Previous Issue
Volume 13, June
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
1.9
Journals
Axioms
Volume 13
Issue 7
share announcement

Axioms, Volume 13, Issue 7 (July 2024) – 27 articles

  • Issues are regarded as officially published after their release is announced to the table of contents alert mailing list.
  • You may sign up for e-mail alerts to receive table of contents of newly released issues.
  • PDF is the official format for papers published in both, html and pdf forms. To view the papers in pdf format, click on the "PDF Full-text" link, and use the free Adobe Reader to open them.
Order results
Result details
Section
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
23 pages, 443 KiB  
Article
Statistical Inferences about Parameters of the Pseudo Lindley Distribution with Acceptance Sampling Plans
by Fatehi Yahya Eissa, Chhaya Dhanraj Sonar, Osama Abdulaziz Alamri and Ahlam H. Tolba
Axioms 2024, 13(7), 443; https://doi.org/10.3390/axioms13070443 (registering DOI) - 29 Jun 2024
Viewed by 123
Abstract
Different non-Bayesian and Bayesian techniques were used to estimate the pseudo-Lindley (PsL) distribution’s parameters in this study. To derive Bayesian estimators, one must assume appropriate priors on the parameters and use loss functions such as squared error (SE), general entropy (GE), and linear-exponential [...] Read more.
Different non-Bayesian and Bayesian techniques were used to estimate the pseudo-Lindley (PsL) distribution’s parameters in this study. To derive Bayesian estimators, one must assume appropriate priors on the parameters and use loss functions such as squared error (SE), general entropy (GE), and linear-exponential (LINEX). Since no closed-form solutions are accessible for Bayes estimates under these loss functions, the Markov Chain Monte Carlo (MCMC) approach was used. Simulation studies were conducted to evaluate the estimators’ performance under the given loss functions. Furthermore, we exhibited the adaptability and practicality of the PsL distribution through real-world data applications, which is essential for evaluating the various estimation techniques. Also, the acceptance sampling plans were developed in this work for items whose lifespans approximate the PsL distribution. Full article
(This article belongs to the Special Issue Computational Statistics and Its Applications)
23 pages, 354 KiB  
Article
Sharp Coefficient Bounds for Starlike Functions Associated with Cosine Function
by Rashid Ali, Mohsan Raza and Teodor Bulboacă
Axioms 2024, 13(7), 442; https://doi.org/10.3390/axioms13070442 (registering DOI) - 29 Jun 2024
Viewed by 110
Abstract
Let Scos* denote the class of normalized analytic functions f in the open unit disk D satisfying the subordination zf′(z)f(z)≺cosz. In the first result of this article, we [...] Read more.
Let Scos* denote the class of normalized analytic functions f in the open unit disk D satisfying the subordination zf′(z)f(z)≺cosz. In the first result of this article, we find the sharp upper bounds for the initial coefficients a3, a4 and a5 and the sharp upper bound for module of the Hankel determinant |H2,3(f)| for the functions from the class Scos*. The next section deals with the sharp upper bounds of the logarithmic coefficients γ3 and γ4. Then, in addition, we found the sharp upper bound for H2,2Ff/2. To obtain these results we utilized the very useful and appropriate Lemma 2.4 of N.E. Cho et al. [Filomat 34(6) (2020), 2061–2072], which gave a most accurate description for the first five coefficients of the functions from the Carathéodory’s functions class, and provided a technique for finding the maximum value of a three-variable function on a closed cuboid. All the maximum found values were checked by using MAPLE™ 2016 computer software, and we also found the extremal functions in each case. All of our most recent results are the best ones and give sharp versions of those recently published in [Hacet. J. Math. Stat. 52, 596–618, 2023]. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Related Topics)
22 pages, 2752 KiB  
Article
On the Impact of Some Fixed Point Theorems on Dynamic Programming and RLC Circuit Models in R-Modular b-Metric-like Spaces
by Ekber Girgin, Abdurrahman Büyükkaya, Neslihan Kaplan Kuru and Mahpeyker Öztürk
Axioms 2024, 13(7), 441; https://doi.org/10.3390/axioms13070441 (registering DOI) - 28 Jun 2024
Viewed by 188
Abstract
In this study, we significantly extend the concept of modular metric-like spaces to introduce the notion of b-metric-like spaces. Furthermore, by incorporating a binary relation R, we develop the framework of R-modular b-metric-like spaces. We establish a groundbreaking fixed [...] Read more.
