Pub Date : 2024-10-24DOI: 10.1016/j.amc.2024.129119
Qiansheng Han , Antti Rasila , Tommi Sottinen
We present a stochastic method for the simulation of Laplace's equation with a mixed boundary condition in planar domains that are polygonal or bounded by circular arcs. We call this method the Reflected Walk-on-Spheres algorithm. The method combines a traditional Walk-on-Spheres algorithm with use of reflections at the Neumann boundaries. We apply our algorithm to simulate numerical conformal mappings from certain quadrilaterals to the corresponding canonical domains, and to compute their conformal moduli. Finally, we give examples of the method on three dimensional polyhedral domains, and use it to simulate the heat flow on an L-shaped insulated polyhedron.
我们提出了一种在多边形或以圆弧为界的平面域中模拟具有混合边界条件的拉普拉斯方程的随机方法。我们称这种方法为反射随走随谢算法。该方法结合了传统的 "边走边球 "算法和诺伊曼边界反射算法。我们应用我们的算法来模拟从某些四边形到相应规范域的数值保角映射，并计算它们的保角模量。最后，我们举例说明了该方法在三维多面体域上的应用，并用它模拟了 L 型绝热多面体上的热流。
{"title":"Efficient simulation of mixed boundary value problems and conformal mappings","authors":"Qiansheng Han , Antti Rasila , Tommi Sottinen","doi":"10.1016/j.amc.2024.129119","DOIUrl":"10.1016/j.amc.2024.129119","url":null,"abstract":"<div><div>We present a stochastic method for the simulation of Laplace's equation with a mixed boundary condition in planar domains that are polygonal or bounded by circular arcs. We call this method the Reflected Walk-on-Spheres algorithm. The method combines a traditional Walk-on-Spheres algorithm with use of reflections at the Neumann boundaries. We apply our algorithm to simulate numerical conformal mappings from certain quadrilaterals to the corresponding canonical domains, and to compute their conformal moduli. Finally, we give examples of the method on three dimensional polyhedral domains, and use it to simulate the heat flow on an L-shaped insulated polyhedron.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142528994","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 : 2024-10-24DOI: 10.1016/j.amc.2024.129145
Haifeng Ma , Wen Wang , Predrag S. Stanimirović
Characteristics of weighted Moore-Penrose inverses for dual matrices (W-MP-D inverse) are studied in this investigation. First, we introduce the weighted compact dual singular value decomposition (WCDSVD) on the set of dual matrices. A few equivalent conditions for the existence of the W-MP-D inverse on the set of dual matrices and several explicit representations are given using WCDSVD. Finally, the simulation of standing waves (s-waves) and traveling waves (t-waves) and the application of that simulation in the t-waves identification in the brain are given.
本文研究了对偶矩阵的加权摩尔-彭罗斯逆（W-MP-D 逆）的特征。首先，我们介绍了对偶矩阵集合上的加权紧凑对偶奇异值分解（WCDSVD）。利用 WCDSVD 给出了对偶矩阵集合上 W-MP-D 逆存在的几个等价条件和几个显式表示。最后，给出了驻波（s 波）和行波（t 波）的模拟以及该模拟在大脑 t 波识别中的应用。
{"title":"Weighted Moore-Penrose inverses for dual matrices and its applications","authors":"Haifeng Ma , Wen Wang , Predrag S. Stanimirović","doi":"10.1016/j.amc.2024.129145","DOIUrl":"10.1016/j.amc.2024.129145","url":null,"abstract":"<div><div>Characteristics of weighted Moore-Penrose inverses for dual matrices (W-MP-D inverse) are studied in this investigation. First, we introduce the weighted compact dual singular value decomposition (WCDSVD) on the set of dual matrices. A few equivalent conditions for the existence of the W-MP-D inverse on the set of dual matrices and several explicit representations are given using WCDSVD. Finally, the simulation of standing waves (s-waves) and traveling waves (t-waves) and the application of that simulation in the t-waves identification in the brain are given.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531840","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 : 2024-10-21DOI: 10.1016/j.amc.2024.129118
Wei-Ru Xu , Qian-Yu Shu , Natália Bebiano
Let be a signature matrix, where . Consider endowed with the indefinite inner product for all . A pseudo-Jacobi matrix of order n is a real tridiagonal symmetric matrix with respect to this indefinite inner product. In this paper, the reconstruction of a pair of n-by-n pseudo-Jacobi matrices, one obtained from the other by a rank-one modification, is investigated given their prescribed spectra. Necessary and sufficient conditions under which this problem has a solution are presented. As a special case of the obtained results, a related problem for Jacobi matrices proposed by de Boor and Golub is thoroughly solved.
