Pub Date : 2025-01-23DOI: 10.1016/j.amc.2025.129306
K.R. Arun, A. Krishnamurthy, H. Maharna
In this work, we design and analyze an asymptotic preserving (AP), semi-implicit finite volume scheme for the scaled compressible isentropic Euler system with a singular pressure law known as the congestion pressure law. The congestion pressure law imposes a maximal density constraint of the form 0≤ϱ<1, and the scaling introduces a small parameter ε in order to control the stiffness of the density constraint. As ε→0, the solutions of the compressible system converge to solutions of the so-called free-congested Euler equations that couples compressible and incompressible dynamics. We show that the proposed scheme is positivity preserving and energy stable. In addition, we also show that the numerical densities satisfy a discrete variant of the constraint. By means of extensive numerical case studies, we verify the efficacy of the scheme and show that the scheme is able to capture the two dynamics in the limiting regime, thereby proving the AP property.
{"title":"An asymptotic preserving and energy stable scheme for the Euler system with congestion constraint","authors":"K.R. Arun, A. Krishnamurthy, H. Maharna","doi":"10.1016/j.amc.2025.129306","DOIUrl":"https://doi.org/10.1016/j.amc.2025.129306","url":null,"abstract":"In this work, we design and analyze an asymptotic preserving (AP), semi-implicit finite volume scheme for the scaled compressible isentropic Euler system with a singular pressure law known as the congestion pressure law. The congestion pressure law imposes a maximal density constraint of the form <mml:math altimg=\"si1.svg\"><mml:mn>0</mml:mn><mml:mo>≤</mml:mo><mml:mi>ϱ</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\"><</mml:mo><mml:mn>1</mml:mn></mml:math>, and the scaling introduces a small parameter <ce:italic>ε</ce:italic> in order to control the stiffness of the density constraint. As <mml:math altimg=\"si2.svg\"><mml:mi>ε</mml:mi><mml:mo stretchy=\"false\">→</mml:mo><mml:mn>0</mml:mn></mml:math>, the solutions of the compressible system converge to solutions of the so-called free-congested Euler equations that couples compressible and incompressible dynamics. We show that the proposed scheme is positivity preserving and energy stable. In addition, we also show that the numerical densities satisfy a discrete variant of the constraint. By means of extensive numerical case studies, we verify the efficacy of the scheme and show that the scheme is able to capture the two dynamics in the limiting regime, thereby proving the AP property.","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"58 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143035321","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 : 2025-01-22DOI: 10.1016/j.amc.2025.129303
Idriss Boutaayamou, Fouad Et-tahri, Lahcen Maniar
This paper is devoted to the theoretical and numerical analysis of the null controllability of a coupled ODE-heat system internally and at the boundary with Neumann boundary control. First, we establish the null controllability of the ODE-heat with distributed control using Carleman estimates. Then, we conclude by the strategy of space domain extension. Finally, we illustrate the analysis with some numerical experiments.
{"title":"Null controllability of an ODE-heat system with coupled boundary and internal terms","authors":"Idriss Boutaayamou, Fouad Et-tahri, Lahcen Maniar","doi":"10.1016/j.amc.2025.129303","DOIUrl":"https://doi.org/10.1016/j.amc.2025.129303","url":null,"abstract":"This paper is devoted to the theoretical and numerical analysis of the null controllability of a coupled ODE-heat system internally and at the boundary with Neumann boundary control. First, we establish the null controllability of the ODE-heat with distributed control using Carleman estimates. Then, we conclude by the strategy of space domain extension. Finally, we illustrate the analysis with some numerical experiments.","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"38 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143035229","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 : 2025-01-22DOI: 10.1016/j.amc.2025.129308
Pengcheng Zhang, Yajuan Liu, Shiyu Jiao, Chen Yang
This paper mainly investigates the observer-based non-fragile control issue for a class of T-S fuzzy switched systems under cyber attacks. Firstly, the system under consideration comprises a finite number of subsystems governed by the switching logic subject to the persistent dwell-time constraints, with each local subsystem represented by a T-S fuzzy model. Secondly, the switching logic with persistent dwell-time constraints is also used to make assumptions about the frequency and duration of attacks, and the system under cyber attacks is constructed as a double-layer switched system that satisfies two independent rules simultaneously. In addition, a non-fragile control strategy relying on observed states is developed, and the criterion for the global exponential stability and the synthesis conditions for the observer/controller are established by constructing a Lyapunov function associated with two switching signals. Finally, an electric circuit model is simulated to demonstrate the feasibility of the method.