In this study, we significantly extend the concept of modular metric-like spaces to introduce the notion of b-metric-like spaces. Furthermore, by incorporating a binary relation R, we develop the framework of R-modular b-metric-like spaces. We establish a groundbreaking fixed point theorem for certain extensions of Geraghty-type contraction mappings, incorporating both Z simulation function and E-type contraction within this innovative structure. Moreover, we present several novel outcomes that stem from our newly defined notations. Afterwards, we introduce an unprecedented concept, the graphical modular b-metric-like space, which is derived from the binary relation R. Finally, we examine the existence of solutions for a class of functional equations that are pivotal in dynamic programming and in solving initial value problems related to the electric current in an RLC parallel circuit. Full article
47 pages, 1014 KiB  
Article
Brain Connectivity Dynamics and Mittag–Leffler Synchronization in Asymmetric Complex Networks for a Class of Coupled Nonlinear Fractional-Order Memristive Neural Network System with Coupling Boundary Conditions
by Aziz Belmiloudi
Axioms 2024, 13(7), 440; https://doi.org/10.3390/axioms13070440 (registering DOI) - 28 Jun 2024
Viewed by 139
Abstract
This paper investigates the long-time behavior of fractional-order complex memristive neural networks in order to analyze the synchronization of both anatomical and functional brain networks, for predicting therapy response, and ensuring safe diagnostic and treatments of neurological disorder (such as epilepsy, Alzheimer’s disease, [...] Read more.
This paper investigates the long-time behavior of fractional-order complex memristive neural networks in order to analyze the synchronization of both anatomical and functional brain networks, for predicting therapy response, and ensuring safe diagnostic and treatments of neurological disorder (such as epilepsy, Alzheimer’s disease, or Parkinson’s disease). A new mathematical brain connectivity model, taking into account the memory characteristics of neurons and their past history, the heterogeneity of brain tissue, and the local anisotropy of cell diffusion, is proposed. This developed model, which depends on topology, interactions, and local dynamics, is a set of coupled nonlinear Caputo fractional reaction–diffusion equations, in the shape of a fractional-order ODE coupled with a set of time fractional-order PDEs, interacting via an asymmetric complex network. In order to introduce into the model the connection structure between neurons (or brain regions), the graph theory, in which the discrete Laplacian matrix of the communication graph plays a fundamental role, is considered. The existence of an absorbing set in state spaces for system is discussed, and then the dissipative dynamics result, with absorbing sets, is proved. Finally, some Mittag–Leffler synchronization results are established for this complex memristive neural network under certain threshold values of coupling forces, memristive weight coefficients, and diffusion coefficients. Full article
(This article belongs to the Topic Advances in Nonlinear Dynamics: Methods and Applications)
43 pages, 431 KiB  
Article
A Theory for Interpolation of Metric Spaces
by Robledo Mak’s Miranda Sette, Dicesar Lass Fernandez and Eduardo Brandani da Silva
Axioms 2024, 13(7), 439; https://doi.org/10.3390/axioms13070439 (registering DOI) - 28 Jun 2024
Viewed by 75
Abstract
In this work, we develop an interpolation theory for metric spaces inspired by the real method of interpolation. These interpolation spaces preserve Lipschitz operators under certain conditions. We also show that this method, valid in metrics spaces, still holds in normed spaces without [...] Read more.
In this work, we develop an interpolation theory for metric spaces inspired by the real method of interpolation. These interpolation spaces preserve Lipschitz operators under certain conditions. We also show that this method, valid in metrics spaces, still holds in normed spaces without any algebraic structure required. Furthermore, this interpolation method for metric spaces when applied to normed spaces is equivalent to the K-method, which has been widely studied in the literature. As an application, we interpolate Fréchet sequence spaces. Full article
(This article belongs to the Special Issue Research on Functional Analysis and Its Applications)
27 pages, 368 KiB  
Article
Qualitative Analysis for the Solutions of Fractional Stochastic Differential Equations
by Abdelhamid Mohammed Djaouti and Muhammad Imran Liaqat
Axioms 2024, 13(7), 438; https://doi.org/10.3390/axioms13070438 - 28 Jun 2024
Viewed by 158
Abstract
Fractional pantograph stochastic differential equations (FPSDEs) combine elements of fractional calculus, pantograph equations, and stochastic processes to model complex systems with memory effects, time delays, and random fluctuations. Ensuring the well-posedness of these equations is crucial as it guarantees meaningful, reliable, and applicable [...] Read more.
