Read more.
In this paper, we introduce the skew-symmetric generalized normal and the skew-symmetric generalized t distributions, which are skewed extensions of symmetric special cases of generalized skew-normal and generalized skew-t distributions, respectively. We derive key distributional properties for these new distributions, including a recurrence relation and an explicit form for the cumulative distribution function (cdf) of the skew-symmetric generalized t distribution. Numerical examples including a simulation study and a real data analysis are presented to illustrate the practical applicability of these distributions. Full article
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15 pages, 297 KiB  
Article
Robust Semi-Infinite Interval Equilibrium Problem Involving Data Uncertainty: Optimality Conditions and Duality
by Gabriel Ruiz-Garzón, Rafaela Osuna-Gómez, Antonio Rufián-Lizana and Antonio Beato-Moreno
Axioms 2024, 13(11), 781; https://doi.org/10.3390/axioms13110781 - 13 Nov 2024
Viewed by 386
Abstract
In this paper, we model uncertainty in both the objective function and the constraints for the robust semi-infinite interval equilibrium problem involving data uncertainty. We particularize these conditions for the robust semi-infinite mathematical programming problem with interval-valued functions by extending the results from [...] Read more.
In this paper, we model uncertainty in both the objective function and the constraints for the robust semi-infinite interval equilibrium problem involving data uncertainty. We particularize these conditions for the robust semi-infinite mathematical programming problem with interval-valued functions by extending the results from the literature. We introduce the dual robust version of the above problem, prove the Mond–Weir-type weak and strong duality theorems, and illustrate our results with an example. Full article
(This article belongs to the Special Issue New Perspectives in Fuzzy Sets and Their Applications)
23 pages, 613 KiB  
Article
Application of Triple- and Quadruple-Generalized Laplace Transform to (2+1)- and (3+1)-Dimensional Time-Fractional Navier–Stokes Equation
by Hassan Eltayeb Gadain and Said Mesloub
Axioms 2024, 13(11), 780; https://doi.org/10.3390/axioms13110780 - 12 Nov 2024
Viewed by 376
Abstract
In this study, the solution of the (2+1)- and (3+1)-dimensional system of the time-fractional Navier–Stokes equations is gained by utilizing the triple-generalized Laplace transform decomposition method (TGLTDM) and quadruple-generalized Laplace transform decomposition method (FGLTDM). In addition, the results of the offered methods match [...] Read more.
In this study, the solution of the (2+1)- and (3+1)-dimensional system of the time-fractional Navier–Stokes equations is gained by utilizing the triple-generalized Laplace transform decomposition method (TGLTDM) and quadruple-generalized Laplace transform decomposition method (FGLTDM). In addition, the results of the offered methods match with the exact solutions of the problems, which proves that, as the terms of the series increase, the approximate solutions are closer to the exact solutions of each problem. To verify the appropriateness of these methods, some examples are offered. The TGLTDM and FGLTDM results indicate that the suggested methods have higher evaluation convergence as compared to the ADM and HPM. Full article
(This article belongs to the Special Issue Advances in Differential Equations and Its Applications)
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