Applied Mathematics and Computation最新文献

{"title":"Lyapunov-like conditions for prescribed-time stability of perturbed impulsive systems","authors":"Arnab Mapui,&nbsp;Santwana Mukhopadhyay","doi":"10.1016/j.amc.2024.129187","DOIUrl":"10.1016/j.amc.2024.129187","url":null,"abstract":"<div><div>The present work deals with the problem of prescribed-time control of non-linear impulsive systems consisting of external perturbations. Lyapunov-like sufficient conditions for prescribed-time and practical prescribed-time stability are provided for vanishing and non-vanishing perturbations, respectively. Depending on the user's requirements, some sequences of stabilizing impulses are constructed in this regard. It is shown that the systems consisting of vanishing-type disturbances can attain prescribed-time stabilization at the origin. On the other hand, in the presence of non-vanishing disturbances, which can consist of bounded or <strong><em>unbounded</em></strong> disturbances, the trajectories of the system can enter a stable region only within the prescribed time. Moreover, the stable region is independent of the impulsive strength and the prescribed-time. The efficacy of the proposed results is provided through various examples and their numerical simulations.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"490 ","pages":"Article 129187"},"PeriodicalIF":3.5,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696447","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":"2-Edge Hamiltonian connectedness: Characterization and results in data center networks","authors":"Mei-Li Wang ,&nbsp;Rong-Xia Hao ,&nbsp;Jou-Ming Chang ,&nbsp;Sejeong Bang","doi":"10.1016/j.amc.2024.129197","DOIUrl":"10.1016/j.amc.2024.129197","url":null,"abstract":"<div><div>A graph <em>G</em> is 2-edge Hamiltonian connected if for any edge set <span><math><mi>E</mi><mo>⊆</mo><mo>{</mo><mi>u</mi><mi>v</mi><mo>:</mo><mspace></mspace><mi>u</mi><mo>,</mo><mi>v</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>,</mo><mi>u</mi><mo>≠</mo><mi>v</mi><mo>}</mo></math></span> with <span><math><mo>|</mo><mi>E</mi><mo>|</mo><mo>≤</mo><mn>2</mn></math></span>, <span><math><mi>G</mi><mo>∪</mo><mi>E</mi></math></span> has a Hamiltonian cycle containing all edges of <span><math><mi>E</mi></math></span>, where <span><math><mi>G</mi><mo>∪</mo><mi>E</mi></math></span> is the graph obtained from <em>G</em> by including all edges of <span><math><mi>E</mi></math></span>. The problem of determining whether a graph is 2-edge Hamiltonian connected is challenging, as it is known to be NP-complete. This property is stronger than Hamiltonian connectedness, which indicates the existence of a Hamiltonian path between every pair of vertices in a graph. This paper first provides a characterization and a sufficiency for 2-edge Hamiltonian connectedness. Through this, we shed light on the fact that many well-known networks are 2-edge Hamiltonian connected, including BCube data center networks and some variations of hypercubes, and so on. Additionally, we demonstrate that DCell data center networks and Cartesian product graphs containing almost all generalized hypercubes are 2-edge Hamiltonian connected.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"490 ","pages":"Article 129197"},"PeriodicalIF":3.5,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696446","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 conjecture on Boros-Moll polynomials due to Ma, Qi, Yeh and Yeh","authors":"Donna Quanjie Dou ,&nbsp;Lisa Hui Sun","doi":"10.1016/j.amc.2024.129186","DOIUrl":"10.1016/j.amc.2024.129186","url":null,"abstract":"<div><div>Gamma-positivity is one of the basic properties that may be possessed by polynomials with symmetric coefficients, which directly implies that they are unimodal. It originates from the study of Eulerian polynomials by Foata and Schützenberger. Then, the alternatingly gamma-positivity for symmetric polynomials was defined by Sagan and Tirrell. Later, Ma et al. further introduced the notions of <em>bi-gamma-positive</em> and <em>alternatingly bi-gamma-positive</em> for a polynomial <span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> which correspond to that both of the polynomials in the symmetric decomposition of <span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> are gamma-positive and alternatingly gamma-positive, respectively. In this paper we establish the alternatingly bi-gamma-positivity of the Boros–Moll polynomials by verifying both polynomials in the symmetric decomposition of their reciprocals are unimodal and alternatingly gamma-positive. It confirms a conjecture proposed by Ma, Qi, Yeh and Yeh.