{"title":"Observer-based non-fragile control for T-S fuzzy switched systems against cyber attacks: A double-layer PDT switching method","authors":"Pengcheng Zhang, Yajuan Liu, Shiyu Jiao, Chen Yang","doi":"10.1016/j.amc.2025.129308","DOIUrl":"https://doi.org/10.1016/j.amc.2025.129308","url":null,"abstract":"This paper mainly investigates the observer-based non-fragile control issue for a class of T-S fuzzy switched systems under cyber attacks. Firstly, the system under consideration comprises a finite number of subsystems governed by the switching logic subject to the persistent dwell-time constraints, with each local subsystem represented by a T-S fuzzy model. Secondly, the switching logic with persistent dwell-time constraints is also used to make assumptions about the frequency and duration of attacks, and the system under cyber attacks is constructed as a double-layer switched system that satisfies two independent rules simultaneously. In addition, a non-fragile control strategy relying on observed states is developed, and the criterion for the global exponential stability and the synthesis conditions for the observer/controller are established by constructing a Lyapunov function associated with two switching signals. Finally, an electric circuit model is simulated to demonstrate the feasibility of the method.","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"49 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143035327","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 : 2025-01-21DOI: 10.1016/j.amc.2025.129298
Wei Liu, Kai Li
A coupling of compressible Darcy-Brinkman flow and advection-diffusion transport problem is considered in fractured media. Treating the fracture as hyperplane, we obtain a two-layer reduced coupled model and the whole considered media is divided into low dimensional fracture-interfaces and surrounding high dimensional subdomains. To improve efficiency, two decoupled algorithms are constructed to solve the reduced coupled model. One decoupled algorithm is proposed based on interpolating vectors as inner boundaries and the other is constructed by interpolating scalars as iterative terms. By using both algorithms, the models in each subdomain are solved in parallel. The BDF2 formula and modified upwind scheme are employed to maintain the accuracy. For advection-diffusion model, we develop a novel bound-preserving scheme to keep the concentration within [0,1] combined with finite volume method by the Lagrange multiplier approach. The accuracy and efficiency of the proposed algorithms are verified by numerical experiments including three-dimensional case and benchmark testing.
{"title":"Decoupled bound-preserving algorithms for compressible Darcy-Brinkman flow with advection-diffusion transport problem in fractured media","authors":"Wei Liu, Kai Li","doi":"10.1016/j.amc.2025.129298","DOIUrl":"https://doi.org/10.1016/j.amc.2025.129298","url":null,"abstract":"A coupling of compressible Darcy-Brinkman flow and advection-diffusion transport problem is considered in fractured media. Treating the fracture as hyperplane, we obtain a two-layer reduced coupled model and the whole considered media is divided into low dimensional fracture-interfaces and surrounding high dimensional subdomains. To improve efficiency, two decoupled algorithms are constructed to solve the reduced coupled model. One decoupled algorithm is proposed based on interpolating vectors as inner boundaries and the other is constructed by interpolating scalars as iterative terms. By using both algorithms, the models in each subdomain are solved in parallel. The BDF2 formula and modified upwind scheme are employed to maintain the accuracy. For advection-diffusion model, we develop a novel bound-preserving scheme to keep the concentration within <mml:math altimg=\"si1.svg\"><mml:mo stretchy=\"false\">[</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">]</mml:mo></mml:math> combined with finite volume method by the Lagrange multiplier approach. The accuracy and efficiency of the proposed algorithms are verified by numerical experiments including three-dimensional case and benchmark testing.","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"10 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143035328","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 : 2025-01-20DOI: 10.1016/j.amc.2025.129295