Fractional pantograph stochastic differential equations (FPSDEs) combine elements of fractional calculus, pantograph equations, and stochastic processes to model complex systems with memory effects, time delays, and random fluctuations. Ensuring the well-posedness of these equations is crucial as it guarantees meaningful, reliable, and applicable solutions across various disciplines. In differential equations, regularity refers to the smoothness of solution behavior. The averaging principle offers an approximation that balances complexity and simplicity. Our research contributes to establishing the well-posedness, regularity, and averaging principle of FPSDE solutions in Lp spaces with p≥2 under Caputo derivatives. The main ingredients in the proof include the use of Hölder, Burkholder–Davis–Gundy, Jensen, and Grönwall–Bellman inequalities, along with the interval translation approach. To understand the theoretical results, we provide numerical examples at the end. Full article
(This article belongs to the Special Issue Advances in Partial Differential Equations: Qualitative Analysis and Numerical Methods)
22 pages, 692 KiB  
Article
Biequivalent Planar Graphs
by Bernard Piette
Axioms 2024, 13(7), 437; https://doi.org/10.3390/axioms13070437 - 28 Jun 2024
Viewed by 144
Abstract
We define biequivalent planar graphs, which are a generalisation of the uniform polyhedron graphs, as planar graphs made out of two families of equivalent nodes. Such graphs are required to identify polyhedral cages with geometries suitable for artificial protein cages. We use an [...] Read more.
We define biequivalent planar graphs, which are a generalisation of the uniform polyhedron graphs, as planar graphs made out of two families of equivalent nodes. Such graphs are required to identify polyhedral cages with geometries suitable for artificial protein cages. We use an algebraic method, which is followed by an algorithmic method, to determine all such graphs with up to 300 nodes each with valencies ranging between three and six. We also present a graphic representation of every graph found. Full article
(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics)
►▼ Show Figures

Figure 1

12 pages, 259 KiB  
Article
Some Refinements and Generalizations of Bohr’s Inequality
by Salma Aljawi, Cristian Conde and Kais Feki
Axioms 2024, 13(7), 436; https://doi.org/10.3390/axioms13070436 - 28 Jun 2024
Viewed by 146
Abstract
In this article, we delve into the classic Bohr inequality for complex numbers, a fundamental result in complex analysis with broad mathematical applications. We offer refinements and generalizations of Bohr’s inequality, expanding on the established inequalities of N. G. de Bruijn and Radon, [...] Read more.
In this article, we delve into the classic Bohr inequality for complex numbers, a fundamental result in complex analysis with broad mathematical applications. We offer refinements and generalizations of Bohr’s inequality, expanding on the established inequalities of N. G. de Bruijn and Radon, as well as leveraging the class of functions defined by the Daykin–Eliezer–Carlitz inequality. Our novel contribution lies in demonstrating that Bohr’s and Bergström’s inequalities can be derived from one another, revealing a deeper interconnectedness between these results. Furthermore, we present several new generalizations of Bohr’s inequality, along with other notable inequalities from the literature, and discuss their various implications. By providing more comprehensive and verifiable conditions, our work extends previous research and enhances the understanding and applicability of Bohr’s inequality in mathematical studies. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities II)
41 pages, 429 KiB  
Article
The Existence and Representation of the Solutions to the System of Operator Equations AiXBi + CiYDi + EiZFi = Gi(i = 1, 2)
by Gen Che, Guojun Hai, Jiarui Mei and Xiang Cao
Axioms 2024, 13(7), 435; https://doi.org/10.3390/axioms13070435 - 27 Jun 2024
Viewed by 161
Abstract
In this paper, we give the necessary and sufficient conditions for the existence of general solutions, self-adjoint solutions, and positive solutions to the system of [...] Read more.
In this paper, we give the necessary and sufficient conditions for the existence of general solutions, self-adjoint solutions, and positive solutions to the system of AiXBi+CiYDi+EiZFi=Gi(i=1,2) under additional conditions. In addition, we derive the representation of general solutions to the system of AiXBi+CiYDi+EiZFi=Gi(i=1,2), and provide the matrix representation of the self-adjoint solutions and the positive solutions in the sense of the star order. Full article
18 pages, 307 KiB  
Article
Harmonic Series with Multinomial Coefficient 4nn,n,n,n and Central Binomial Coefficient 2nn
by Chunli Li and Wenchang Chu
Axioms 2024, 13(7), 434; https://doi.org/10.3390/axioms13070434 - 27 Jun 2024
Viewed by 136
Abstract
Classical hypergeometric series are reformulated as analytic functions of their parameters (in both the numerator and the denominator). Then, the coefficient extraction method is applied to examine hypergeometric series transformations. Several new closed form evaluations are established for harmonic series containing multinomial coefficient [...] Read more.
Classical hypergeometric series are reformulated as analytic functions of their parameters (in both the numerator and the denominator). Then, the coefficient extraction method is applied to examine hypergeometric series transformations. Several new closed form evaluations are established for harmonic series containing multinomial coefficient 4nn,n,n,n and central binomial coefficient 2nn. These results exclusively concern the alternating series of convergence rate “−1/4”. Full article
(This article belongs to the Special Issue Research in Special Functions)
15 pages, 280 KiB  
Article
On Bivariate Distributions with Singular Part
by Carles M. Cuadras
Axioms 2024, 13(7), 433; https://doi.org/10.3390/axioms13070433 - 27 Jun 2024
Viewed by 165
Abstract
There are many families of bivariate distributions with given marginals. Most families, such as the Farlie–Gumbel–Morgenstern (FGM) and the Ali–Mikhail–Haq (AMH), are absolutely continuous, with an ordinary probability density. In contrast, there are few families with a singular part or a positive mass [...] Read more.
