Pub Date : 2025-01-07DOI: 10.1016/j.amc.2024.129270
Ruixiao Jing, Yuefang Sun
<div><div>Let <em>D</em> be a digraph of order <span><math><mi>n</mi><mo>≥</mo><mi>l</mi><mo>+</mo><mn>1</mn></math></span>, where <em>l</em> is a positive integer. Let <em>S</em>=<span><math><mo>{</mo><mi>s</mi><mo>}</mo></math></span> and <em>T</em>=<span><math><mo>{</mo><mi>t</mi><mo>}</mo></math></span>. A set of <em>l</em> paths <span><math><mo>{</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>l</mi></mrow></msub><mo>}</mo></math></span> of <em>D</em> is a one-to-one <em>l</em>-disjoint directed path cover (one-to-one <em>l</em>-DDPC for short) for <em>S</em> and <em>T</em>, if <span><math><msubsup><mrow><mo>⋃</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>l</mi></mrow></msubsup><mi>V</mi><mo>(</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo><mo>=</mo><mi>V</mi><mo>(</mo><mi>D</mi><mo>)</mo></math></span>, each <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> is an <span><math><mi>s</mi><mo>−</mo><mi>t</mi></math></span> path and <span><math><mi>V</mi><mo>(</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo><mo>∩</mo><mi>V</mi><mo>(</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>)</mo><mo>=</mo><mo>{</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>}</mo></math></span> for <span><math><mi>i</mi><mo>≠</mo><mi>j</mi></math></span>. If there is a one-to-one <em>l</em>-DDPC in <em>D</em> for any disjoint source set <em>S</em>=<span><math><mo>{</mo><mi>s</mi><mo>}</mo></math></span> and sink set <span><math><mi>T</mi><mo>=</mo><mo>{</mo><mi>t</mi><mo>}</mo></math></span>, then <em>D</em> is one-to-one <em>l</em>-coverable. In this paper, we study one-to-one disjoint path covers in digraphs with faulty edges.</div><div>We first consider complete digraphs. It is proved that for sufficiently large <em>n</em>, <span><math><msub><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>↔</mo></mrow></mover></mrow><mrow><mi>n</mi></mrow></msub><mo>−</mo><mi>M</mi></math></span> is one-to-one <em>l</em>-coverable if <span><math><mrow><mo>|</mo><mi>M</mi><mo>|</mo></mrow><mo>≤</mo><mrow><mo>⌊</mo><mo>(</mo><mi>n</mi><mo>−</mo><mi>l</mi><mo>−</mo><mn>3</mn><mo>)</mo><mo>/</mo><mn>2</mn><mo>⌋</mo></mrow></math></span>. Moreover, we prove that for <span><math><mrow><mo>|</mo><mi>M</mi><mo>|</mo></mrow><mo>≤</mo><mrow><mo>⌊</mo><mo>(</mo><mi>n</mi><mo>−</mo><mi>l</mi><mo>)</mo><mo>/</mo><mn>2</mn><mo>⌋</mo></mrow></math></span>, <span><math><msub><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>↔</mo></mrow></mover></mrow><mrow><mi>n</mi></mrow></msub><mo>−</mo><mi>M</mi></math></span> is <em>l</em>-ordered Hamiltonian. Also, we show that when <span><math><mi>n</mi><mo>≥</mo><mn>1600</mn><msup><mrow><mi>l</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> and <span><math><mrow><mo>|</mo><mi>M</mi><mo>|</mo></m
{"title":"One-to-one disjoint path covers in digraphs with faulty edges","authors":"Ruixiao Jing, Yuefang Sun","doi":"10.1016/j.amc.2024.129270","DOIUrl":"10.1016/j.amc.2024.129270","url":null,"abstract":"<div><div>Let <em>D</em> be a digraph of order <span><math><mi>n</mi><mo>≥</mo><mi>l</mi><mo>+</mo><mn>1</mn></math></span>, where <em>l</em> is a positive integer. Let <em>S</em>=<span><math><mo>{</mo><mi>s</mi><mo>}</mo></math></span> and <em>T</em>=<span><math><mo>{</mo><mi>t</mi><mo>}</mo></math></span>. A set of <em>l</em> paths <span><math><mo>{</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>l</mi></mrow></msub><mo>}</mo></math></span> of <em>D</em> is a one-to-one <em>l</em>-disjoint directed path cover (one-to-one <em>l</em>-DDPC for short) for <em>S</em> and <em>T</em>, if <span><math><msubsup><mrow><mo>⋃</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>l</mi></mrow></msubsup><mi>V</mi><mo>(</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo><mo>=</mo><mi>V</mi><mo>(</mo><mi>D</mi><mo>)</mo></math></span>, each <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> is an <span><math><mi>s</mi><mo>−</mo><mi>t</mi></math></span> path and <span><math><mi>V</mi><mo>(</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo><mo>∩</mo><mi>V</mi><mo>(</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>)</mo><mo>=</mo><mo>{</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>}</mo></math></span> for <span><math><mi>i</mi><mo>≠</mo><mi>j</mi></math></span>. If there is a one-to-one <em>l</em>-DDPC in <em>D</em> for any disjoint source set <em>S</em>=<span><math><mo>{</mo><mi>s</mi><mo>}</mo></math></span> and sink set <span><math><mi>T</mi><mo>=</mo><mo>{</mo><mi>t</mi><mo>}</mo></math></span>, then <em>D</em> is one-to-one <em>l</em>-coverable. In this paper, we study one-to-one disjoint path covers in digraphs with faulty edges.</div><div>We first consider complete digraphs. It is proved that for sufficiently large <em>n</em>, <span><math><msub><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>↔</mo></mrow></mover></mrow><mrow><mi>n</mi></mrow></msub><mo>−</mo><mi>M</mi></math></span> is one-to-one <em>l</em>-coverable if <span><math><mrow><mo>|</mo><mi>M</mi><mo>|</mo></mrow><mo>≤</mo><mrow><mo>⌊</mo><mo>(</mo><mi>n</mi><mo>−</mo><mi>l</mi><mo>−</mo><mn>3</mn><mo>)</mo><mo>/</mo><mn>2</mn><mo>⌋</mo></mrow></math></span>. Moreover, we prove that for <span><math><mrow><mo>|</mo><mi>M</mi><mo>|</mo></mrow><mo>≤</mo><mrow><mo>⌊</mo><mo>(</mo><mi>n</mi><mo>−</mo><mi>l</mi><mo>)</mo><mo>/</mo><mn>2</mn><mo>⌋</mo></mrow></math></span>, <span><math><msub><mrow><mover><mrow><mi>K</mi></mrow><mrow><mo>↔</mo></mrow></mover></mrow><mrow><mi>n</mi></mrow></msub><mo>−</mo><mi>M</mi></math></span> is <em>l</em>-ordered Hamiltonian. Also, we show that when <span><math><mi>n</mi><mo>≥</mo><mn>1600</mn><msup><mrow><mi>l</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> and <span><math><mrow><mo>|</mo><mi>M</mi><mo>|</mo></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}
Pub Date : 2025-01-07DOI: 10.1016/j.amc.2024.129266
Muhammad Adnan Anwar, Jorge Tiago
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 -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.
{"title":"Time-dependent strategy for improving aortic blood flow simulations with boundary control and data assimilation","authors":"Muhammad Adnan Anwar, 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}
Pub Date : 2025-01-06DOI: 10.1016/j.amc.2024.129267
Sangui Zeng, Xiulan Yang, Jianren Long
Our work is focused on discrete stochastic p-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 converge to . The main challenges addressed include handling the superlinear diffusion, nonlinear drift terms, and the nonlinear p-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 p-Laplacian Ginzburg-Landau model disturbed by superlinear Lévy noise ought to be a invariant probability measure of the discrete stochastic p-Laplacian Schrödinger model disturbed by superlinear Lévy noise.
