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Optimal Fourth-Order Methods for Multiple Zeros: Design, Convergence Analysis and Applications 多重零点的最优四阶方法：设计、收敛分析和应用
IF 2 3区 数学
Axioms Pub Date : 2024-02-23 DOI: 10.3390/axioms13030143
Sunil Kumar, J. Sharma, L. Jäntschi
{"title":"Optimal Fourth-Order Methods for Multiple Zeros: Design, Convergence Analysis and Applications","authors":"Sunil Kumar, J. Sharma, L. Jäntschi","doi":"10.3390/axioms13030143","DOIUrl":"https://doi.org/10.3390/axioms13030143","url":null,"abstract":"Nonlinear equations are frequently encountered in many areas of applied science and engineering, and they require efficient numerical methods to solve. To ensure quick and precise root approximation, this study presents derivative-free iterative methods for finding multiple zeros with an ideal fourth-order convergence rate. Furthermore, the study explores applications of the methods in both real-life and academic contexts. In particular, we examine the convergence of the methods by applying them to the problems, namely Van der Waals equation of state, Planck’s law of radiation, the Manning equation for isentropic supersonic flow and some academic problems. Numerical results reveal that the proposed derivative-free methods are more efficient and consistent than existing methods.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139957638","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
Portmanteau Test for ARCH-Type Models by Using High-Frequency Data 利用高频数据对 ARCH 型模型进行波特曼检验
IF 2 3区 数学
Axioms Pub Date : 2024-02-22 DOI: 10.3390/axioms13030141
Yanshan Chen, Xingfa Zhang, Chunliang Deng, Yujiao Liu
{"title":"Portmanteau Test for ARCH-Type Models by Using High-Frequency Data","authors":"Yanshan Chen, Xingfa Zhang, Chunliang Deng, Yujiao Liu","doi":"10.3390/axioms13030141","DOIUrl":"https://doi.org/10.3390/axioms13030141","url":null,"abstract":"The portmanteau test is an effective tool for testing the goodness of fit of models. Motivated by the fact that high-frequency data can improve the estimation accuracy of models, a modified portmanteau test using high-frequency data is proposed for ARCH-type models in this paper. Simulation results show that the empirical size and power of the modified test statistics of the model using high-frequency data are better than those of the daily model. Three stock indices (CSI 300, SSE 50, CSI 500) are taken as an example to illustrate the practical application of the test.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140441715","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
More Effective Criteria for Testing the Oscillation of Solutions of Third-Order Differential Equations 测试三阶微分方程解振荡的更有效标准
IF 2 3区 数学
Axioms Pub Date : 2024-02-22 DOI: 10.3390/axioms13030139
Najiyah Omar, Stefano Serra-Capizzano, B. Qaraad, Faizah Alharbi, O. Moaaz, E. Elabbasy
{"title":"More Effective Criteria for Testing the Oscillation of Solutions of Third-Order Differential Equations","authors":"Najiyah Omar, Stefano Serra-Capizzano, B. Qaraad, Faizah Alharbi, O. Moaaz, E. Elabbasy","doi":"10.3390/axioms13030139","DOIUrl":"https://doi.org/10.3390/axioms13030139","url":null,"abstract":"In the current paper, we aim to study the oscillatory behavior of a new class of third-order differential equations. In the present study, we are interested in a better understanding of the relationships between the solutions and their derivatives. The recursive nature of these relationships enables us to obtain new criteria that ensure the oscillation of all solutions of the studied equation. In comparison with previous studies, our results are more general and include models in a wider range of applications. Furthermore, our findings are also significant because no additional restrictive conditions are required. The presented examples illustrate the significance of the results.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140441281","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
Bayesian Inference for a Hidden Truncated Bivariate Exponential Distribution with Applications 隐藏截断双变量指数分布的贝叶斯推断及其应用
IF 2 3区 数学
Axioms Pub Date : 2024-02-22 DOI: 10.3390/axioms13030140
Indranil Ghosh, H. Ng, Kipum Kim, Seong W. Kim