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"490 ","pages":"Article 129186"},"PeriodicalIF":3.5,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696448","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 least eigenvalue of genuine strongly 3-walk-regular graphs","authors":"Jiahao Zhang ,&nbsp;Changxiang He ,&nbsp;Rongquan Feng","doi":"10.1016/j.amc.2024.129202","DOIUrl":"10.1016/j.amc.2024.129202","url":null,"abstract":"<div><div>As a generalization of strongly regular graphs, van Dam and Omidi <span><span>[8]</span></span> introduced the concept of strongly walk-regular graphs. A graph is called strongly <em>ℓ</em>-walk-regular if the number of walks of length <em>ℓ</em> from a vertex to another vertex depends only on whether the two vertices are adjacent, not adjacent, or identical. They proved that this class of graphs falls into several subclasses including connected regular graphs with four eigenvalues, which are called genuine strongly <em>ℓ</em>-walk-regular. In this paper, we prove that the least eigenvalue of a connected genuine strongly 3-walk-regular graph is no more than −2 and characterize all graphs reaching this upper bound.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"490 ","pages":"Article 129202"},"PeriodicalIF":3.5,"publicationDate":"2024-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696451","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":"Extremizing antiregular graphs by modifying total σ-irregularity","authors":"Martin Knor ,&nbsp;Riste Škrekovski ,&nbsp;Slobodan Filipovski ,&nbsp;Darko Dimitrov","doi":"10.1016/j.amc.2024.129199","DOIUrl":"10.1016/j.amc.2024.129199","url":null,"abstract":"<div><div>The total <em>σ</em>-irregularity is given by <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><msub><mrow><mo>∑</mo></mrow><mrow><mo>{</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>}</mo><mo>⊆</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></msub><msup><mrow><mo>(</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>u</mi><mo>)</mo><mo>−</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>v</mi><mo>)</mo><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span>, where <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></span> indicates the degree of a vertex <em>z</em> within the graph <em>G</em>. It is known that the graphs maximizing <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span>-irregularity are split graphs with only a few distinct degrees. Since one might typically expect that graphs with as many distinct degrees as possible achieve maximum irregularity measures, we modify this invariant to <span><math><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>t</mi></mrow><mrow><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msubsup><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><msub><mrow><mo>∑</mo></mrow><mrow><mo>{</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>}</mo><mo>⊆</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></msub><mo>|</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>u</mi><mo>)</mo><mo>−</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>v</mi><mo>)</mo><msup><mrow><mo>|</mo></mrow><mrow><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msup></math></span>, where <span><math><mi>n</mi><mo>=</mo><mo>|</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>|</mo></math></span> and <span><math><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>&gt;</mo><mn>0</mn></math></span>. We study under what conditions the above modification obtains its maximum for antiregular graphs. We consider general graphs, trees, and chemical graphs, and accompany our results with a few problems and conjectures.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"490 ","pages":"Article 129199"},"PeriodicalIF":3.5,"publicationDate":"2024-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696454","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":"Bounds for the incidence Q-spectral radius of uniform hypergraphs","authors":"Peng-Li Zhang ,&nbsp;Xiao-Dong Zhang","doi":"10.1016/j.amc.2024.129201","DOIUrl":"10.1016/j.amc.2024.129201","url":null,"abstract":"<div><div>The incidence <span><math><mi>Q</mi></math></span>-spectral radius of a <em>k</em>-uniform hypergraph <em>G</em> with <em>n</em> vertices and <em>m</em> edges is defined as the spectral radius of the incidence <span><math><mi>Q</mi></math></span>-tensor <span><math><msup><mrow><mi>Q</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>:</mo><mo>=</mo><mi>R</mi><mi>I</mi><msup><mrow><mi>R</mi></mrow><mrow><mi>T</mi></mrow></msup></math></span>, where <em>R</em> is the incidence matrix of <em>G</em>, and <span><math><mi>I</mi></math></span> is an order <em>k</em> dimension <em>m</em> identity tensor. Since the <span><math><mo>(</mo><msub><mrow><mi>i</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>i</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>i</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo></math></span>-entry of <span><math><msup><mrow><mi>Q</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> is involved in the number of edges in <em>G</em> containing vertices <span><math><msub><mrow><mi>i</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>i</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>i</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> simultaneously, more structural properties of <em>G</em> from the entry of <span><math><msup><mrow><mi>Q</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> than other commonly used tensors associated with hypergraphs may be discovered. In this paper, we present several bounds on the incidence <span><math><mi>Q</mi></math></span>-spectral radius of <em>G</em> in terms of degree sequences, which are better than some known results in some cases.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"490 ","pages":"Article 129201"},"PeriodicalIF":3.5,"publicationDate":"2024-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696453","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":"Fault tolerance assessment for hamming graphs based on r-restricted R-structure(substructure) fault pattern","authors":"Yayu Yang,&nbsp;Mingzu Zhang,&nbsp;Jixiang Meng","doi":"10.1016/j.amc.2024.129160","DOIUrl":"10.1016/j.amc.2024.129160","url":null,"abstract":"&lt;div&gt;&lt;div&gt;The interconnection network between the storage system and the multi-core computing system is the bridge for communication of enormous amounts of data access and storage, which is the critical factor in affecting the performance of high-performance computing systems. By enforcing additional restrictions on the definition of &lt;em&gt;R&lt;/em&gt;-structure and &lt;em&gt;R&lt;/em&gt;-substructure connectivities to satisfy that each remaining vertex has not less than &lt;em&gt;r&lt;/em&gt; neighbors, we can dynamically assess the cardinality of the separated component to meet the above conditions under structure faulty, thereby enhancing the evaluation of the fault tolerance and reliability of high-performance computing systems. Let &lt;em&gt;R&lt;/em&gt; be a connected subgraph of a connected graph &lt;em&gt;G&lt;/em&gt;. The &lt;em&gt;r&lt;/em&gt;-restricted &lt;em&gt;R&lt;/em&gt;-structure connectivity &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;κ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;;&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; (resp. &lt;em&gt;r&lt;/em&gt;-restricted &lt;em&gt;R&lt;/em&gt;-substructure connectivity &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;κ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;;&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;) of &lt;em&gt;G&lt;/em&gt; is the minimum cardinality of a set of subgraphs &lt;span&gt;&lt;math&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;F&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;F&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;F&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; such that &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;F&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 isomorphic to &lt;em&gt;R&lt;/em&gt; (resp. &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;F&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 a connected subgraph of &lt;em&gt;R&lt;/em&gt;) for &lt;span&gt;&lt;math&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, and &lt;span&gt;&lt;math&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is disconnected with the minimum degree of each component being at least &lt;em&gt;r&lt;/em&gt;. Note that &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;κ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;;&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;K&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;/math&gt;&lt;/span&gt; reduces to &lt;em&gt;r&lt;/em&gt;-restricted connectivity &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;κ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; (also called &lt;em&gt;r&lt;/em&gt;-good neighbor connectivity). In this paper, we focus on &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;κ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;;&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;κ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;;&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; for the &lt;em&gt;L&lt;/em&gt;-ary &lt;em&gt;n&lt;/em&gt;-dimensional hamming