Yaoping Wang, Shasha Li, Zeng Zhao
Given a graph <mml:math altimg="si1.svg"><mml:mi>G</mml:mi><mml:mo linebreak="goodbreak" linebreakstyle="after">=</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>V</mml:mi><mml:mo>,</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> and a set <mml:math altimg="si2.svg"><mml:mi>S</mml:mi><mml:mo>⊆</mml:mo><mml:mi>V</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> with <mml:math altimg="si3.svg"><mml:mo stretchy="false">|</mml:mo><mml:mi>S</mml:mi><mml:mo stretchy="false">|</mml:mo><mml:mo>≥</mml:mo><mml:mn>2</mml:mn></mml:math>, an <ce:italic>S-path</ce:italic> in <ce:italic>G</ce:italic> is a path that connects all vertices of <ce:italic>S</ce:italic>. Let <mml:math altimg="si4.svg"><mml:msub><mml:mrow><mml:mi>ω</mml:mi></mml:mrow><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>S</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> represent the maximum number of edge-disjoint <ce:italic>S</ce:italic>-paths in <ce:italic>G</ce:italic>. The <ce:italic>k-path-edge-connectivity</ce:italic><mml:math altimg="si5.svg"><mml:msub><mml:mrow><mml:mi>ω</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> of <ce:italic>G</ce:italic> is then defined as min<mml:math altimg="si6.svg"><mml:mo stretchy="false">{</mml:mo><mml:msub><mml:mrow><mml:mi>ω</mml:mi></mml:mrow><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>S</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>:</mml:mo><mml:mi>S</mml:mi><mml:mo>⊆</mml:mo><mml:mi>V</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mspace width="0.25em"></mml:mspace><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mspace width="0.25em"></mml:mspace><mml:mo stretchy="false">|</mml:mo><mml:mi>S</mml:mi><mml:mo stretchy="false">|</mml:mo><mml:mo linebreak="badbreak" linebreakstyle="after">=</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy="false">}</mml:mo></mml:math>, where <mml:math altimg="si7.svg"><mml:mn>2</mml:mn><mml:mo>≤</mml:mo><mml:mi>k</mml:mi><mml:mo>≤</mml:mo><mml:mo stretchy="false">|</mml:mo><mml:mi>V</mml:mi><mml:mo stretchy="false">|</mml:mo></mml:math>. Therefore, <mml:math altimg="si8.svg"><mml:msub><mml:mrow><mml:mi>ω</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> is precisely the edge-connectivity <mml:math altimg="si9.svg"><mml:mi>λ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>. In this paper, we focus on the <ce:italic>k</ce:italic>-path-edge-connectivity of the complete balanced bipartite graph <mml:math altimg="si10.svg"><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><m
{"title":"k-path-edge-connectivity of the complete balanced bipartite graph","authors":"Yaoping Wang, Shasha Li, Zeng Zhao","doi":"10.1016/j.amc.2025.129295","DOIUrl":"https://doi.org/10.1016/j.amc.2025.129295","url":null,"abstract":"Given a graph <mml:math altimg=\"si1.svg\"><mml:mi>G</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">=</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>V</mml:mi><mml:mo>,</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:math> and a set <mml:math altimg=\"si2.svg\"><mml:mi>S</mml:mi><mml:mo>⊆</mml:mo><mml:mi>V</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:math> with <mml:math altimg=\"si3.svg\"><mml:mo stretchy=\"false\">|</mml:mo><mml:mi>S</mml:mi><mml:mo stretchy=\"false\">|</mml:mo><mml:mo>≥</mml:mo><mml:mn>2</mml:mn></mml:math>, an <ce:italic>S-path</ce:italic> in <ce:italic>G</ce:italic> is a path that connects all vertices of <ce:italic>S</ce:italic>. Let <mml:math altimg=\"si4.svg\"><mml:msub><mml:mrow><mml:mi>ω</mml:mi></mml:mrow><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:msub><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>S</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:math> represent the maximum number of edge-disjoint <ce:italic>S</ce:italic>-paths in <ce:italic>G</ce:italic>. The <ce:italic>k-path-edge-connectivity</ce:italic><mml:math altimg=\"si5.svg\"><mml:msub><mml:mrow><mml:mi>ω</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:math> of <ce:italic>G</ce:italic> is then defined as min<mml:math altimg=\"si6.svg\"><mml:mo