{"title":"On discrete stochastic p-Laplacian complex-valued Ginzburg-Landau equations driven by superlinear Lévy noise","authors":"Sangui Zeng, Xiulan Yang, 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}
Pub Date : 2025-01-06DOI: 10.1016/j.amc.2024.129271
Jing Huang , Minjie Zhang
For a given graph G, the eccentricity matrix of it, written as , 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., where denotes the eccentricity of a vertex u. The eccentricity inertia index of a graph G is represented by a triple , , , where (resp., ) is the count of positive (resp., zero, negative) eigenvalues of . In this paper, for each chain graph (a graph which does not contain , or as induced subgraphs), the eccentricity inertia index of it is completely determined.
{"title":"On the eccentricity inertia indices of chain graphs","authors":"Jing Huang , 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}
Pub Date : 2025-01-03DOI: 10.1016/j.amc.2024.129265
Marcelo V. Flamarion , Efim Pelinovsky
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.
{"title":"Features of the interaction of paired solitary waves with the Cubic Vortical Whitham equation","authors":"Marcelo V. Flamarion , 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}
Pub Date : 2025-01-03DOI: 10.1016/j.amc.2024.129257
Sangeetha Rajendran, Palanivel Kaliyaperumal
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.
{"title":"Prescribed-time synchronization of hyperchaotic fuzzy stochastic PMSM model with an application to secure communications","authors":"Sangeetha Rajendran, 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}
Pub Date : 2025-01-02DOI: 10.1016/j.amc.2024.129252
Hossein Hosseinzadeh, Zeinab Sedaghatjoo
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.
{"title":"Radial boundary elements method, a new approach on using radial basis functions to solve partial differential equations, efficiently","authors":"Hossein Hosseinzadeh, 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}
Pub Date : 2024-12-31DOI: 10.1016/j.amc.2024.129256
Hongpeng Shi, Zhenli Zhao, Shuping Ma
The dissipative control problem for nonlinear discrete-time switched singular systems (NDSSSs) is investigated via a novel reduced-order observer in this paper. Firstly, based on the generalized Sylvester equations and the introduced nonlinear injection term, a novel reduced-order observer is designed for each subsystem. The designed reduced-order observer can still produce accurate full-information estimation even though the dynamics and the output of the systems both contain unknown inputs. Then, by using average dwell-time scheme and multi-Lyapunov functions, some new sufficient conditions are proposed such that the resulted closed-loop NDSSSs are regular and causal, have a unique solution, and are globally uniformly asymptotically stable with a strict -γ-dissipative. A novel relaxation technique is proposed for decoupling nonlinear inequalities involving products of multiple nonsquare unknown variables. The design procedures of reduced-order observer and controller are presented by a specific algorithm. Finally, two numerical examples and an electronic circuit example are provided to illustrate the effectiveness of the theoretical results.
