Applied Mathematics and Computation最新文献

{"title":"An algebraic algorithm for the total least squares problem in commutative quaternionic theory","authors":"Tongsong Jiang ,&nbsp;Dong Zhang ,&nbsp;Zhenwei Guo ,&nbsp;V.I. Vasil'ev","doi":"10.1016/j.amc.2024.129268","DOIUrl":"10.1016/j.amc.2024.129268","url":null,"abstract":"<div><div>A commutative quaternion total least squares (CQTLS) problem is a method of solving overdetermined sets of linear equations <span><math><mi>A</mi><mi>X</mi><mo>≈</mo><mi>B</mi></math></span> with errors in the matrices <em>A</em> and <em>B</em>. In the theoretical studies and numerical calculations of commutative quaternionic theory, the CQTLS problem is an extremely effective tool for the study of telecommunications, geodesy, and image processing theory. This paper, by means of the real representation of a commutative quaternion matrix, studies the CQTLS problem, derives necessary and sufficient conditions for the CQTLS problem has a commutative quaternion solution, and gives an algebraic algorithm for solving the CQTLS problem.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"494 ","pages":"Article 129268"},"PeriodicalIF":3.5,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142968140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A learning-based sliding mode control for switching systems with dead zone","authors":"Bo Wang ,&nbsp;Fucheng Zou ,&nbsp;Junhui Wu ,&nbsp;Jun Cheng","doi":"10.1016/j.amc.2025.129283","DOIUrl":"10.1016/j.amc.2025.129283","url":null,"abstract":"<div><div>This paper focuses on the problem of adaptive neural network sliding mode control for switching systems affected by dead zones. Distinct from existing rules defined by transition and sojourn probabilities, a broader switching rule is proposed based on duration-time-dependent sojourn probabilities. A neural network strategy for compensation is implemented to mitigate the effects of the dead zone. Moreover, a sliding mode control law incorporating a learning term is designed, effectively reducing chattering compared to conventional sliding mode control. Employing a stochastic Lyapunov function grounded in the joint distribution of duration time and system mode, sufficient criteria for designing the adaptive neural network-based controller are established. Finally, the effectiveness of the proposed method is demonstrated through two simulated examples.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"494 ","pages":"Article 129283"},"PeriodicalIF":3.5,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142968139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Branch points of homotopies: Distribution and probability of failure","authors":"Jonathan D. Hauenstein ,&nbsp;Caroline Hills ,&nbsp;Andrew J. Sommese,&nbsp;Charles W. Wampler","doi":"10.1016/j.amc.2024.129273","DOIUrl":"10.1016/j.amc.2024.129273","url":null,"abstract":"<div><div>Homotopy continuation is a standard method used in numerical algebraic geometry for solving multivariate systems of polynomial equations. Techniques such as the so-called gamma trick yield trackable homotopies with probability one. However, since numerical algebraic geometry employs numerical path tracking methods, being close to a branch point may cause concern with finite precision computations. This paper provides a systematic study of branch points of homotopies to elucidate how branch points are distributed and use this information to study the probability of failure when using finite precision. Several examples, including a system arising in kinematics, with various start systems are included to demonstrate the theoretical analysis.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"493 ","pages":"Article 129273"},"PeriodicalIF":3.5,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142968141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"One-to-one disjoint path covers in digraphs with faulty edges","authors":"Ruixiao Jing,&nbsp;Yuefang Sun","doi":"10.1016/j.amc.2024.129270","DOIUrl":"10.1016/j.amc.2024.129270","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Let &lt;em&gt;D&lt;/em&gt; be a digraph of order &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;em&gt;l&lt;/em&gt; is a positive integer. Let &lt;em&gt;S&lt;/em&gt;=&lt;span&gt;&lt;math&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and &lt;em&gt;T&lt;/em&gt;=&lt;span&gt;&lt;math&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. A set of &lt;em&gt;l&lt;/em&gt; paths &lt;span&gt;&lt;math&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;…&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; of &lt;em&gt;D&lt;/em&gt; is a one-to-one &lt;em&gt;l&lt;/em&gt;-disjoint directed path cover (one-to-one &lt;em&gt;l&lt;/em&gt;-DDPC for short) for &lt;em&gt;S&lt;/em&gt; and &lt;em&gt;T&lt;/em&gt;, if &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;⋃&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, each &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is an &lt;span&gt;&lt;math&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; path and &lt;span&gt;&lt;math&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∩&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; for &lt;span&gt;&lt;math&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;≠&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. If there is a one-to-one &lt;em&gt;l&lt;/em&gt;-DDPC in &lt;em&gt;D&lt;/em&gt; for any disjoint source set &lt;em&gt;S&lt;/em&gt;=&lt;span&gt;&lt;math&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and sink set &lt;span&gt;&lt;math&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, then &lt;em&gt;D&lt;/em&gt; is one-to-one &lt;em&gt;l&lt;/em&gt;-coverable. In this paper, we study one-to-one disjoint path covers in digraphs with faulty edges.&lt;/div&gt;&lt;div&gt;We first consider complete digraphs. It is proved that for sufficiently large &lt;em&gt;n&lt;/em&gt;, &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;↔&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is one-to-one &lt;em&gt;l&lt;/em&gt;-coverable if &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;⌊&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;⌋&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. Moreover, we prove that for &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;⌊&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;⌋&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;↔&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is &lt;em&gt;l&lt;/em&gt;-ordered Hamiltonian. Also, we show that when &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;1600&lt;/mn&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/m","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"493 ","pages":"Article 129270"},"PeriodicalIF":3.5,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142968142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Time-dependent strategy for improving aortic blood flow simulations with boundary control and data assimilation","authors":"Muhammad Adnan Anwar,&nbsp;Jorge Tiago","doi":"10.1016/j.amc.2024.129266","DOIUrl":"10.1016/j.amc.2024.129266","url":null,"abstract":"<div><div>Understanding time-dependent blood flow dynamics in arteries is crucial for diagnosing and treating cardiovascular diseases. However, accurately predicting time-varying flow patterns requires integrating observational data with computational models in a dynamic environment. This study investigates the application of data assimilation and boundary optimization techniques to improve the accuracy of time-dependent blood flow simulations. We propose an integrated approach that combines data assimilation methods with boundary optimization strategies tailored for time-dependent cases. Our method aims to minimize the disparity between model predictions and observed data over time, thereby enhancing the fidelity of time-dependent blood flow simulations. Using synthetic time-series observational data with added noise, we validate our approach by comparing its predictions with the known exact solution, computing the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm to demonstrate improved accuracy in time-dependent blood flow simulations. Our results indicate that the optimization process consistently aligns the optimized data with the exact data. In particular, velocity magnitudes showed reduced discrepancies compared to the noisy data, aligning more closely with the exact solutions. The analysis of pressure data revealed a remarkable correspondence between the optimized and exact pressure values, highlighting the potential of this methodology for accurate pressure estimation without any previous knowledge on this quantity. Furthermore, wall shear stress (WSS) analysis demonstrated the effectiveness of our optimization scheme in reducing noise and improving prediction of a relevant indicator determined at the postprocessing level. These findings suggest that our approach can significantly enhance the accuracy of blood flow simulations, ultimately contributing to better diagnostic and therapeutic strategies.