stretchy=\"false\">{</mml:mo><mml:msub><mml:mrow><mml:mi>ω</mml:mi></mml:mrow><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:msub><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>S</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>:</mml:mo><mml:mi>S</mml:mi><mml:mo>⊆</mml:mo><mml:mi>V</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mspace width=\"0.25em\"></mml:mspace><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>d</mml:mi><mml:mspace width=\"0.25em\"></mml:mspace><mml:mo stretchy=\"false\">|</mml:mo><mml:mi>S</mml:mi><mml:mo stretchy=\"false\">|</mml:mo><mml:mo linebreak=\"badbreak\" linebreakstyle=\"after\">=</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy=\"false\">}</mml:mo></mml:math>, where <mml:math altimg=\"si7.svg\"><mml:mn>2</mml:mn><mml:mo>≤</mml:mo><mml:mi>k</mml:mi><mml:mo>≤</mml:mo><mml:mo stretchy=\"false\">|</mml:mo><mml:mi>V</mml:mi><mml:mo stretchy=\"false\">|</mml:mo></mml:math>. Therefore, <mml:math altimg=\"si8.svg\"><mml:msub><mml:mrow><mml:mi>ω</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:math> is precisely the edge-connectivity <mml:math altimg=\"si9.svg\"><mml:mi>λ</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:math>. In this paper, we focus on the <ce:italic>k</ce:italic>-path-edge-connectivity of the complete balanced bipartite graph <mml:math altimg=\"si10.svg\"><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><m","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"3 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143035331","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 : 2025-01-20DOI: 10.1016/j.amc.2025.129304
Qingqin Wu, Weifan Wang, Jiangxu Kong
A graph is 1-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. A graph is k-degenerate if each of its subgraphs contains a vertex of degree no greater than k. It was known that 1-planar graphs are 7-degenerate. In this paper, we show that every 1-planar graph without 5-cycles is 5-degenerate, which extends some known results on the 5-degeneracy of some 1-planar graphs.
{"title":"1-Planar graphs with no 5-cycles are 5-degenerate","authors":"Qingqin Wu, Weifan Wang, Jiangxu Kong","doi":"10.1016/j.amc.2025.129304","DOIUrl":"https://doi.org/10.1016/j.amc.2025.129304","url":null,"abstract":"A graph is 1-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. A graph is <ce:italic>k</ce:italic>-degenerate if each of its subgraphs contains a vertex of degree no greater than <ce:italic>k</ce:italic>. It was known that 1-planar graphs are 7-degenerate. In this paper, we show that every 1-planar graph without 5-cycles is 5-degenerate, which extends some known results on the 5-degeneracy of some 1-planar graphs.","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"20 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143035330","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 : 2025-01-17DOI: 10.1016/j.amc.2025.129299
Ziyao Fan, Chen Yang
The reduced-order model (ROM), as a crucial research avenue in control system design, effectively simplifies complexity and enhances computational efficiency when handling high-dimensional models. However, considering the presence of uncertainties caused by the incompleteness of the system model and the errors induced by sensors, conventional probabilistic methods rely on a substantial number of samples and may struggle to be applicable when there is an insufficient quantity of samples available. To address this challenge, this paper presents an interval-oriented reduced-order model (IROM) tailored for uncertain linear systems, aiming to improve the accuracy of the uncertain reduced-order model under small-sample conditions. Based on the unknown but bounded parameters, the interval state-space equations are established, and transformed into interval balanced equations. The uncertainty bounds for controllability and observability matrices, as well as Hankel singular values, are obtained via interval Lyapunov equations and an interval perturbation-based singular value decomposition method. Considering the dense distributions of uncertain Hankel singular values, a novel interval truncation criterion is introduced to determine the reduced model order. After order selection using the optimization method, the reduced-order models and output predictions can be obtained. Two application examples are provided to demonstrate the accuracy and efficiency of the developed methodology.