{"title":"Reduced-order full information estimation observer-based dissipative control for nonlinear discrete-time switched singular systems with unknown inputs","authors":"Hongpeng Shi, Zhenli Zhao, Shuping Ma","doi":"10.1016/j.amc.2024.129256","DOIUrl":"10.1016/j.amc.2024.129256","url":null,"abstract":"<div><div>The dissipative control problem for nonlinear discrete-time switched singular systems (NDSSSs) is investigated via a novel reduced-order observer in this paper. Firstly, based on the generalized Sylvester equations and the introduced nonlinear injection term, a novel reduced-order observer is designed for each subsystem. The designed reduced-order observer can still produce accurate full-information estimation even though the dynamics and the output of the systems both contain unknown inputs. Then, by using average dwell-time scheme and multi-Lyapunov functions, some new sufficient conditions are proposed such that the resulted closed-loop NDSSSs are regular and causal, have a unique solution, and are globally uniformly asymptotically stable with a strict <span><math><mo>(</mo><mi>Q</mi><mo>,</mo><mi>S</mi><mo>,</mo><mi>V</mi><mo>)</mo></math></span>-<em>γ</em>-dissipative. A novel relaxation technique is proposed for decoupling nonlinear inequalities involving products of multiple nonsquare unknown variables. The design procedures of reduced-order observer and controller are presented by a specific algorithm. Finally, two numerical examples and an electronic circuit example are provided to illustrate the effectiveness of the theoretical results.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"493 ","pages":"Article 129256"},"PeriodicalIF":3.5,"publicationDate":"2024-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142925326","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}
Pub Date : 2024-12-30DOI: 10.1016/j.amc.2024.129251
Fangyuan Liu, Guobao Liu, Huai Liu, Shicheng Huo
This paper explores the extended dissipative analysis of integral sliding mode control in the context of singular interval type-2 (IT-2) fuzzy systems with time delays. To better align with the characteristics of type-2 fuzzy models, a suitable integral fuzzy switching surface is introduced, taking into account state-dependent input matrices. Additionally, to address conservatism resulting from time delays, the paper utilizes suitable augmented Lyapunov-Krasovskii functionals and integral inequalities based on auxiliary functions to analyze the system's extended dissipative properties. Furthermore, by leveraging membership function dependency (MFD), this article effectively addresses the premise variable mismatch issue. The paper also provides relaxed stability conditions for feedback system stability and attainability of the desired sliding surface. Finally, the inclusion of illustrative examples serves to validate the efficacy of this approach.
{"title":"Extended dissipative analysis of integral sliding mode control for singular interval type-2 fuzzy systems with time delay","authors":"Fangyuan Liu, Guobao Liu, Huai Liu, Shicheng Huo","doi":"10.1016/j.amc.2024.129251","DOIUrl":"10.1016/j.amc.2024.129251","url":null,"abstract":"<div><div>This paper explores the extended dissipative analysis of integral sliding mode control in the context of singular interval type-2 (IT-2) fuzzy systems with time delays. To better align with the characteristics of type-2 fuzzy models, a suitable integral fuzzy switching surface is introduced, taking into account state-dependent input matrices. Additionally, to address conservatism resulting from time delays, the paper utilizes suitable augmented Lyapunov-Krasovskii functionals and integral inequalities based on auxiliary functions to analyze the system's extended dissipative properties. Furthermore, by leveraging membership function dependency (MFD), this article effectively addresses the premise variable mismatch issue. The paper also provides relaxed stability conditions for feedback system stability and attainability of the desired sliding surface. Finally, the inclusion of illustrative examples serves to validate the efficacy of this approach.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"493 ","pages":"Article 129251"},"PeriodicalIF":3.5,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142925327","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}
Pub Date : 2024-12-27DOI: 10.1016/j.amc.2024.129253
Panpan Cheng, Yunshu Gao
Let G be a bipartite graph. In this paper, by constructing two extremal graphs, we completely determine the minimum number of edges of G that guaranteeing the existence of two independent chorded cycles. As a byproduct, our result also implies that G contains two independent cycles of different lengths.
{"title":"Extremal function of two independent chorded cycles in a bipartite graph","authors":"Panpan Cheng, Yunshu Gao","doi":"10.1016/j.amc.2024.129253","DOIUrl":"10.1016/j.amc.2024.129253","url":null,"abstract":"<div><div>Let <em>G</em> be a bipartite graph. In this paper, by constructing two extremal graphs, we completely determine the minimum number of edges of <em>G</em> that guaranteeing the existence of two independent chorded cycles. As a byproduct, our result also implies that <em>G</em> contains two independent cycles of different lengths.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"493 ","pages":"Article 129253"},"PeriodicalIF":3.5,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889268","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}
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