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The Estimation of Different Kinds of Integral Inequalities for a Generalized Class of Convex Mapping and a Harmonic Set via Fuzzy Inclusion Relations and Their Applications in Quadrature Theory 通过模糊包容关系估算广义类凸映射和谐集的各类积分不等式及其在正交理论中的应用
IF 2 3区 数学
Axioms Pub Date : 2024-05-22 DOI: 10.3390/axioms13060344
A. Althobaiti, Saad Althobaiti, Miguel Vivas Cortez
{"title":"The Estimation of Different Kinds of Integral Inequalities for a Generalized Class of Convex Mapping and a Harmonic Set via Fuzzy Inclusion Relations and Their Applications in Quadrature Theory","authors":"A. Althobaiti, Saad Althobaiti, Miguel Vivas Cortez","doi":"10.3390/axioms13060344","DOIUrl":"https://doi.org/10.3390/axioms13060344","url":null,"abstract":"The relationship between convexity and symmetry is widely recognized. In fuzzy theory, both concepts exhibit similar behavior. It is crucial to remember that real and interval-valued mappings are special instances of fuzzy-number-valued mappings (F-N-V-Ms), as fuzzy theory relies on the unit interval, which is crucial to resolving problems with interval analysis and fuzzy number theory. In this paper, a new harmonic convexities class of fuzzy numbers has been introduced via up and down relation. We show several Hermite–Hadamard (H ⋅ H) and Fejér-type inequalities by the implementation of fuzzy Aumann integrals using the newly defined class of convexities. Some nontrivial examples are also presented to validate the main outcomes.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141113278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Conditioning Theory for ML-Weighted Pseudoinverse and ML-Weighted Least Squares Problem ML 加权伪逆和 ML 加权最小二乘法问题的条件理论
IF 2 3区 数学
Axioms Pub Date : 2024-05-22 DOI: 10.3390/axioms13060345
Mahvish Samar, Xinzhong Zhu, Huiying Xu
{"title":"Conditioning Theory for ML-Weighted Pseudoinverse and ML-Weighted Least Squares Problem","authors":"Mahvish Samar, Xinzhong Zhu, Huiying Xu","doi":"10.3390/axioms13060345","DOIUrl":"https://doi.org/10.3390/axioms13060345","url":null,"abstract":"The conditioning theory of the ML-weighted least squares and ML-weighted pseudoinverse problems is explored in this article. We begin by introducing three types of condition numbers for the ML-weighted pseudoinverse problem: normwise, mixed, and componentwise, along with their explicit expressions. Utilizing the derivative of the ML-weighted pseudoinverse problem, we then provide explicit condition number expressions for the solution of the ML-weighted least squares problem. To ensure reliable estimation of these condition numbers, we employ the small-sample statistical condition estimation method for all three algorithms. The article concludes with numerical examples that highlight the results obtained.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141112236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Explicit Numerical Manifold Characteristic Galerkin Method for Solving Burgers’ Equation 用于求解布尔格斯方程的显式流形特征 Galerkin 数值方法
IF 2 3区 数学
Axioms Pub Date : 2024-05-22 DOI: 10.3390/axioms13060343
Yue Sun, Qian Chen, Tao Chen, Longquan Yong
{"title":"Explicit Numerical Manifold Characteristic Galerkin Method for Solving Burgers’ Equation","authors":"Yue Sun, Qian Chen, Tao Chen, Longquan Yong","doi":"10.3390/axioms13060343","DOIUrl":"https://doi.org/10.3390/axioms13060343","url":null,"abstract":"This paper presents a nonstandard numerical manifold method (NMM) for solving Burgers’ equation. Employing the characteristic Galerkin method, we initially apply the Crank–Nicolson method for temporal discretization along the characteristic. Subsequently, utilizing the Taylor expansion, we transform the semi-implicit formula into a fully explicit form. For spacial discretization, we construct the NMM dual-cover system tailored to Burgers’ equation. We choose constant cover functions and first-order weight functions to enhance computational efficiency and exactly import boundary constraints. Finally, the integrated computing scheme is derived by using the standard Galerkin method, along with a Thomas algorithm-based solution procedure. The proposed method is verified through six benchmark numerical examples under various initial boundary conditions. Extensive comparisons with analytical solutions and results from alternative methods are conducted, demonstrating the accuracy and stability of our approach, particularly in solving Burgers’ equation at high Reynolds numbers.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141109727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Progressive Outlook on Possibility Multi-Fuzzy Soft Ordered Semigroups: Theory and Analysis 可能性多模糊软有序半群的渐进展望》：理论与分析
IF 2 3区 数学
Axioms Pub Date : 2024-05-21 DOI: 10.3390/axioms13060340
Sana Habib, Faiz Muhammad Khan, Violeta Leoreanu-Fotea