{"title":"Interval-oriented reduced-order model for uncertain control systems","authors":"Ziyao Fan, Chen Yang","doi":"10.1016/j.amc.2025.129299","DOIUrl":"https://doi.org/10.1016/j.amc.2025.129299","url":null,"abstract":"The reduced-order model (ROM), as a crucial research avenue in control system design, effectively simplifies complexity and enhances computational efficiency when handling high-dimensional models. However, considering the presence of uncertainties caused by the incompleteness of the system model and the errors induced by sensors, conventional probabilistic methods rely on a substantial number of samples and may struggle to be applicable when there is an insufficient quantity of samples available. To address this challenge, this paper presents an interval-oriented reduced-order model (IROM) tailored for uncertain linear systems, aiming to improve the accuracy of the uncertain reduced-order model under small-sample conditions. Based on the unknown but bounded parameters, the interval state-space equations are established, and transformed into interval balanced equations. The uncertainty bounds for controllability and observability matrices, as well as Hankel singular values, are obtained via interval Lyapunov equations and an interval perturbation-based singular value decomposition method. Considering the dense distributions of uncertain Hankel singular values, a novel interval truncation criterion is introduced to determine the reduced model order. After order selection using the optimization method, the reduced-order models and output predictions can be obtained. Two application examples are provided to demonstrate the accuracy and efficiency of the developed methodology.","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"26 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990376","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 : 2025-01-17DOI: 10.1016/j.amc.2025.129300
Zhiquan Hu, Jie Wang, Changlong Shen
For a graph <ce:italic>G</ce:italic>, define <mml:math altimg="si1.svg"><mml:msub><mml:mrow><mml:mi>μ</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>:</mml:mo><mml:mo linebreak="goodbreak" linebreakstyle="after">=</mml:mo><mml:mi mathvariant="normal">min</mml:mi><mml:mo></mml:mo><mml:mspace width="0.25em"></mml:mspace><mml:mo stretchy="false">{</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant="normal">max</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi><mml:mo>∈</mml:mo><mml:mi>S</mml:mi></mml:mrow></mml:msub><mml:mo></mml:mo><mml:msub><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>:</mml:mo><mml:mspace width="0.25em"></mml:mspace><mml:mi>S</mml:mi><mml:mo>∈</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant="script">S</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">}</mml:mo></mml:math>, where <mml:math altimg="si2.svg"><mml:msub><mml:mrow><mml:mi mathvariant="script">S</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:math> is the set consisting of all independent sets <mml:math altimg="si3.svg"><mml:mo stretchy="false">{</mml:mo><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">}</mml:mo></mml:math> of <ce:italic>G</ce:italic> such that some vertex, say <mml:math altimg="si4.svg"><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math> (<mml:math altimg="si5.svg"><mml:mn>1</mml:mn><mml:mo>≤</mml:mo><mml:mi>i</mml:mi><mml:mo>≤</mml:mo><mml:mi>k</mml:mi></mml:math>), is at distance two from every other vertex in it. A graph <ce:italic>G</ce:italic> is called 1-tough if for each cut set <mml:math altimg="si6.svg"><mml:mi>S</mml:mi><mml:mo>⊆</mml:mo><mml:mi>V</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>, <mml:math altimg="si7.svg"><mml:mi>G</mml:mi><mml:mo linebreak="goodbreak" linebreakstyle="after">−</mml:mo><mml:mi>S</mml:mi></mml:math> has no more than <mml:math altimg="si8.svg"><mml:mo stretchy="false">|</mml:mo><mml:mi>S</mml:mi><mml:mo stretchy="false">|</mml:mo></mml:math> components. Recently, Shi and Shan <ce:cross-ref ref>[19]</ce:cross-ref> conjectured that for each integer <mml:math altimg="si62.svg"><mml:mi>k</mml:mi><mml:mo>≥</mml:mo><mml:mn>4</mml:mn></mml:math>, being 2<ce:italic>k</ce:italic>-connected is sufficient for 1-tough <mml:math altimg="si10.svg"><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mro