graph ","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"489 ","pages":"Article 129160"},"PeriodicalIF":3.5,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142661265","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":"Event-triggered approximately optimized formation control of multi-agent systems with unknown disturbances via simplified reinforcement learning","authors":"Yang Yang ,&nbsp;Shuocong Geng ,&nbsp;Dong Yue ,&nbsp;Sergey Gorbachev ,&nbsp;Iakov Korovin","doi":"10.1016/j.amc.2024.129149","DOIUrl":"10.1016/j.amc.2024.129149","url":null,"abstract":"<div><div>An event-triggered formation control strategy is proposed for a multi-agent system (MAS) suffered from unknown disturbances. In identifier-critic-actor neural networks (NNs), the strategy only needs to calculate the negative gradient of an approximated Hamilton-Jacobi-Bellman (HJB) equation, instead of the gradient descent method associated with Bellman residual errors. This simplified method removes the requirement for a complicated gradient calculation process of residual square of HJB equation. The weights in critic-actor NNs only update as the triggered condition is violated, and the computational burdens caused by frequent updates are thus reduced. Without dynamics information in prior, a disturbance observer is also constructed to approximate disturbances in an MAS. From stability analysis, it is proven that all signals are bounded. Two numerical examples are illustrated to verify that the proposed control strategy is effective.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"489 ","pages":"Article 129149"},"PeriodicalIF":3.5,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142661266","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":"Fuzzy discrete fractional granular calculus and its application to fractional cobweb models","authors":"Xuelong Liu,&nbsp;Guoju Ye,&nbsp;Wei Liu,&nbsp;Fangfang Shi","doi":"10.1016/j.amc.2024.129176","DOIUrl":"10.1016/j.amc.2024.129176","url":null,"abstract":"<div><div>This work aims to solve a fuzzy initial value problem for fractional difference equations and to study a class of discrete fractional cobweb models with fuzzy data under the Caputo granular difference operator. Based on relative-distance-measure fuzzy interval arithmetic, we first present several new concepts for fuzzy functions in the field of fuzzy discrete fractional calculus, such as the forward granular difference operator, Riemann-Liouville fractional granular sum, Riemann-Liouville and Caputo granular differences. The composition rules and Leibniz laws used to solve a fuzzy initial value problem for fractional difference equations are also presented. As applications, we obtain the solutions of fuzzy discrete Caputo fractional cobweb models, provide conditions for the convergence of the solution to the equilibrium value, and discuss different cases of how the trajectory of the granular solution converges to the equilibrium value. The developed results are also illustrated through several numerical examples.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"489 ","pages":"Article 129176"},"PeriodicalIF":3.5,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142661263","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":"Nonlinear MIMO observable normal forms with output injection and output diffeomorphism","authors":"Jie Liu ,&nbsp;Driss Boutat ,&nbsp;Da-Yan Liu ,&nbsp;Xue-Feng Zhang","doi":"10.1016/j.amc.2024.129174","DOIUrl":"10.1016/j.amc.2024.129174","url":null,"abstract":"<div><div>This research note establishes a specific framework for transforming nonlinear multi-input and multi-output diffeomorphism systems into extended observable normal forms without using differential geometry techniques. For this purpose, the nonlinear MIMO systems whose nonlinear terms do not need to be Lipschitz, are proposed. First, a change of coordinates is designed to eliminate the square items and coupled items for each nonlinear dynamical subsystem. Second, coupled auxiliary dynamics are constructed to transform the nonlinear multi-input and multi-output diffeomorphism systems into extended observable normal forms such that the finite-time and robust step-by-step sliding mode observer can be applied. Then, the state variables for the considered nonlinear dynamical systems are estimated by using the inverse of the transformations. Finally, the validity of the proposed design methods is verified by two numerical examples.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"489 ","pages":"Article 129174"},"PeriodicalIF":3.5,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142661264","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}