{"title":"A pseudo-Jacobi inverse eigenvalue problem with a rank-one modification","authors":"Wei-Ru Xu , Qian-Yu Shu , Natália Bebiano","doi":"10.1016/j.amc.2024.129118","DOIUrl":"10.1016/j.amc.2024.129118","url":null,"abstract":"<div><div>Let <span><math><mi>H</mi><mo>=</mo><mtext>diag</mtext><mo>(</mo><msub><mrow><mi>δ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>δ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>δ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span> be a signature matrix, where <span><math><msub><mrow><mi>δ</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>∈</mo><mo>{</mo><mo>−</mo><mn>1</mn><mo>,</mo><mo>+</mo><mn>1</mn><mo>}</mo></math></span>. Consider <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> endowed with the indefinite inner product <span><math><msub><mrow><mo>〈</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>〉</mo></mrow><mrow><mi>H</mi></mrow></msub><mo>:</mo><mo>=</mo><mo>〈</mo><mi>H</mi><mi>x</mi><mo>,</mo><mi>y</mi><mo>〉</mo><mo>=</mo><msup><mrow><mi>y</mi></mrow><mrow><mi>T</mi></mrow></msup><mi>H</mi><mi>x</mi></math></span> for all <span><math><mi>x</mi><mo>,</mo><mi>y</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. A pseudo-Jacobi matrix of order <em>n</em> is a real tridiagonal symmetric matrix with respect to this indefinite inner product. In this paper, the reconstruction of a pair of <em>n</em>-by-<em>n</em> pseudo-Jacobi matrices, one obtained from the other by a rank-one modification, is investigated given their prescribed spectra. Necessary and sufficient conditions under which this problem has a solution are presented. As a special case of the obtained results, a related problem for Jacobi matrices proposed by de Boor and Golub is thoroughly solved.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142528992","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 : 2024-10-21DOI: 10.1016/j.amc.2024.129105
Davide Trevisani, José Germán López-Salas, Carlos Vázquez, José Antonio García-Rodríguez
In this work we rigorously establish mathematical models to obtain the capital valuation adjustment (KVA) as part of the total valuation adjustments (XVAs). For this purpose, we use a semi-replication strategy based on market theory. We formulate single-factor models in terms of expectations and PDEs. For PDEs formulation, we rigorously obtain the existence and uniqueness of the solution, as well as some regularity and qualitative properties of the solution. Moreover, appropriate numerical methods are proposed for solving the corresponding PDEs. Finally, some examples show the numerical results for call and put European options and the corresponding XVA that includes the KVA.