对于图 G，定义 μk(G):=min{maxx∈SdG(x):S∈Sk}，其中 Sk 是由 G 的所有独立集 {u1，...，uk}组成的集合，使得某个顶点，例如 ui (1≤i≤k)，与其中的每个其他顶点的距离都是 2。如果对于每个切集 S⊆V(G)，G-S 的分量不超过 |S|，则图 G 称为 1-韧图。最近，Shi 和 Shan [19]猜想，对于每个整数 k≥4，2k-连通足以使无 1-韧（P2∪kP1）图成为哈密顿图，这一点分别被 Xu 等人 [20] 和 Ota 和 Sanka [16] 所证实。在本文中，我们通过下面的范型定理来推广上述结果：如果 G 是一个 1韧且 k 连接的 (P2∪kP1)-free 图，并且满足 μk+1(G)≥7k-65，其中 k≥2 是整数，那么 G 是哈密顿图或彼得森图。
{"title":"A Fan-type condition for cycles in 1-tough and k-connected (P2 ∪ kP1)-free graphs","authors":"Zhiquan Hu, Jie Wang, Changlong Shen","doi":"10.1016/j.amc.2025.129300","DOIUrl":"https://doi.org/10.1016/j.amc.2025.129300","url":null,"abstract":"For a graph <ce:italic>G</ce:italic>, define <mml:math altimg=\"si1.svg\"><mml:msub><mml:mrow><mml:mi>μ</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>:</mml:mo><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">=</mml:mo><mml:mi mathvariant=\"normal\">min</mml:mi><mml:mo></mml:mo><mml:mspace width=\"0.25em\"></mml:mspace><mml:mo stretchy=\"false\">{</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"normal\">max</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi><mml:mo>∈</mml:mo><mml:mi>S</mml:mi></mml:mrow></mml:msub><mml:mo></mml:mo><mml:msub><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:msub><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>:</mml:mo><mml:mspace width=\"0.25em\"></mml:mspace><mml:mi>S</mml:mi><mml:mo>∈</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant=\"script\">S</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo stretchy=\"false\">}</mml:mo></mml:math>, where <mml:math altimg=\"si2.svg\"><mml:msub><mml:mrow><mml:mi mathvariant=\"script\">S</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:math> is the set consisting of all independent sets <mml:math altimg=\"si3.svg\"><mml:mo stretchy=\"false\">{</mml:mo><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo stretchy=\"false\">}</mml:mo></mml:math> of <ce:italic>G</ce:italic> such that some vertex, say <mml:math altimg=\"si4.svg\"><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math> (<mml:math altimg=\"si5.svg\"><mml:mn>1</mml:mn><mml:mo>≤</mml:mo><mml:mi>i</mml:mi><mml:mo>≤</mml:mo><mml:mi>k</mml:mi></mml:math>), is at distance two from every other vertex in it. A graph <ce:italic>G</ce:italic> is called 1-tough if for each cut set <mml:math altimg=\"si6.svg\"><mml:mi>S</mml:mi><mml:mo>⊆</mml:mo><mml:mi>V</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:math>, <mml:math altimg=\"si7.svg\"><mml:mi>G</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">−</mml:mo><mml:mi>S</mml:mi></mml:math> has no more than <mml:math altimg=\"si8.svg\"><mml:mo stretchy=\"false\">|</mml:mo><mml:mi>S</mml:mi><mml:mo stretchy=\"false\">|</mml:mo></mml:math> components. Recently, Shi and Shan <ce:cross-ref ref>[19]</ce:cross-ref> conjectured that for each integer <mml:math altimg=\"si62.svg\"><mml:mi>k</mml:mi><mml:mo>≥</mml:mo><mml:mn>4</mml:mn></mml:math>, being 2<ce:italic>k</ce:italic>-connected is sufficient for 1-tough <mml:math altimg=\"si10.svg\"><mml:mo stretchy=\"false\">(</mml:mo><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mro","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"23 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990377","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 : 2025-01-16DOI: 10.1016/j.amc.2025.129296
Jin Li, Yongxin Lan, Changqing Xu
A graph without a copy of T as a subgraph is called T-free. The outerplanar Turán number exOP(n,T) of T represents the maximum number of edges among all n-vertex T-free outerplanar graphs. In this paper, we investigate exOP(n,rPs) and determine its exact value for r,s≥2 and n≥rs. This extends a result of Fang and Zhai (2023) [7].