{"title":"A Progressive Outlook on Possibility Multi-Fuzzy Soft Ordered Semigroups: Theory and Analysis","authors":"Sana Habib, Faiz Muhammad Khan, Violeta Leoreanu-Fotea","doi":"10.3390/axioms13060340","DOIUrl":"https://doi.org/10.3390/axioms13060340","url":null,"abstract":"The concept of possibility fuzzy soft sets is a step in a new direction towards a soft set approach that can be used to solve decision-making issues. In this piece of research, an innovative and comprehensive conceptual framework for possibility multi-fuzzy soft ordered semigroups by making use of the notions that are associated with possibility multi-fuzzy soft sets as well as ordered semigroups is introduced. Possibility multi-fuzzy soft ordered semigroups mark a newly developed theoretical avenue, and the central aim of this paper is to investigate it. The focus lies on investigating this newly developed theoretical direction, with practical examples drawn from decision-making and diagnosis practices to enhance understanding and appeal to researchers’ interests. We strictly build the notions of possibility multi-fuzzy soft left (right) ideals, as well as l-idealistic and r-idealistic possibility multi-fuzzy soft ordered semigroups. Furthermore, various algebraic operations, such as union, intersection, as well as AND and OR operations are derived, while also providing a comprehensive discussion of their properties. To clarify these innovative ideas, the theoretical constructs are further reinforced with a set of demonstrative examples in order to guarantee deep and improved comprehension of the proposed framework.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141117347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A New Optimal Numerical Root-Solver for Solving Systems of Nonlinear Equations Using Local, Semi-Local, and Stability Analysis 利用局部、半局部和稳定性分析求解非线性方程系统的新型最优数值根求解器
IF 2 3区 数学
Axioms Pub Date : 2024-05-21 DOI: 10.3390/axioms13060341
Sania Qureshi, F. Chicharro, Ioannis K. Argyros, Amanullah Soomro, Jihan Alahmadi, E. Hıncal
{"title":"A New Optimal Numerical Root-Solver for Solving Systems of Nonlinear Equations Using Local, Semi-Local, and Stability Analysis","authors":"Sania Qureshi, F. Chicharro, Ioannis K. Argyros, Amanullah Soomro, Jihan Alahmadi, E. Hıncal","doi":"10.3390/axioms13060341","DOIUrl":"https://doi.org/10.3390/axioms13060341","url":null,"abstract":"This paper introduces an iterative method with a remarkable level of accuracy, namely fourth-order convergence. The method is specifically tailored to meet the optimality condition under the Kung–Traub conjecture by linear combination. This method, with an efficiency index of approximately 1.5874, employs a blend of localized and semi-localized analysis to improve both efficiency and convergence. This study aims to investigate semi-local convergence, dynamical analysis to assess stability and convergence rate, and the use of the proposed solver for systems of nonlinear equations. The results underscore the potential of the proposed method for several applications in polynomiography and other areas of mathematical research. The improved performance of the proposed optimal method is demonstrated with mathematical models taken from many domains, such as physics, mechanics, chemistry, and combustion, to name a few.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141115774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uniformly Shifted Exponential Distribution 均匀移动指数分布
IF 2 3区 数学
Axioms Pub Date : 2024-05-21 DOI: 10.3390/axioms13060339
A. Alzaid, Najla Qarmalah
{"title":"Uniformly Shifted Exponential Distribution","authors":"A. Alzaid, Najla Qarmalah","doi":"10.3390/axioms13060339","DOIUrl":"https://doi.org/10.3390/axioms13060339","url":null,"abstract":"The use of life distributions has increased over the past decade, receiving particular attention in recent years, both from a practical and theoretical point of view. Life distributions can be used in a number of applied fields, such as medicine, biology, public health, epidemiology, engineering, economics, and demography. This paper presents and investigates a new life distribution. The proposed model shows favorable characteristics in terms of reliability theory, which makes it competitive against other commonly used life distributions, such as the exponential, gamma, and Weibull distributions. The methods of maximum likelihood and moments are used to estimate the parameters of the proposed model. Additionally, real-life data drawn from different fields are used to illustrate the usefulness of the new distribution. Further, the R programming language is used to perform all computations and produce all graphs.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141113194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
High Perturbations of a Fractional Kirchhoff Equation with Critical Nonlinearities 具有临界非线性的分数基尔霍夫方程的高扰动
IF 2 3区 数学
Axioms Pub Date : 2024-05-20 DOI: 10.3390/axioms13050337
Shengbin Yu, Lingmei Huang, Jiangbin Chen