{"title":"Bayesian Inference for a Hidden Truncated Bivariate Exponential Distribution with Applications","authors":"Indranil Ghosh, H. Ng, Kipum Kim, Seong W. Kim","doi":"10.3390/axioms13030140","DOIUrl":"https://doi.org/10.3390/axioms13030140","url":null,"abstract":"In many real-life scenarios, one variable is observed only if the other concomitant variable or the set of concomitant variables (in the multivariate scenario) is truncated from below, above, or from a two-sided approach. Hidden truncation models have been applied to analyze data when bivariate or multivariate observations are subject to some form of truncation. While the statistical inference for hidden truncation models (truncation from above) under the frequentist and the Bayesian paradigms has been adequately discussed in the literature, the estimation of a two-sided hidden truncation model under the Bayesian framework has not yet been discussed. In this paper, we consider the Bayesian inference for a general two-sided hidden truncation model based on the Arnold–Strauss bivariate exponential distribution. In addition, a Bayesian model selection approach based on the Bayes factor to select between models without truncation, with truncation from below, from above, and two-sided truncation is also explored. An extensive simulation study is carried out for varying parameter choices under the conjugate prior set-up. For illustrative purposes, a real-life dataset is re-analyzed to demonstrate the applicability of the proposed methodology.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140439618","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
N-Dimensional Lattice Integrable Systems and Their bi-Hamiltonian Structure on the Time Scale Using the R-Matrix Approach 使用 R 矩阵方法研究 N 维晶格可积分系统及其时间尺度上的双哈密顿结构
IF 2 3区 数学
Axioms Pub Date : 2024-02-21 DOI: 10.3390/axioms13030136
Yong Fang, Xue Sang, Manwai Yuen, Yong Zhang
{"title":"N-Dimensional Lattice Integrable Systems and Their bi-Hamiltonian Structure on the Time Scale Using the R-Matrix Approach","authors":"Yong Fang, Xue Sang, Manwai Yuen, Yong Zhang","doi":"10.3390/axioms13030136","DOIUrl":"https://doi.org/10.3390/axioms13030136","url":null,"abstract":"A time scale is a special measure chain that can unify continuous and discrete spaces, enabling the construction of integrable equations. In this paper, with the Lax operator generated by the displacement operator, N-dimensional lattice integrable systems on the time scale are given by the R-matrix approach. The recursion operators of the lattice systems are derived on the time scale. Finally, two integrable hierarchies of the discrete chain with a bi-Hamiltonian structure are obtained. In particular, we give the structure of two-field and four-field systems.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140442503","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
Compact Data Learning for Machine Learning Classifications 机器学习分类的紧凑型数据学习
IF 2 3区 数学
Axioms Pub Date : 2024-02-21 DOI: 10.3390/axioms13030137
S. Kim
{"title":"Compact Data Learning for Machine Learning Classifications","authors":"S. Kim","doi":"10.3390/axioms13030137","DOIUrl":"https://doi.org/10.3390/axioms13030137","url":null,"abstract":"This paper targets the area of optimizing machine learning (ML) training data by constructing compact data. The methods of optimizing ML training have improved and become a part of artificial intelligence (AI) system development. Compact data learning (CDL) is an alternative practical framework to optimize a classification system by reducing the size of the training dataset. CDL originated from compact data design, which provides the best assets without handling complex big data. CDL is a dedicated framework for improving the speed of the machine learning training phase without affecting the accuracy of the system. The performance of an ML-based arrhythmia detection system and its variants with CDL maintained the same statistical accuracy. ML training with CDL could be maximized by applying an 85% reduced input dataset, which indicated that a trained ML system could have the same statistical accuracy by only using 15% of the original training dataset.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140443197","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: 1
Szász–Durrmeyer Operators Involving Confluent Appell Polynomials 涉及共容 Appell 多项式的 Szász-Durrmeyer 算子
IF 2 3区 数学
Axioms Pub Date : 2024-02-20 DOI: 10.3390/axioms13030135
Kadir Kanat, Selin Erdal
{"title":"Szász–Durrmeyer Operators Involving Confluent Appell Polynomials","authors":"Kadir Kanat, Selin Erdal","doi":"10.3390/axioms13030135","DOIUrl":"https://doi.org/10.3390/axioms13030135","url":null,"abstract":"This article is concerned with the Durrmeyer-type generalization of Szász operators, including confluent Appell polynomials and their approximation properties. Also, the rate of convergence of the confluent Durrmeyer operators is found by using the modulus of continuity and Peetre’s K-functional. Then, we show that, under special choices of A(t), the newly constructed operators reduce confluent Hermite polynomials and confluent Bernoulli polynomials, respectively. Finally, we present a comparison of newly constructed operators with the Durrmeyer-type Szász operators graphically.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140446772","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