There are many families of bivariate distributions with given marginals. Most families, such as the Farlie–Gumbel–Morgenstern (FGM) and the Ali–Mikhail–Haq (AMH), are absolutely continuous, with an ordinary probability density. In contrast, there are few families with a singular part or a positive mass on a curve. We define a general condition useful to detect the singular part of a distribution. By continuous extension of the bivariate diagonal expansion, we define and study a wide family containing these singular distributions, obtain the probability density, and find the canonical correlations and functions. The set of canonical correlations is described by a continuous function rather than a countable sequence. An application to statistical inference is given. Full article
(This article belongs to the Special Issue Applications of Bayesian Methods in Statistical Analysis)
20 pages, 502 KiB  
Article
Small Area Estimation under Poisson–Dirichlet Process Mixture Models
by Xiang Qiu, Qinchun Ke, Xueqin Zhou and Yulu Liu
Axioms 2024, 13(7), 432; https://doi.org/10.3390/axioms13070432 - 27 Jun 2024
Viewed by 156
Abstract
In this paper, we propose an improved Nested Error Regression model in which the random effects for each area are given a prior distribution using the Poisson–Dirichlet Process. Based on this model, we mainly investigate the construction of the parameter estimation using the [...] Read more.
In this paper, we propose an improved Nested Error Regression model in which the random effects for each area are given a prior distribution using the Poisson–Dirichlet Process. Based on this model, we mainly investigate the construction of the parameter estimation using the Empirical Bayesian(EB) estimation method, and we adopt various methods such as the Maximum Likelihood Estimation(MLE) method and the Markov chain Monte Carlo algorithm to solve the model parameter estimation jointly. The viability of the model is verified using numerical simulation, and the proposed model is applied to an actual small area estimation problem. Compared to the conventional normal random effects linear model, the proposed model is more accurate for the estimation of complex real-world application data, which makes it suitable for a broader range of application contexts. Full article
11 pages, 273 KiB  
Article
A Study of Structural Stability on the Bidispersive Flow in a Semi-Infinite Cylinder
by Yuanfei Li
Axioms 2024, 13(7), 431; https://doi.org/10.3390/axioms13070431 - 27 Jun 2024
Viewed by 215
Abstract
We consider the bidispersive flow with nonlinear boundary conditions in a bounded region. By using the differential inequality technique, we get the bound for the L4-norm of the salinity which plays an important role. The continuous dependence and the convergence results [...] Read more.
We consider the bidispersive flow with nonlinear boundary conditions in a bounded region. By using the differential inequality technique, we get the bound for the L4-norm of the salinity which plays an important role. The continuous dependence and the convergence results on the Soret coefficient are established. Full article
(This article belongs to the Special Issue Advances in Differential Equations and Its Applications)
25 pages, 893 KiB  
Article
Comparative Analysis of Exact Methods for Testing Equivalence of Prevalences in Bilateral and Unilateral Combined Data with and without Assumptions of Correlation
by Shuyi Liang and Chang-Xing Ma
Axioms 2024, 13(7), 430; https://doi.org/10.3390/axioms13070430 - 26 Jun 2024
Viewed by 182
Abstract
In clinical studies focusing on paired body parts, diseases can manifest on either both sides (bilateral) or just one side (unilateral) of the organs. Consequently, the data in these studies may consist of records from both bilateral and unilateral cases. There are two [...] Read more.
In clinical studies focusing on paired body parts, diseases can manifest on either both sides (bilateral) or just one side (unilateral) of the organs. Consequently, the data in these studies may consist of records from both bilateral and unilateral cases. There are two different methods of analyzing the data. One of the methods is assuming that the pair of measurements from the same subject are independent, while the other considers the correlation between paired organs. In terms of the homogeneity test of proportions, asymptotic methods have been proposed given the moderate size of data. This article extends the existing work by proposing exact methods to deal with the scenarios when the sample size is small and asymptotic methods perform poorly. The impact of the correlation assumption is also explored. Among the proposed methods, calculating p-values by replacing unknown parameters with estimated values while accounting for the correlation is recommended based on its satisfactory type I error controls and statistical powers. The proposed methods are applied to three real examples for illustration. Full article
(This article belongs to the Special Issue New Perspectives in Mathematical Statistics)
16 pages, 318 KiB  
Review
Monogenity and Power Integral Bases: Recent Developments
by István Gaál
Axioms 2024, 13(7), 429; https://doi.org/10.3390/axioms13070429 - 26 Jun 2024
Viewed by 155
Abstract
Monogenity is a classical area of algebraic number theory that continues to be actively researched. This paper collects the results obtained over the past few years in this area. Several of the listed results were presented at a series of online conferences titled [...] Read more.
