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An Efficient Anti-Noise Zeroing Neural Network for Time-Varying Matrix Inverse 用于时变矩阵反演的高效抗噪归零神经网络
IF 1.9 3区 数学
Axioms Pub Date : 2024-08-09 DOI: 10.3390/axioms13080540
Jiaxin Hu, Feixiang Yang, Yun Huang
{"title":"An Efficient Anti-Noise Zeroing Neural Network for Time-Varying Matrix Inverse","authors":"Jiaxin Hu, Feixiang Yang, Yun Huang","doi":"10.3390/axioms13080540","DOIUrl":"https://doi.org/10.3390/axioms13080540","url":null,"abstract":"The Time-Varying Matrix Inversion (TVMI) problem is integral to various fields in science and engineering. Countless studies have highlighted the effectiveness of Zeroing Neural Networks (ZNNs) as a dependable approach for addressing this challenge. To effectively solve the TVMI problem, this paper introduces a novel Efficient Anti-Noise Zeroing Neural Network (EANZNN). This model employs segmented time-varying parameters and double integral terms, where the segmented time-varying parameters can adaptively adjust over time, offering faster convergence speeds compared to fixed parameters. The double integral term enables the model to effectively handle the interference of constant noise, linear noise, and other noises. Using the Lyapunov approach, we theoretically analyze and show the convergence and robustness of the proposed EANZNN model. Experimental findings showcase that in scenarios involving linear, constant noise and noise-free environments, the EANZNN model exhibits superior performance compared to traditional models like the Double Integral-Enhanced ZNN (DIEZNN) and the Parameter-Changing ZNN (PCZNN). It demonstrates faster convergence and better resistance to interference, affirming its efficacy in addressing TVMI problems.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141925025","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
Exact Reliability and Signature Formulas for Linear m-Consecutive-k-out-of-n: F Systems 线性 m-Consecutive-k-out-of-n 的精确可靠性和签名公式：F 系统
IF 1.9 3区 数学
Axioms Pub Date : 2024-08-09 DOI: 10.3390/axioms13080541
Gökhan Gökdere, Ayse Bugatekin
{"title":"Exact Reliability and Signature Formulas for Linear m-Consecutive-k-out-of-n: F Systems","authors":"Gökhan Gökdere, Ayse Bugatekin","doi":"10.3390/axioms13080541","DOIUrl":"https://doi.org/10.3390/axioms13080541","url":null,"abstract":"An m-consecutive-k-out-of-n: F (m/C/k/n: F) system consists of n linearly ordered components such that the system fails if and only if there are at least m nonoverlapping runs of k consecutive failed components. Our motivation in this work is to obtain efficient formulas for the signature and reliability of the m/C/k/n: F system with independent and identical (i.i.d) components that are easy to implement and have a low computational time. We demonstrate that the reliability formula derived for this system requires less computational time than the m/C/k/n: F system formula currently in use. For the minimal and maximal signatures of the m/C/k/n: F system, we provide precise equations. In addition, the average number of faulty components at the time of an m/C/k/n: F system failure and mean time to failure (MTTF) of an m/C/k/n: F system are analyzed through the system signature.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141923781","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
Review on Some Boundary Value Problems Defining the Mean First-Passage Time in Cell Migration 细胞迁移中定义平均首过时间的若干边界值问题综述
IF 1.9 3区 数学
Axioms Pub Date : 2024-08-08 DOI: 10.3390/axioms13080537
Hélia Serrano, Ramón F. Álvarez-Estrada
{"title":"Review on Some Boundary Value Problems Defining the Mean First-Passage Time in Cell Migration","authors":"Hélia Serrano, Ramón F. Álvarez-Estrada","doi":"10.3390/axioms13080537","DOIUrl":"https://doi.org/10.3390/axioms13080537","url":null,"abstract":"The mean first-passage time represents the average time for a migrating cell within its environment, starting from a certain position, to reach a specific location or target for the first time. In this feature article, we provide an overview of the characterization of the mean first-passage time of cells moving inside two- or three-dimensional domains, subject to various boundary conditions (Dirichlet, Neumann, Robin, or mixed), through the so-called adjoint diffusion equation. We concentrate on reducing the latter to inhomogeneous linear integral equations for certain density functions on the boundaries. The integral equations yield the mean first-passage time exactly for a very reduced set of boundaries. For various boundary surfaces, which include small deformations of the exactly solvable boundaries, the integral equations provide approximate solutions. Moreover, the method also allows to deal approximately with mixed boundary conditions, which constitute a genuine long-standing and open problem. New plots, figures, and discussions are presented, aimed at clarifying the analysis.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141928315","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
