Examples and Counterexamples最新文献_第7页

Quadrature based innovative techniques concerning nonlinear equations having unknown multiplicity 基于正交的有关未知倍数非线性方程的创新技术

Examples and Counterexamples Pub Date : 2024-12-01 Epub Date: 2024-07-09 DOI: 10.1016/j.exco.2024.100150

Farooq Ahmed Shah , Muhammad Waseem

{"title":"Quadrature based innovative techniques concerning nonlinear equations having unknown multiplicity","authors":"Farooq Ahmed Shah , Muhammad Waseem","doi":"10.1016/j.exco.2024.100150","DOIUrl":"https://doi.org/10.1016/j.exco.2024.100150","url":null,"abstract":"<div><p>Solution of nonlinear equations is one of the most frequently encountered issue in engineering and applied sciences. Most of the intricateed engineering problems are modeled in the frame work of nonlinear equation <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>0</mn><mo>.</mo></mrow></math></span> The significance of iterative algorithms executed by computers in resolving such functions is of paramount importance and undeniable in contemporary times. If we study the simple roots and the roots having multiplicity greater of any nonlinear equations we come to the point that finding the roots of nonlinear equations having multiplicity greater than one is not trivialvia classical iterative methods. Instability or slow convergence rate is faced by these methods, and also sometimes these methods diverge. In this article, we give some innovative and robust iterative techniques for obtaining the approximate solution of nonlinear equations having multiplicity <span><math><mrow><mi>m</mi><mo>></mo><mn>1</mn></mrow></math></span>. Quadrature formulas are implemented to obtain iterative techniques for finding roots of nonlinear equations having unknown multiplicity. The derived methods are the variants of modified Newton method with high order of convergence and better accuracy. The convergence criteria of the new techniques are studied by using Taylor series method. Some examples are tested for the sack of implementations of these techniques. Numerical and graphical comparison shows the performance and efficiency of these new techniques.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"6 ","pages":"Article 100150"},"PeriodicalIF":0.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X24000168/pdfft?md5=1401656be5f763d7bc65918548e7c152&pid=1-s2.0-S2666657X24000168-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141594856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the elastic instability of a simple truss structure subjected to a tensile dead load 关于简单桁架结构在拉伸自重作用下的弹性失稳问题

Examples and Counterexamples Pub Date : 2024-12-01 Epub Date: 2024-10-23 DOI: 10.1016/j.exco.2024.100165

Alfredo Canelas, Ana I. Abreu

引用次数: 0

Whether the singularities are removable in some metrics 奇点在某些度量中是否可移动

Examples and Counterexamples Pub Date : 2024-12-01 Epub Date: 2024-10-15 DOI: 10.1016/j.exco.2024.100164

Ting-Han Pei

引用次数: 0

A dispersive dynamical system that is chain transitive 具有链传递性的分散动力系统

Examples and Counterexamples Pub Date : 2024-12-01 Epub Date: 2024-07-16 DOI: 10.1016/j.exco.2024.100153

Eduardo C. Viscovini, Josiney A. Souza

引用次数: 0

Degree-based topological indices of the idempotent graph of the ring Zn 环 Zn 的幂等图的基于度的拓扑指数

Examples and Counterexamples Pub Date : 2024-12-01 Epub Date: 2024-10-05 DOI: 10.1016/j.exco.2024.100161

Osman Gani Mondal, Sk. Md. Abu Nayeem

{"title":"Degree-based topological indices of the idempotent graph of the ring Zn","authors":"Osman Gani Mondal, Sk. Md. Abu Nayeem","doi":"10.1016/j.exco.2024.100161","DOIUrl":"10.1016/j.exco.2024.100161","url":null,"abstract":"<div><div>Let <span><math><mi>R</mi></math></span> be a finite commutative ring with a non-zero identity, and <span><math><mrow><mi>I</mi><mi>d</mi><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> be the set of idempotent elements of <span><math><mi>R</mi></math></span>. The idempotent graph of <span><math><mi>R</mi></math></span>, denoted by <span><math><mrow><msub><mrow><mi>G</mi></mrow><mrow><mi>I</mi><mi>d</mi></mrow></msub><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span>, is a simple undirected graph with all elements of <span><math><mi>R</mi></math></span> as vertices, and two distinct vertices <span><math><mi>u</mi></math></span>, <span><math><mi>v</mi></math></span> are adjacent if and only if <span><math><mrow><mi>u</mi><mo>+</mo><mi>v</mi><mo>∈</mo><mi>I</mi><mi>d</mi><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span>. In this paper, we consider the idempotent graph of the ring <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> and investigate some degree-based topological indices, such as the general sum-connectivity index, the general Randić index, the general Zagreb index, and the Sombor index of that graph by considering the <span><math><mi>M</mi></math></span>-polynomial of the graph.</div></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"6 ","pages":"Article 100161"},"PeriodicalIF":0.0,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142438424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the extension of quadrant dependence 关于象限依存性的扩展

Examples and Counterexamples Pub Date : 2024-06-01 Epub Date: 2024-06-04 DOI: 10.1016/j.exco.2024.100146

João Lita da Silva

引用次数: 0

A note on non-supercyclic vectors of Hilbert space operators 关于希尔伯特空间算子的非超循环向量的说明

Examples and Counterexamples Pub Date : 2024-06-01 Epub Date: 2024-01-12 DOI: 10.1016/j.exco.2023.100131

Masoumeh Faghih-Ahmadi, Karim Hedayatian

引用次数: 0

On a convex combination of Lotka–Volterra operators 关于洛特卡-伏特拉算子的凸组合

Examples and Counterexamples Pub Date : 2024-06-01 Epub Date: 2023-12-29 DOI: 10.1016/j.exco.2023.100133

Farrukh Mukhamedov , Chin Hee Pah , Azizi Rosli

引用次数: 0

Exploration of novel analytical solutions of boundary layer equation via the modified sumudu transform 通过修正的苏木杜变换探索边界层方程的新型解析解

Examples and Counterexamples Pub Date : 2024-06-01 Epub Date: 2024-02-04 DOI: 10.1016/j.exco.2024.100140

Shailesh A. Bhanotar

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引用次数: 0

New examples of self-dual near-extremal ternary codes of length 48 derived from 2-(47,23,11) designs 从 2-(47,23,11) 设计衍生出长度为 48 的自双近极三元码的新实例

Examples and Counterexamples Pub Date : 2024-06-01 Epub Date: 2023-12-15 DOI: 10.1016/j.exco.2023.100130

Sanja Rukavina , Vladimir D. Tonchev

引用次数: 0