Monogenity is a classical area of algebraic number theory that continues to be actively researched. This paper collects the results obtained over the past few years in this area. Several of the listed results were presented at a series of online conferences titled “Monogenity and Power Integral Bases”. We also give a collection of the most important methods used in several of these papers. A list of open problems for further research is also given. Full article
(This article belongs to the Special Issue Advances in Generalized Hypergeometric Functions, Integral Transforms and Number Theory)
12 pages, 930 KiB  
Article
Constructing Approximations to Bivariate Piecewise-Smooth Functions
by David Levin
Axioms 2024, 13(7), 428; https://doi.org/10.3390/axioms13070428 - 26 Jun 2024
Viewed by 178
Abstract
This paper demonstrates that the space of piecewise-smooth bivariate functions can be well-approximated by the space of the functions defined by a set of simple (non-linear) operations on smooth uniform tensor product splines. The examples include bivariate functions with jump discontinuities or normal [...] Read more.
This paper demonstrates that the space of piecewise-smooth bivariate functions can be well-approximated by the space of the functions defined by a set of simple (non-linear) operations on smooth uniform tensor product splines. The examples include bivariate functions with jump discontinuities or normal discontinuities across curves, and even across more involved geometries such as a three-corner discontinuity. The provided data may be uniform or non-uniform, and noisy, and the approximation procedure involves non-linear least-squares minimization. Also included is a basic approximation theorem for functions with jump discontinuity across a smooth curve. Full article
(This article belongs to the Special Issue Numerical Computation, Approximation of Functions and Applied Mathematics, 2nd Edition)
►▼ Show Figures

Figure 1

14 pages, 413 KiB  
Article
From the Crossing Numbers of K5 + Pn and K5 + Cn to the Crossing Numbers of Wm + Sn and Wm + Wn
by Michal Staš, Jana Fortes and Mária Švecová
Axioms 2024, 13(7), 427; https://doi.org/10.3390/axioms13070427 - 25 Jun 2024
Viewed by 394
Abstract
The crossing number of a graph is a significant measure that indicates the complexity of the graph and the difficulty of visualizing it. In this paper, we examine the crossing numbers of join products involving the complete graph K5 with discrete graphs, [...] Read more.
The crossing number of a graph is a significant measure that indicates the complexity of the graph and the difficulty of visualizing it. In this paper, we examine the crossing numbers of join products involving the complete graph K5 with discrete graphs, paths, and cycles. We analyze optimal drawings of K5, identify all five non-isomorphic drawings, and address previously hypothesized crossing numbers for K5+Pn, and K5+Cn. Through a simplified approach, we first establish cr(K5+Dn) and then extend our method to prove the crossing numbers cr(K5+Pn) and cr(K5+Cn). These results also lead to new hypotheses for cr(Wm+Sn) and cr(Wm+Wn) involving wheels and stars. Our findings correct previous inaccuracies in the literature and provide a foundation for future research. Full article
(This article belongs to the Special Issue Advances in Graph Theory and Combinatorial Optimization)
►▼ Show Figures

Figure 1

16 pages, 384 KiB  
Article
Optimal and Efficient Approximations of Gradients of Functions with Nonindependent Variables
by Matieyendou Lamboni
Axioms 2024, 13(7), 426; https://doi.org/10.3390/axioms13070426 - 25 Jun 2024
Viewed by 375
Abstract
Gradients of smooth functions with nonindependent variables are relevant for exploring complex models and for the optimization of the functions subjected to constraints. In this paper, we investigate new and simple approximations and computations of such gradients by making use of independent, central, [...] Read more.