在这项工作中，我们严格地建立了数学模型，以获得作为总估值调整（XVAs）一部分的资本估值调整（KVA）。为此，我们采用了基于市场理论的半复制策略。我们用预期和 PDEs 来制定单因素模型。对于 PDEs 的表述，我们严格获得了解的存在性和唯一性，以及解的一些规律性和定性属性。此外，我们还提出了求解相应 PDE 的适当数值方法。最后，一些实例展示了看涨和看跌欧式期权的数值结果，以及包括 KVA 的相应 XVA。
{"title":"Mathematical models and numerical methods for a capital valuation adjustment (KVA) problem","authors":"Davide Trevisani, José Germán López-Salas, Carlos Vázquez, José Antonio García-Rodríguez","doi":"10.1016/j.amc.2024.129105","DOIUrl":"10.1016/j.amc.2024.129105","url":null,"abstract":"<div><div>In this work we rigorously establish mathematical models to obtain the capital valuation adjustment (KVA) as part of the total valuation adjustments (XVAs). For this purpose, we use a semi-replication strategy based on market theory. We formulate single-factor models in terms of expectations and PDEs. For PDEs formulation, we rigorously obtain the existence and uniqueness of the solution, as well as some regularity and qualitative properties of the solution. Moreover, appropriate numerical methods are proposed for solving the corresponding PDEs. Finally, some examples show the numerical results for call and put European options and the corresponding XVA that includes the KVA.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142528993","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 : 2024-10-21DOI: 10.1016/j.amc.2024.129127
Zhaoping Du, Chi Zhang, Xiaofei Yang, Hui Ye, Jianzhen Li
This paper investigates the problems of modeling and H∞ control for discrete three closed-loop cyber-physical system (CPS) with network delay, disturbance, and event-triggered control for the first time. A new even-triggered scheme is designed by incorporating a disturbance term, which reduces the number of triggers compared with some previous ones due to the inclusion of disturbance, and leads to the expansion of the triggered intervals. First, a new model of the system is constructed. Then, to provide sufficient conditions of the stability for the system with H∞ control, Lyapunov function and linear matrix inequality (LMI) techniques are used. Furthermore, the co-design method of three controllers and event-triggered matrix is proposed. Finally, the feasibility and practicality of the method proposed in this paper are verified by a simulation example of a marine boiler power generation control system. This kind of three closed-loop CPS model is constructed for the first time, which has been applied in different control systems such as servo motors, thermal power generation, etc.
{"title":"Discrete-time event-triggered H-infinity stabilization for three closed-loop cyber-physical system with uncertain delay","authors":"Zhaoping Du, Chi Zhang, Xiaofei Yang, Hui Ye, Jianzhen Li","doi":"10.1016/j.amc.2024.129127","DOIUrl":"10.1016/j.amc.2024.129127","url":null,"abstract":"<div><div>This paper investigates the problems of modeling and <em>H</em>∞ control for discrete three closed-loop cyber-physical system (CPS) with network delay, disturbance, and event-triggered control for the first time. A new even-triggered scheme is designed by incorporating a disturbance term, which reduces the number of triggers compared with some previous ones due to the inclusion of disturbance, and leads to the expansion of the triggered intervals. First, a new model of the system is constructed. Then, to provide sufficient conditions of the stability for the system with <em>H</em>∞ control, Lyapunov function and linear matrix inequality (LMI) techniques are used. Furthermore, the co-design method of three controllers and event-triggered matrix is proposed. Finally, the feasibility and practicality of the method proposed in this paper are verified by a simulation example of a marine boiler power generation control system. This kind of three closed-loop CPS model is constructed for the first time, which has been applied in different control systems such as servo motors, thermal power generation, etc.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142528990","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 : 2024-10-21DOI: 10.1016/j.amc.2024.129135
Yuan Yu , Zuojian Qin , Haizhuan Yuan , Shi Shu
In this paper, a new two-relaxation-time regularized (TRT-R) lattice Boltzmann (LB) model for the convection-diffusion equation (CDE) with spatially dependent coefficients is proposed. Within this framework, we first derive a TRT-R collision operator (CO) by constructing a new regularized procedure through the high-order Hermite expansion of non-equilibrium part. Then, a first-order discrete-velocity form of discrete source term is introduced to improve the accuracy of the source term. Finally, a new first-order space-derivative auxiliary term is proposed to recover the correct CDE. To assess this model, we simulated non-homogeneous convection-diffusion problems with adjustable diffusion intensity in both two and three dimensions. The findings indicate that the newly introduced source terms markedly enhance the model's precision and stability under varying time steps, grid resolutions, diffusion scaling coefficients, and magic parameters. The adoption of the TRT-R CO leads to a significant error reduction compared to the classic BGK CO in most scenarios. Furthermore, the influence of the magic parameter on the performance of the TRT-R CO was investigated. Beyond this, the study also confirms the efficacy of the TRT-R CO in eliminating numerical slip when enforcing Dirichlet boundary conditions with a halfway bounce-back scheme, thereby providing further evidence of the algorithm's advantages.