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"493 ","pages":"Article 129266"},"PeriodicalIF":3.5,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142968143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On discrete stochastic p-Laplacian complex-valued Ginzburg-Landau equations driven by superlinear Lévy noise","authors":"Sangui Zeng,&nbsp;Xiulan Yang,&nbsp;Jianren Long","doi":"10.1016/j.amc.2024.129267","DOIUrl":"10.1016/j.amc.2024.129267","url":null,"abstract":"<div><div>Our work is focused on discrete stochastic <em>p</em>-Laplacian complex-valued Ginzburg-Landau equations influenced by superlinear Lévy noise, under the assumption that the drift and diffusion terms satisfy local Lipschitz continuity. We begin by demonstrating the existence and uniqueness of solutions, as well as the weak pullback mean random attractors of the system. Following this, we demonstrate the existence of invariant probability measures and explore their limit properties as the parameters <span><math><mo>(</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mi>ε</mi><mo>,</mo><mover><mrow><mi>ε</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>)</mo></math></span> converge to <span><math><mo>(</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>ε</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mover><mrow><mi>ε</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo><mo>×</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo><mo>×</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>. The main challenges addressed include handling the superlinear diffusion, nonlinear drift terms, and the nonlinear <em>p</em>-Laplacian operator, as well as establishing the tightness of the distribution law for the solution family and corresponding invariant probability measures. To find solutions to these challenges, we use the strategy of stopping times and uniform tail-end bounds. Finally, it should be noted that each limit of a sequence of invariant probability measures of discrete stochastic <em>p</em>-Laplacian Ginzburg-Landau model disturbed by superlinear Lévy noise ought to be a invariant probability measure of the discrete stochastic <em>p</em>-Laplacian Schrödinger model disturbed by superlinear Lévy noise.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"493 ","pages":"Article 129267"},"PeriodicalIF":3.5,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142968146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the eccentricity inertia indices of chain graphs","authors":"Jing Huang ,&nbsp;Minjie Zhang","doi":"10.1016/j.amc.2024.129271","DOIUrl":"10.1016/j.amc.2024.129271","url":null,"abstract":"<div><div>For a given graph <em>G</em>, the eccentricity matrix of it, written as <span><math><mi>ε</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>, is created by retaining the largest non-zero entries for each row and column of the distance matrix, while filling the rest with zeros, i.e.,<span><span><span><math><mi>ε</mi><msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mrow><mi>u</mi><mi>v</mi></mrow></msub><mo>=</mo><mrow><mo>{</mo><mtable><mtr><mtd><mi>d</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo><mo>,</mo><mspace></mspace></mtd><mtd><mtext>if</mtext><mspace></mspace><mi>d</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo><mo>=</mo><mi>min</mi><mo>⁡</mo><mo>{</mo><mi>ε</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>,</mo><mi>ε</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>}</mo><mo>,</mo></mtd></mtr><mtr><mtd><mn>0</mn><mo>,</mo><mspace></mspace></mtd><mtd><mtext>otherwise</mtext><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> where <span><math><mi>ε</mi><mo>(</mo><mi>u</mi><mo>)</mo></math></span> denotes the eccentricity of a vertex <em>u</em>. The eccentricity inertia index of a graph <em>G</em> is represented by a triple <span><math><mo>(</mo><msub><mrow><mi>n</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>(</mo><mi>ε</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>)</mo></math></span>, <span><math><msub><mrow><mi>n</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>ε</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>)</mo></math></span>, <span><math><msub><mrow><mi>n</mi></mrow><mrow><mo>−</mo></mrow></msub><mo>(</mo><mi>ε</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>)</mo><mo>)</mo></math></span>, where <span><math><msub><mrow><mi>n</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>(</mo><mi>ε</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>)</mo></math></span> (resp., <span><math><msub><mrow><mi>n</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>ε</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>)</mo><mo>,</mo><msub><mrow><mi>n</mi></mrow><mrow><mo>−</mo></mrow></msub><mo>(</mo><mi>ε</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>)</mo></math></span>) is the count of positive (resp., zero, negative) eigenvalues of <span><math><mi>ε</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. In this paper, for each chain graph (a graph which does not contain <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>5</mn></mrow></msub></math></span>, or <span><math><mn>2</mn><msub><mrow><mi>K</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> as induced subgraphs), the eccentricity inertia index of it is completely determined.