{"title":"High Perturbations of a Fractional Kirchhoff Equation with Critical Nonlinearities","authors":"Shengbin Yu, Lingmei Huang, Jiangbin Chen","doi":"10.3390/axioms13050337","DOIUrl":"https://doi.org/10.3390/axioms13050337","url":null,"abstract":"This paper concerns a fractional Kirchhoff equation with critical nonlinearities and a negative nonlocal term. In the case of high perturbations (large values of α, i.e., the parameter of a subcritical nonlinearity), existence results are obtained by the concentration compactness principle together with the mountain pass theorem and cut-off technique. The multiplicity of solutions are further considered with the help of the symmetric mountain pass theorem. Moreover, the nonexistence and asymptotic behavior of positive solutions are also investigated.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141120258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Blow-Up Analysis of L2-Norm Solutions for an Elliptic Equation with a Varying Nonlocal Term 具有变化非局部项的椭圆方程 L2 准则解的炸开分析
IF 2 3区 数学
Axioms Pub Date : 2024-05-20 DOI: 10.3390/axioms13050336
Xincai Zhu, Chunxia He
{"title":"Blow-Up Analysis of L2-Norm Solutions for an Elliptic Equation with a Varying Nonlocal Term","authors":"Xincai Zhu, Chunxia He","doi":"10.3390/axioms13050336","DOIUrl":"https://doi.org/10.3390/axioms13050336","url":null,"abstract":"This paper is devoted to studying a type of elliptic equation that contains a varying nonlocal term. We provide a detailed analysis of the existence, non-existence, and blow-up behavior of L2-norm solutions for the related equation when the potential function V(x) fulfills an appropriate choice.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141121268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Respiratory Condition Detection Using Audio Analysis and Convolutional Neural Networks Optimized by Modified Metaheuristics 利用音频分析和修正元搜索优化的卷积神经网络检测呼吸状况
IF 2 3区 数学
Axioms Pub Date : 2024-05-18 DOI: 10.3390/axioms13050335
Nebojša Bačanin, Luka Jovanovic, R. Stoean, C. Stoean, M. Zivkovic, Milos Antonijevic, M. Dobrojevic
{"title":"Respiratory Condition Detection Using Audio Analysis and Convolutional Neural Networks Optimized by Modified Metaheuristics","authors":"Nebojša Bačanin, Luka Jovanovic, R. Stoean, C. Stoean, M. Zivkovic, Milos Antonijevic, M. Dobrojevic","doi":"10.3390/axioms13050335","DOIUrl":"https://doi.org/10.3390/axioms13050335","url":null,"abstract":"Respiratory conditions have been a focal point in recent medical studies. Early detection and timely treatment are crucial factors in improving patient outcomes for any medical condition. Traditionally, doctors diagnose respiratory conditions through an investigation process that involves listening to the patient’s lungs. This study explores the potential of combining audio analysis with convolutional neural networks to detect respiratory conditions in patients. Given the significant impact of proper hyperparameter selection on network performance, contemporary optimizers are employed to enhance efficiency. Moreover, a modified algorithm is introduced that is tailored to the specific demands of this study. The proposed approach is validated using a real-world medical dataset and has demonstrated promising results. Two experiments are conducted: the first tasked models with respiratory condition detection when observing mel spectrograms of patients’ breathing patterns, while the second experiment considered the same data format for multiclass classification. Contemporary optimizers are employed to optimize the architecture selection and training parameters of models in both cases. Under identical test conditions, the best models are optimized by the introduced modified metaheuristic, with an accuracy of 0.93 demonstrated for condition detection, and a slightly reduced accuracy of 0.75 for specific condition identification.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141125666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Regular, Beating and Dilogarithmic Breathers in Biased Photorefractive Crystals 偏置光折射晶体中的规则、跳动和二对数呼吸器
IF 2 3区 数学
Axioms Pub Date : 2024-05-16 DOI: 10.3390/axioms13050338
C. A. Betancur-Silvera, Á. Espinosa-Cerón, B. Malomed, Jorge Fujioka
{"title":"Regular, Beating and Dilogarithmic Breathers in Biased Photorefractive Crystals","authors":"C. A. Betancur-Silvera, Á. Espinosa-Cerón, B. Malomed, Jorge Fujioka","doi":"10.3390/axioms13050338","DOIUrl":"https://doi.org/10.3390/axioms13050338","url":null,"abstract":"The propagation of light beams in photovoltaic pyroelectric photorefractive crystals is modelled by a specific generalization of the nonlinear Schrödinger equation (GNLSE). We use a variational approximation (VA) to predict the propagation of solitary-wave inputs in the crystals, finding that the VA equations involve a dilogarithm special function. The VA predicts that solitons and breathers exist, and the Vakhitov–Kolokolov criterion predicts that the solitons are stable solutions. Direct simulations of the underlying GNLSE corroborates the existence of such stable modes. The numerical solutions produce both regular breathers and ones featuring beats (long-period modulations of fast oscillations). In the latter case, the Fourier transform of amplitude oscillations reveals a nearly discrete spectrum characterizing the beats dynamics. Numerical solutions of another type demonstrate the spontaneous splitting of the input pulse in two or several secondary ones.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141127350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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