本文为具有空间依赖系数的对流扩散方程（CDE）提出了一种新的双松弛-时间正则化（TRT-R）晶格玻尔兹曼（LB）模型。在此框架内，我们首先通过对非平衡态部分进行高阶赫米特展开，构建一个新的正则化程序，从而推导出 TRT-R 碰撞算子（CO）。然后，引入离散源项的一阶离散速度形式，以提高源项的精度。最后，我们提出了一个新的一阶空间衍生辅助项来恢复正确的 CDE。为了评估这一模型，我们模拟了扩散强度可调的二维和三维非均质对流扩散问题。研究结果表明，在不同的时间步长、网格分辨率、扩散比例系数和魔法参数条件下，新引入的源项明显提高了模型的精度和稳定性。与传统的 BGK CO 相比，在大多数情况下，采用 TRT-R CO 可显著减少误差。此外，还研究了魔法参数对 TRT-R CO 性能的影响。除此以外，研究还证实了 TRT-R CO 在使用半程反弹方案强制执行 Dirichlet 边界条件时消除数值滑移的功效，从而进一步证明了该算法的优势。
{"title":"Two-relaxation-time regularized lattice Boltzmann model for convection-diffusion equation with spatially dependent coefficients","authors":"Yuan Yu , Zuojian Qin , Haizhuan Yuan , Shi Shu","doi":"10.1016/j.amc.2024.129135","DOIUrl":"10.1016/j.amc.2024.129135","url":null,"abstract":"<div><div>In this paper, a new two-relaxation-time regularized (TRT-R) lattice Boltzmann (LB) model for the convection-diffusion equation (CDE) with spatially dependent coefficients is proposed. Within this framework, we first derive a TRT-R collision operator (CO) by constructing a new regularized procedure through the high-order Hermite expansion of non-equilibrium part. Then, a first-order discrete-velocity form of discrete source term is introduced to improve the accuracy of the source term. Finally, a new first-order space-derivative auxiliary term is proposed to recover the correct CDE. To assess this model, we simulated non-homogeneous convection-diffusion problems with adjustable diffusion intensity in both two and three dimensions. The findings indicate that the newly introduced source terms markedly enhance the model's precision and stability under varying time steps, grid resolutions, diffusion scaling coefficients, and magic parameters. The adoption of the TRT-R CO leads to a significant error reduction compared to the classic BGK CO in most scenarios. Furthermore, the influence of the magic parameter on the performance of the TRT-R CO was investigated. Beyond this, the study also confirms the efficacy of the TRT-R CO in eliminating numerical slip when enforcing Dirichlet boundary conditions with a halfway bounce-back scheme, thereby providing further evidence of the algorithm's advantages.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142528988","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 : 2024-10-21DOI: 10.1016/j.amc.2024.129129
Hui Zhang , Shenglong Zhou , Geoffrey Ye Li , Naihua Xiu , Yiju Wang
The deep neural network with step function activation (0/1 DNNs) is a fundamental composite model in deep learning which has high efficiency and robustness to outliers. However, due to the discontinuity and lacking subgradient information of the 0/1 DNNs model, prior researches are largely focused on designing continuous functions to approximate the step activation and developing continuous optimization methods. In this paper, by introducing two sets of network node variables into the 0/1 DNNs and by exploring the composite structure of the resulted model, the 0/1 DNNs is decomposed into a unary optimization model associated with the step function and three derivational optimization subproblems associated with the other variables. For the unary optimization model and two derivational optimization subproblems, we present a closed form solution, and for the third derivational optimization subproblem, we propose an efficient proximal method. Based on this, a globally convergent step function based recursion method for the 0/1 DNNs is developed. The efficiency and performance of the proposed algorithm are validated via theoretical analysis as well as some illustrative numerical examples on classifying MNIST, FashionMNIST and Cifar10 datasets.