Gradients of smooth functions with nonindependent variables are relevant for exploring complex models and for the optimization of the functions subjected to constraints. In this paper, we investigate new and simple approximations and computations of such gradients by making use of independent, central, and symmetric variables. Such approximations are well suited for applications in which the computations of the gradients are too expansive or impossible. The derived upper bounds of the biases of our approximations do not suffer from the curse of dimensionality for any 2-smooth function, and they theoretically improve the known results. Also, our estimators of such gradients reach the optimal (mean squared error) rates of convergence (i.e., O(N−1)) for the same class of functions. Numerical comparisons based on a test case and a high-dimensional PDE model show the efficiency of our approach. Full article
(This article belongs to the Special Issue Recent Research on Functions with Non-Independent Variables)
►▼ Show Figures

Figure 1

14 pages, 252 KiB  
Article
Three Existence Results in the Fixed Point Theory
by Alexander J. Zaslavski
Axioms 2024, 13(7), 425; https://doi.org/10.3390/axioms13070425 - 25 Jun 2024
Viewed by 473
Abstract
In the present paper, we obtain three results on the existence of a fixed point for nonexpansive mappings. Two of them are generalizations of the result for F-contraction, while third one is a generalization of a recent result for set-valued contractions. Full article
(This article belongs to the Special Issue Trends in Fixed Point Theory and Fractional Calculus)
31 pages, 13721 KiB  
Article
An Enhanced Fuzzy Hybrid of Fireworks and Grey Wolf Metaheuristic Algorithms
by Juan Barraza, Luis Rodríguez, Oscar Castillo, Patricia Melin and Fevrier Valdez
Axioms 2024, 13(7), 424; https://doi.org/10.3390/axioms13070424 - 24 Jun 2024
Viewed by 352
Abstract
This research work envisages addressing fuzzy adjustment of parameters into a hybrid optimization algorithm for solving mathematical benchmark function problems. The problem of benchmark mathematical functions consists of finding the minimal values. In this study, we considered function optimization. We are presenting an [...] Read more.
This research work envisages addressing fuzzy adjustment of parameters into a hybrid optimization algorithm for solving mathematical benchmark function problems. The problem of benchmark mathematical functions consists of finding the minimal values. In this study, we considered function optimization. We are presenting an enhanced Fuzzy Hybrid Algorithm, which is called Enhanced Fuzzy Hybrid Fireworks and Grey Wolf Metaheuristic Algorithm, and denoted as EF-FWA-GWO. The fuzzy adjustment of parameters is achieved using Fuzzy Inference Systems. For this work, we implemented two variants of the Fuzzy Systems. The first variant utilizes Triangular membership functions, and the second variant employs Gaussian membership functions. Both variants are of a Mamdani Fuzzy Inference Type. The proposed method was applied to 22 mathematical benchmark functions, divided into two parts: the first part consists of 13 functions that can be classified as unimodal and multimodal, and the second part consists of the 9 fixed-dimension multimodal benchmark functions. The proposed method presents better performance with 60 and 90 dimensions, averaging 51% and 58% improvement in the benchmark functions, respectively. And then, a statistical comparison between the conventional hybrid algorithm and the Fuzzy Enhanced Hybrid Algorithm is presented to complement the conclusions of this research. Finally, we also applied the Fuzzy Hybrid Algorithm in a control problem to test its performance in designing a Fuzzy controller for a mobile robot. Full article
(This article belongs to the Special Issue Advances in Mathematical Optimization Algorithms and Its Applications)
►▼ Show Figures

Figure 1

28 pages, 772 KiB  
Article
C0-Semigroups Approach to the Reliability Model Based on Robot-Safety System
by Ehmet Kasim and Aihemaitijiang Yumaier
Axioms 2024, 13(7), 423; https://doi.org/10.3390/axioms13070423 - 24 Jun 2024
Viewed by 207
Abstract
This paper considers a system with one robot and n safety units (one of which works while the others remain on standby), which is described by an integro-deferential equation. The system can fail in the following three ways: fails with an incident, fails [...] Read more.
This paper considers a system with one robot and n safety units (one of which works while the others remain on standby), which is described by an integro-deferential equation. The system can fail in the following three ways: fails with an incident, fails safely and fails due to the malfunction of the robot. Using the C0−semigroups theory of linear operators, we first show that the system has a unique non-negative, time-dependent solution. Then, we obtain the exponential convergence of the time-dependent solution to its steady-state solution. In addition, we study the asymptotic behavior of some time-dependent reliability indices and present a numerical example demonstrating the effects of different parameters on the system. Full article
(This article belongs to the Special Issue Infinite Dynamical System and Differential Equations)
19 pages, 292 KiB  
Article
Extensions of Some Statistical Concepts to the Complex Domain
by Arak M. Mathai
Axioms 2024, 13(7), 422; https://doi.org/10.3390/axioms13070422 - 22 Jun 2024
Viewed by 193
Abstract
This paper deals with the extension of principal component analysis, canonical correlation analysis, the Cramer–Rao inequality, and a few other statistical concepts in the real domain to the corresponding complex domain. Optimizations of Hermitian forms under a linear constraint, a bilinear form under [...] Read more.
