Examples and Counterexamples最新文献_第3页

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 : 2024-10-23 DOI: 10.1016/j.exco.2024.100165

Alfredo Canelas, Ana I. Abreu

引用次数: 0

Small examples of mosaics of combinatorial designs 组合设计马赛克小实例

Examples and Counterexamples Pub Date : 2024-10-16 DOI: 10.1016/j.exco.2024.100163

Vedran Krčadinac

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 : 2024-10-15 DOI: 10.1016/j.exco.2024.100164

Ting-Han Pei

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Counting graphs induced by Gauss diagrams and families of mutant alternating knots 高斯图诱导的计数图和突变交替结族

Examples and Counterexamples Pub Date : 2024-10-11 DOI: 10.1016/j.exco.2024.100162

Alexei Lisitsa , Alexei Vernitski

引用次数: 0

An advection–diffusion equation with a generalized advection term: Well-posedness analysis and examples 带有广义平流项的平流扩散方程：拟合优度分析与实例

Examples and Counterexamples Pub Date : 2024-10-08 DOI: 10.1016/j.exco.2024.100159

Tetyana Malysheva , Luther W. White

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 : 2024-10-05 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":"2024-10-05","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

Exact solution of a mathematical model for human muscular motion 人体肌肉运动数学模型的精确解法

Examples and Counterexamples Pub Date : 2024-10-02 DOI: 10.1016/j.exco.2024.100160

Motlatsi Molati

引用次数: 0

On Sombor index and graph energy of some chemically important graphs 论一些重要化学图的松博指数和图能

Examples and Counterexamples Pub Date : 2024-09-27 DOI: 10.1016/j.exco.2024.100158

Md Selim Reja, Sk. Md. Abu Nayeem

{"title":"On Sombor index and graph energy of some chemically important graphs","authors":"Md Selim Reja, Sk. Md. Abu Nayeem","doi":"10.1016/j.exco.2024.100158","DOIUrl":"10.1016/j.exco.2024.100158","url":null,"abstract":"<div><div>Sombor index of a graph <span><math><mrow><mi>G</mi><mo>=</mo><mrow><mo>(</mo><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>,</mo><mi>E</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span> is provided by the expression <span><math><mrow><msub><mrow><mo>∑</mo></mrow><mrow><mi>u</mi><mi>v</mi><mo>∈</mo><mi>E</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></msub><msqrt><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>d</mi></mrow><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></msqrt></mrow></math></span>, where <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>x</mi></mrow></msub></math></span> is the degree of the vertex <span><math><mrow><mi>x</mi><mo>∈</mo><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>. The energy of a graph is the quantity given by the total of the absolute values of its adjacency matrix’s eigenvalues. In this article, we improve the relation between the Sombor index and graph energy and derive the relation between them for unicyclic, bicyclic and tricyclic graphs, trees, triangular chain, square cactus chain and hexagonal cactus chain graphs. At last, we find the bounds of graph energy for zigzag and linear hexagonal chains.</div></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"6 ","pages":"Article 100158"},"PeriodicalIF":0.0,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142356888","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

Optimal boundary control in a micromixer 微搅拌器中的最佳边界控制

Examples and Counterexamples Pub Date : 2024-09-19 DOI: 10.1016/j.exco.2024.100156

Manuel Wegmann , Julius Jeßberger , Gudrun Thäter , Mathias J. Krause

引用次数: 0

Comparison of different elastic strain definitions for largely deformed SEI of chemo-mechanically coupled silicon battery particles 化学机械耦合硅电池颗粒大变形 SEI 不同弹性应变定义的比较

Examples and Counterexamples Pub Date : 2024-09-13 DOI: 10.1016/j.exco.2024.100157

R. Schoof , G.F. Castelli , W. Dörfler

{"title":"Comparison of different elastic strain definitions for largely deformed SEI of chemo-mechanically coupled silicon battery particles","authors":"R. Schoof , G.F. Castelli , W. Dörfler","doi":"10.1016/j.exco.2024.100157","DOIUrl":"10.1016/j.exco.2024.100157","url":null,"abstract":"<div><p>Amorphous silicon is a highly promising anode material for next-generation lithium-ion batteries. Large volume changes of the silicon particle have a critical effect on the surrounding solid-electrolyte interphase (SEI) due to repeated fracture and healing during cycling. Based on a thermodynamically consistent chemo-elasto-plastic continuum model we investigate the stress development inside the particle and the SEI. Using the example of a particle with SEI, we apply a higher order finite element method together with a variable-step, variable-order time integration scheme on a nonlinear system of partial differential equations. Starting from a single silicon particle setting, the surrounding SEI is added in a first step with the typically used elastic Green–St-Venant (GSV) strain definition for a purely elastic deformation. For this type of deformation, the definition of the elastic strain is crucial to get reasonable simulation results. In case of the elastic GSV strain, the simulation aborts. We overcome the simulation failure by using the definition of the logarithmic Hencky strain. However, the particle remains unaffected by the elastic strain definitions in the particle domain. Compared to GSV, plastic deformation with the Hencky strain is straightforward to take into account. For the plastic SEI deformation, a rate-independent and a rate-dependent plastic deformation are newly introduced and numerically compared for three half cycles for the example of a radial symmetric particle.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"6 ","pages":"Article 100157"},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X24000235/pdfft?md5=eb47ebf0227fdbfbf64434e6a7ff02b1&pid=1-s2.0-S2666657X24000235-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142228535","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