不包含T的子图称为无T图。T的外平面Turán number exOP（n，T）表示所有n顶点无T的外平面图的最大边数。本文研究了exOP（n,rPs）在r、s≥2和n≥rs条件下的精确值。这延伸了Fang和Zhai (2023) b[7]的结果。
{"title":"The outerplanar Turán number of disjoint copies of paths","authors":"Jin Li, Yongxin Lan, Changqing Xu","doi":"10.1016/j.amc.2025.129296","DOIUrl":"https://doi.org/10.1016/j.amc.2025.129296","url":null,"abstract":"A graph without a copy of <ce:italic>T</ce:italic> as a subgraph is called <ce:italic>T</ce:italic>-free. The outerplanar Turán number <mml:math altimg=\"si1.svg\"><mml:mi>e</mml:mi><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mrow></mml:mrow><mml:mrow><mml:mi>O</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:math> of <ce:italic>T</ce:italic> represents the maximum number of edges among all <ce:italic>n</ce:italic>-vertex <ce:italic>T</ce:italic>-free outerplanar graphs. In this paper, we investigate <mml:math altimg=\"si2.svg\"><mml:mi>e</mml:mi><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mrow></mml:mrow><mml:mrow><mml:mi>O</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>r</mml:mi><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:math> and determine its exact value for <mml:math altimg=\"si3.svg\"><mml:mi>r</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi><mml:mo>≥</mml:mo><mml:mn>2</mml:mn></mml:math> and <mml:math altimg=\"si4.svg\"><mml:mi>n</mml:mi><mml:mo>≥</mml:mo><mml:mi>r</mml:mi><mml:mi>s</mml:mi></mml:math>. This extends a result of Fang and Zhai (2023) <ce:cross-ref ref>[7]</ce:cross-ref>.","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"205 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990378","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 : 2025-01-15DOI: 10.1016/j.amc.2024.129269
Huage Wang
In this paper, we derive explicit expressions to directly determine the C-eigenvalues and corresponding C-eigenvectors of the three-dimensional piezoelectric tensors through categorical discussions. We further validate the efficacy of this approach by solving the eigenvalues of three classic three-dimensional piezoelectric tensors using this method.
本文通过分类讨论，推导出直接确定三维压电张量 C 特征值和相应 C 特征向量的明确表达式。通过使用这种方法求解三个经典三维压电张量的特征值，我们进一步验证了这种方法的有效性。
{"title":"Calculating the C-eigenvalues of the three-dimensional piezoelectric tensors directly","authors":"Huage Wang","doi":"10.1016/j.amc.2024.129269","DOIUrl":"https://doi.org/10.1016/j.amc.2024.129269","url":null,"abstract":"In this paper, we derive explicit expressions to directly determine the C-eigenvalues and corresponding C-eigenvectors of the three-dimensional piezoelectric tensors through categorical discussions. We further validate the efficacy of this approach by solving the eigenvalues of three classic three-dimensional piezoelectric tensors using this method.","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"16 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142990385","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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