This paper deals with the extension of principal component analysis, canonical correlation analysis, the Cramer–Rao inequality, and a few other statistical concepts in the real domain to the corresponding complex domain. Optimizations of Hermitian forms under a linear constraint, a bilinear form under Hermitian-form constraints, and similar maxima/minima problems in the complex domain are discussed. Some vector/matrix differential operators are developed to handle the above types of problems. These operators in the complex domain and the optimization problems in the complex domain are believed to be new and novel. These operators will also be useful in maximum likelihood estimation problems, which will be illustrated in the concluding remarks. Detailed steps are given in the derivations so that the methods are easily accessible to everyone. Full article
(This article belongs to the Special Issue New Perspectives in Mathematical Statistics)
12 pages, 273 KiB  
Article
Symmetric Identities Involving the Extended Degenerate Central Fubini Polynomials Arising from the Fermionic p-Adic Integral on \({\mathbb{Z}_{p}}\)
by Maryam Salem Alatawi, Waseem Ahmad Khan and Ugur Duran
Axioms 2024, 13(7), 421; https://doi.org/10.3390/axioms13070421 - 22 Jun 2024
Viewed by 221
Abstract
Since the constructions of p-adic q-integrals, these integrals as well as particular cases have been used not only as integral representations of many special functions, polynomials, and numbers, but they also allow for deep examinations of many families of special numbers [...] Read more.
Since the constructions of p-adic q-integrals, these integrals as well as particular cases have been used not only as integral representations of many special functions, polynomials, and numbers, but they also allow for deep examinations of many families of special numbers and polynomials, such as central Fubini, Bernoulli, central Bell, and Changhee numbers and polynomials. One of the key applications of these integrals is for obtaining the symmetric identities of certain special polynomials. In this study, we focus on a novel generalization of degenerate central Fubini polynomials. First, we introduce two variable degenerate w-torsion central Fubini polynomials by means of their exponential generating function. Then, we provide a fermionic p-adic integral representation of these polynomials. Through this representation, we investigate several symmetric identities for these polynomials using special p-adic integral techniques. Also, using series manipulation methods, we obtain an identity of symmetry for the two variable degenerate w-torsion central Fubini polynomials. Finally, we provide a representation of the degenerate differential operator on the two variable degenerate w-torsion central Fubini polynomials related to the degenerate central factorial polynomials of the second kind. Full article
(This article belongs to the Special Issue Advanced Approximation Techniques and Their Applications II)
16 pages, 582 KiB  
Article
Generalization of the Distance Fibonacci Sequences
by Nur Şeyma Yilmaz, Andrej Włoch and Engin Özkan
Axioms 2024, 13(7), 420; https://doi.org/10.3390/axioms13070420 - 21 Jun 2024
Viewed by 329
Abstract
In this study, we introduced a generalization of distance Fibonacci sequences and investigate some of its basic properties. We then proposed a generalization of distance Fibonacci sequences for negative integers and investigated some basic properties. Additionally, we explored the construction of matrix generators [...] Read more.
In this study, we introduced a generalization of distance Fibonacci sequences and investigate some of its basic properties. We then proposed a generalization of distance Fibonacci sequences for negative integers and investigated some basic properties. Additionally, we explored the construction of matrix generators for these sequences and offered a graphical representation to clarify their structure. Furthermore, we demonstrated how these generalizations can be applied to obtain the Padovan and Narayana sequences for specific parameter values. Full article
(This article belongs to the Special Issue Advances in Generalized Hypergeometric Functions, Integral Transforms and Number Theory)
32 pages, 1415 KiB  
Article
Enhanced Kepler Optimization Method for Nonlinear Multi-Dimensional Optimal Power Flow
by Mohammed H. Alqahtani, Sulaiman Z. Almutairi, Abdullah M. Shaheen and Ahmed R. Ginidi
Axioms 2024, 13(7), 419; https://doi.org/10.3390/axioms13070419 - 21 Jun 2024
Viewed by 210
Abstract
Multi-Dimensional Optimal Power Flow (MDOPF) is a fundamental task in power systems engineering aimed at optimizing the operation of electrical networks while considering various constraints such as power generation, transmission, and distribution. The mathematical model of MDOPF involves formulating it as a non-linear, [...] Read more.