Boundedness and Compactness of Weighted Composition Operators from (α, k)-Bloch Spaces to A(β,k) Spaces on Generalized Hua Domains of the Fourth Kind 第四类广义华域上从（α，k）布洛赫空间到 A（β，k）空间的加权合成算子的有界性与紧凑性
IF 1.9 3区 数学
Axioms Pub Date : 2024-08-08 DOI: 10.3390/axioms13080539
Jiaqi Wang, Jianbing Su
{"title":"Boundedness and Compactness of Weighted Composition Operators from (α, k)-Bloch Spaces to A(β,k) Spaces on Generalized Hua Domains of the Fourth Kind","authors":"Jiaqi Wang, Jianbing Su","doi":"10.3390/axioms13080539","DOIUrl":"https://doi.org/10.3390/axioms13080539","url":null,"abstract":"This paper addresses the weighted composition operators Cϕψ from the (α,k)-Bloch spaces to the A(β,k) spaces of bounded holomorphic functions on W, where W is a generalized Hua domain of the fourth kind. Additionally, we obtain some necessary and sufficient conditions for the boundedness and compactness of these operators.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141925578","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 Normality Criterion for Sharing a Holomorphic Function 共享全形函数的规范性标准
IF 1.9 3区 数学
Axioms Pub Date : 2024-08-08 DOI: 10.3390/axioms13080538
Sheng Wang, Xiaojun Huang
{"title":"A Normality Criterion for Sharing a Holomorphic Function","authors":"Sheng Wang, Xiaojun Huang","doi":"10.3390/axioms13080538","DOIUrl":"https://doi.org/10.3390/axioms13080538","url":null,"abstract":"In this paper, we scrutinize a collection of meromorphic functions known as normal families, prove the theorem that normal families share a holomorphic function, and present several illustrative counterexamples.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141928900","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
Weighted Convolution for Quaternion Linear Canonical Cosine Transform and Its Application 四元线性余弦变换的加权卷积及其应用
IF 2 3区 数学
Axioms Pub Date : 2024-06-14 DOI: 10.3390/axioms13060402
Rong-bo Wang, Qiang Feng
{"title":"Weighted Convolution for Quaternion Linear Canonical Cosine Transform and Its Application","authors":"Rong-bo Wang, Qiang Feng","doi":"10.3390/axioms13060402","DOIUrl":"https://doi.org/10.3390/axioms13060402","url":null,"abstract":"Convolution plays a pivotal role in the domains of signal processing and optics. This paper primarily focuses on studying the weighted convolution for quaternion linear canonical cosine transform (QLCcT) and its application in multiplicative filter analysis. Firstly, we propose QLCcT by combining quaternion algebra with linear canonical cosine transform (LCcT), which extends LCcT to Hamiltonian quaternion algebra. Secondly, we introduce weighted convolution and correlation operations for QLCcT, accompanied by their corresponding theorems. We also explore the properties of QLCcT. Thirdly, we utilize these proposed convolution structures to analyze multiplicative filter models that offer lower computational complexity compared to existing methods based on quaternion linear canonical transform (QLCT). Additionally, we discuss the rationale behind studying such transforms using quaternion functions as an illustrative example.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141343265","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 Conservative Difference Scheme for Solving the Coupled Fractional Schrödinger–Boussinesq System 求解耦合分数薛定谔-布西尼斯克系统的保守差分方案
IF 2 3区 数学
Axioms Pub Date : 2024-06-14 DOI: 10.3390/axioms13060400
Yao Shi, Rian Yan, Tao Liu
{"title":"A Conservative Difference Scheme for Solving the Coupled Fractional Schrödinger–Boussinesq System","authors":"Yao Shi, Rian Yan, Tao Liu","doi":"10.3390/axioms13060400","DOIUrl":"https://doi.org/10.3390/axioms13060400","url":null,"abstract":"In this paper, a high-accuracy conservative implicit algorithm for computing the space fractional coupled Schrödinger–Boussinesq system is constructed. Meanwhile, the conservative nature, a priori boundedness, and solvability of the numerical solution are presented. Then, the proposed algorithm is proved to be second-order convergence in temporal and fourth-order spatial convergence using the discrete energy method. Finally, some numerical experiments validate the effectiveness of the conservative algorithm and confirm the accuracy of the theoretical results for different choices of the fractional-order α.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141339179","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
Homotopy Analysis Transform Method for a Singular Nonlinear Second-Order Hyperbolic Pseudo-Differential Equation 奇异非线性二阶双曲伪微分方程的同调分析变换法