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"493 ","pages":"Article 129271"},"PeriodicalIF":3.5,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142968147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Features of the interaction of paired solitary waves with the Cubic Vortical Whitham equation","authors":"Marcelo V. Flamarion ,&nbsp;Efim Pelinovsky","doi":"10.1016/j.amc.2024.129265","DOIUrl":"10.1016/j.amc.2024.129265","url":null,"abstract":"<div><div>In this article, we consider the cubic vortical Whitham equation with both positive and negative nonlinearity to investigate overtaking solitary wave collisions. We compute solitary waves numerically, including “thick” solitary waves. Our results show that in both cases, the geometric Lax categorization holds, however, it is independent of the magnitude of the amplitude of the solitary waves. Besides, for negative cubic nonlinearity, we compute thick solitary waves and investigate their paired interactions. Moreover, we show that Gardner solitons and CV-Whitham solitary waves have nearly the same shape and speed when the sign of cubic nonlinearity term is negative.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"493 ","pages":"Article 129265"},"PeriodicalIF":3.5,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142925324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Prescribed-time synchronization of hyperchaotic fuzzy stochastic PMSM model with an application to secure communications","authors":"Sangeetha Rajendran,&nbsp;Palanivel Kaliyaperumal","doi":"10.1016/j.amc.2024.129257","DOIUrl":"10.1016/j.amc.2024.129257","url":null,"abstract":"<div><div>This study addresses the synchronization problem of grid-connected permanent magnet synchronous motors (PMSMs)-based wind energy conversion systems (WECSs). This study significantly enhances the existing WECSs into the four-dimensional hyperchaotic grid-connected WECSs by integrating the impact of a DC-link capacitor. Moreover, this study treats the aerodynamics of WECSs as stochastic differential equations (SDEs), taking into account the random nature of wind-speed characteristics. Further, the nonlinearities in WECSs are approximated to linear form through Takagi-Sugeno (T–S) fuzzy with the help of IF-THEN membership rules. Each IF-THEN membership rule represents a local linear model valid around specific operating bounds. Moreover, this study considers an adaptive continuous feedback controller scheme to ensure the fixed-time synchronization between WECSs with and without control input. This study utilizes mathematical techniques such as Lyapunov stability theory and Ito's calculus theory to derive the analytical settling-time (ST) expression. This expression aids in identifying the time frame that ensures the convergence of the error model. As an application, this study designs an encryption and decryption algorithm by utilizing the hyperchaotic WECSs as a cryptosystem that may outperform the existing algorithms proposed for secure communications.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"493 ","pages":"Article 129257"},"PeriodicalIF":3.5,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142925323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Radial boundary elements method, a new approach on using radial basis functions to solve partial differential equations, efficiently","authors":"Hossein Hosseinzadeh,&nbsp;Zeinab Sedaghatjoo","doi":"10.1016/j.amc.2024.129252","DOIUrl":"10.1016/j.amc.2024.129252","url":null,"abstract":"<div><div>Conventionally, piecewise polynomials have been used in the boundary element method (BEM) to approximate unknown boundary values. However, since infinitely smooth radial basis functions (RBFs) are more stable and accurate than the polynomials for high dimensional domains, this paper proposes approximating the unknown values using RBFs. This new formulation is called the radial BEM. To calculate the singular boundary integrals in the radial BEM, the authors propose a new distribution of boundary source points that removes the singularity from the integrals. This allows the boundary integrals to be precisely calculated using the standard Gaussian quadrature rule with 16 quadrature nodes. Several numerical examples are presented to evaluate the efficiency of the radial BEM compared to standard BEM and RBF collocation method for solving partial differential equations (PDEs). The analytical and numerical studies demonstrate that the radial BEM is a superior version of BEM that will significantly enhance the application of BEM and RBFs in solving PDEs.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"493 ","pages":"Article 129252"},"PeriodicalIF":3.5,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142925325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}