The Average Sentinel of the Heat Equation with an Unknown Reaction 带有未知反应的热方程的平均哨兵
IF 2 3区 数学
Axioms Pub Date : 2024-02-19 DOI: 10.3390/axioms13020128
H. Selatnia, A. Ayadi, Imad Rezzoug
{"title":"The Average Sentinel of the Heat Equation with an Unknown Reaction","authors":"H. Selatnia, A. Ayadi, Imad Rezzoug","doi":"10.3390/axioms13020128","DOIUrl":"https://doi.org/10.3390/axioms13020128","url":null,"abstract":"In this paper, we analyze the identification of the amount of pollutant discharged problem by each source in a heat system when the dynamics of the state are governed by a parameterized unknown operator. In this way, we introduce the notion of average sentinel. The decomposition method is used to solve the equation of this problem, the gradient method is used to calculate the averaged control, and the combination of the two methods is used to estimate the pollution terms. Numerical example is given to confirm this result.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139959272","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
Analytical Solution of Generalized Bratu-Type Fractional Differential Equations Using the Homotopy Perturbation Transform Method 用同调扰动变换法解析广义布拉图型分微分方程
IF 2 3区 数学
Axioms Pub Date : 2024-02-19 DOI: 10.3390/axioms13020133
Ghaliah Alhamzi, Aafrin Gouri, B. Alkahtani, R. Dubey
{"title":"Analytical Solution of Generalized Bratu-Type Fractional Differential Equations Using the Homotopy Perturbation Transform Method","authors":"Ghaliah Alhamzi, Aafrin Gouri, B. Alkahtani, R. Dubey","doi":"10.3390/axioms13020133","DOIUrl":"https://doi.org/10.3390/axioms13020133","url":null,"abstract":"In this study, we present the generalized form of the higher-order nonlinear fractional Bratu-type equation. In this generalization, we deal with a generalized fractional derivative, which is quite useful from an application point of view. Furthermore, some special cases of the generalized fractional Bratu equation are recognized and examined. To solve these nonlinear differential equations of fractional order, we employ the homotopy perturbation transform method. This work presents a useful computational method for solving these equations and advances our understanding of them. We also plot some numerical outcomes to show the efficiency of the obtained results.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140451502","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
Moduli of Continuity in Metric Models and Extension of Livability Indices 公元模型中的连续性模量与宜居指数的扩展
IF 2 3区 数学
Axioms Pub Date : 2024-02-19 DOI: 10.3390/axioms13030192
Roger Arnau, JM Calabuig, Álvaro González, E. A. Sánchez Pérez
{"title":"Moduli of Continuity in Metric Models and Extension of Livability Indices","authors":"Roger Arnau, JM Calabuig, Álvaro González, E. A. Sánchez Pérez","doi":"10.3390/axioms13030192","DOIUrl":"https://doi.org/10.3390/axioms13030192","url":null,"abstract":"Index spaces serve as valuable metric models for studying properties relevant to various applications, such as social science or economics. These properties are represented by real Lipschitz functions that describe the degree of association with each element within the underlying metric space. After determining the index value within a given sample subset, the classic McShane and Whitney formulas allow a Lipschitz regression procedure to be performed to extend the index values over the entire metric space. To improve the adaptability of the metric model to specific scenarios, this paper introduces the concept of a composition metric, which involves composing a metric with an increasing, positive and subadditive function ϕ. The results presented here extend well-established results for Lipschitz indices on metric spaces to composition metrics. In addition, we establish the corresponding approximation properties that facilitate the use of this functional structure. To illustrate the power and simplicity of this mathematical framework, we provide a concrete application involving the modeling of livability indices in North American cities.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140451256","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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