Multi-Dimensional Optimal Power Flow (MDOPF) is a fundamental task in power systems engineering aimed at optimizing the operation of electrical networks while considering various constraints such as power generation, transmission, and distribution. The mathematical model of MDOPF involves formulating it as a non-linear, non-convex optimization problem aimed at minimizing specific objective functions while adhering to equality and inequality constraints. The objective function typically includes terms representing the Fuel Cost (FC), Entire Network Losses (ENL), and Entire Emissions (EE), while the constraints encompass power balance equations, generator operating limits, and network constraints, such as line flow limits and voltage limits. This paper presents an innovative Improved Kepler Optimization Technique (IKOT) for solving MDOPF problems. The IKOT builds upon the traditional KOT and incorporates enhanced local escaping mechanisms to overcome local optima traps and improve convergence speed. The mathematical model of the IKOT algorithm involves defining a population of candidate solutions (individuals) represented as vectors in a high-dimensional search space. Each individual corresponds to a potential solution to the MDOPF problem, and the algorithm iteratively refines these solutions to converge towards the optimal solution. The key innovation of the IKOT lies in its enhanced local escaping mechanisms, which enable it to explore the search space more effectively and avoid premature convergence to suboptimal solutions. Experimental results on standard IEEE test systems demonstrate the effectiveness of the proposed IKOT in solving MDOPF problems. The proposed IKOT obtained the FC, EE, and ENL of USD 41,666.963/h, 1.039 Ton/h, and 9.087 MW, respectively, in comparison with the KOT, which achieved USD 41,677.349/h, 1.048 Ton/h, 11.277 MW, respectively. In comparison to the base scenario, the IKOT achieved a reduction percentage of 18.85%, 58.89%, and 64.13%, respectively, for the three scenarios. The IKOT consistently outperformed the original KOT and other state-of-the-art metaheuristic optimization algorithms in terms of solution quality, convergence speed, and robustness. Full article
(This article belongs to the Special Issue Advances in Mathematical Methods in Optimal Control and Applications)
15 pages, 1485 KiB  
Article
Analysis of Fat Big Data Using Factor Models and Penalization Techniques: A Monte Carlo Simulation and Application
by Faridoon Khan and Olayan Albalawi
Axioms 2024, 13(7), 418; https://doi.org/10.3390/axioms13070418 - 21 Jun 2024
Viewed by 258
Abstract
This article assesses the predictive accuracy of factor models utilizing Partial·Least·Squares (PLS) and Principal·Component·Analysis (PCA) in comparison to autometrics and penalization techniques. The simulation exercise examines three types of scenarios by introducing the issues of multicollinearity, heteroscedasticity, and autocorrelation. The number of predictors [...] Read more.
This article assesses the predictive accuracy of factor models utilizing Partial·Least·Squares (PLS) and Principal·Component·Analysis (PCA) in comparison to autometrics and penalization techniques. The simulation exercise examines three types of scenarios by introducing the issues of multicollinearity, heteroscedasticity, and autocorrelation. The number of predictors and sample size are adjusted to observe the effects. The accuracy of the models is evaluated by calculating the Root·Mean·Square·Error (RMSE) and the Mean·Absolute·Error (MAE). In the presence of severe multicollinearity, the factor approach utilizing (PLS demonstrates exceptional performance in comparison. Autometrics achieves the lowest RMSE and MAE values across all levels of heteroscedasticity. Autometrics provides better forecasts with low and moderate autocorrelation. However, Elastic·Smoothly·Clipped·Absolute·Deviation (E-SCAD) forecasts well with severe autocorrelation. In addition to the simulation, we employ a popular Pakistani macroeconomic dataset for empirical research. The dataset contains 79 monthly variables from January 2013 to December 2020. The competing approaches perform differently compared to the simulation datasets, although “The PLS factor approach outperforms its competing approaches in forecasting, with lower RMSE and MAE”. It is more probable that the actual dataset exhibits a high degree of multicollinearity. Full article
(This article belongs to the Special Issue Applications of Statistical and Mathematical Models)
►▼ Show Figures

Figure 1

33 pages, 492 KiB  
Article
Some New Estimations of Left and Right Interval Fractional Pachpatte’s Type Integral Inequalities via Rectangle Plane
by Azzh Saad Alshehry, Loredana Ciurdariu, Yaser Saber and Amal F. Soliman
Axioms 2024, 13(7), 417; https://doi.org/10.3390/axioms13070417 - 21 Jun 2024
Viewed by 246
Abstract
Inequalities involving fractional operators have been an active area of research, which is crucial in establishing bounds, estimates, and stability conditions for solutions to fractional integrals. In this paper, we initially presented a new class that is known as coordinated left and right [...] Read more.
Inequalities involving fractional operators have been an active area of research, which is crucial in establishing bounds, estimates, and stability conditions for solutions to fractional integrals. In this paper, we initially presented a new class that is known as coordinated left and right ℏ-pre-invex interval-valued mappings (C·L·R-ℏ-pre-invex Ι·V-M), as well classical convex and nonconvex are also obtained. This newly defined class enabled us to derive novel inequalities, such as Hermite–Hadamard and Pachpatte’s type inequalities. Furthermore, the obtained results allowed us to recapture several special cases of known results for different parameter choices, which can be applications of the main results. Finally, we discussed the validity of the main outcomes. Full article
(This article belongs to the Section Mathematical Analysis)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-27
Previous Issue
Back to TopTop