IF 2 3区 数学
Axioms Pub Date : 2024-06-14 DOI: 10.3390/axioms13060398
S. Mesloub, H. E. Gadain
{"title":"Homotopy Analysis Transform Method for a Singular Nonlinear Second-Order Hyperbolic Pseudo-Differential Equation","authors":"S. Mesloub, H. E. Gadain","doi":"10.3390/axioms13060398","DOIUrl":"https://doi.org/10.3390/axioms13060398","url":null,"abstract":"In this study, we employed the homotopy analysis transform method (HATM) to derive an iterative scheme to numerically solve a singular second-order hyperbolic pseudo-differential equation. We evaluated the effectiveness of the derived scheme in solving both linear and nonlinear equations of similar nature through a series of illustrative examples. The stability of this scheme in handling the approximate solutions of these examples was studied graphically and numerically. A comparative analysis with existing methodologies from the literature was conducted to assess the performance of the proposed approach. Our findings demonstrate that the HATM-based method offers notable efficiency, accuracy, and ease of implementation when compared to the alternative technique considered in this study.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141341520","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
Statistical Advancement of a Flexible Unitary Distribution and Its Applications 灵活单元分布的统计进步及其应用
IF 2 3区 数学
Axioms Pub Date : 2024-06-14 DOI: 10.3390/axioms13060397
Hugo S. Salinas, H. Bakouch, Fatimah E. Almuhayfith, Wilson E. Caimanque, Leonardo Barrios-Blanco, Olayan Albalawi
{"title":"Statistical Advancement of a Flexible Unitary Distribution and Its Applications","authors":"Hugo S. Salinas, H. Bakouch, Fatimah E. Almuhayfith, Wilson E. Caimanque, Leonardo Barrios-Blanco, Olayan Albalawi","doi":"10.3390/axioms13060397","DOIUrl":"https://doi.org/10.3390/axioms13060397","url":null,"abstract":"A flexible distribution has been introduced to handle random variables in the unit interval. This distribution is based on an exponential transformation of the truncated positive normal distribution with two parameters and can effectively fit data with varying degrees of skewness and kurtosis. Therefore, it presents an alternative for modeling this type of data. Several mathematical and statistical properties of this distribution have been derived, such as moments, hazard function, the Bonferroni curve, and entropy. Moreover, we investigate the characterizations of the proposed distribution based on its hazard function. Parameter estimation has been performed using both the maximum likelihood method and method of the moments. Because of this, we were able to determine the best critical region and the information matrix, facilitating the calculation of asymptotic confidence intervals. A simulation study is presented to analyze the behavior of the obtained estimators for different sample sizes. To demonstrate the suitability of the proposed distribution, applications and goodness-of-fit tests have been performed on two practical data sets.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141344138","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
Enhanced Real-Life Data Modeling with the Modified Burr III Odds Ratio–G Distribution 利用修正的伯尔 III 比率-G 分布增强现实生活数据建模能力
IF 2 3区 数学
Axioms Pub Date : 2024-06-14 DOI: 10.3390/axioms13060401
Haochong Yang, Mingfang Huang, Xinyu Chen, Ziyan He, Shusen Pu
{"title":"Enhanced Real-Life Data Modeling with the Modified Burr III Odds Ratio–G Distribution","authors":"Haochong Yang, Mingfang Huang, Xinyu Chen, Ziyan He, Shusen Pu","doi":"10.3390/axioms13060401","DOIUrl":"https://doi.org/10.3390/axioms13060401","url":null,"abstract":"In this study, we introduce the modified Burr III Odds Ratio–G distribution, a novel statistical model that integrates the odds ratio concept with the foundational Burr III distribution. The spotlight of our investigation is cast on a key subclass within this innovative framework, designated as the Burr III Scaled Inverse Odds Ratio–G (B-SIOR-G) distribution. By effectively integrating the odds ratio with the Burr III distribution, this model enhances both flexibility and predictive accuracy. We delve into a thorough exploration of this distribution family’s mathematical and statistical properties, spanning hazard rate functions, quantile functions, moments, and additional features. Through rigorous simulation, we affirm the robustness of the B-SIOR-G model. The flexibility and practicality of the B-SIOR-G model are demonstrated through its application to four datasets, highlighting its enhanced efficacy over several well-established distributions.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141338659","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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