{"title":"A step function based recursion method for 0/1 deep neural networks","authors":"Hui Zhang , Shenglong Zhou , Geoffrey Ye Li , Naihua Xiu , Yiju Wang","doi":"10.1016/j.amc.2024.129129","DOIUrl":"10.1016/j.amc.2024.129129","url":null,"abstract":"<div><div>The deep neural network with step function activation (0/1 DNNs) is a fundamental composite model in deep learning which has high efficiency and robustness to outliers. However, due to the discontinuity and lacking subgradient information of the 0/1 DNNs model, prior researches are largely focused on designing continuous functions to approximate the step activation and developing continuous optimization methods. In this paper, by introducing two sets of network node variables into the 0/1 DNNs and by exploring the composite structure of the resulted model, the 0/1 DNNs is decomposed into a unary optimization model associated with the step function and three derivational optimization subproblems associated with the other variables. For the unary optimization model and two derivational optimization subproblems, we present a closed form solution, and for the third derivational optimization subproblem, we propose an efficient proximal method. Based on this, a globally convergent step function based recursion method for the 0/1 DNNs is developed. The efficiency and performance of the proposed algorithm are validated via theoretical analysis as well as some illustrative numerical examples on classifying MNIST, FashionMNIST and Cifar10 datasets.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142528989","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}
Although the two-layer quasi-geostrophic equations (2QGE) are a simplified model for the dynamics of a stratified, wind-driven ocean, their numerical simulation is still plagued by the need for high resolution to capture the full spectrum of turbulent scales. Since such high resolution would lead to unreasonable computational times, it is typical to resort to coarse low-resolution meshes combined with the so-called eddy viscosity parameterization to account for the diffusion mechanisms that are not captured due to mesh under-resolution. We propose to enable the use of further coarsened meshes by adding a (linear or nonlinear) differential low-pass filter to the 2QGE, without changing the eddy viscosity coefficient. While the linear filter introduces constant (additional) artificial viscosity everywhere in the domain, the nonlinear filter relies on an indicator function to determine where and how much artificial viscosity is needed. Through several numerical results for a double-gyre wind forcing benchmark, we show that with the nonlinear filter we obtain accurate results with very coarse meshes, thereby drastically reducing the computational time (speed up ranging from 30 to 300).
{"title":"Linear and nonlinear filtering for a two-layer quasi-geostrophic ocean model","authors":"Lander Besabe , Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza","doi":"10.1016/j.amc.2024.129121","DOIUrl":"10.1016/j.amc.2024.129121","url":null,"abstract":"<div><div>Although the two-layer quasi-geostrophic equations (2QGE) are a simplified model for the dynamics of a stratified, wind-driven ocean, their numerical simulation is still plagued by the need for high resolution to capture the full spectrum of turbulent scales. Since such high resolution would lead to unreasonable computational times, it is typical to resort to coarse low-resolution meshes combined with the so-called eddy viscosity parameterization to account for the diffusion mechanisms that are not captured due to mesh under-resolution. We propose to enable the use of further coarsened meshes by adding a (linear or nonlinear) differential low-pass filter to the 2QGE, without changing the eddy viscosity coefficient. While the linear filter introduces constant (additional) artificial viscosity everywhere in the domain, the nonlinear filter relies on an indicator function to determine where and how much artificial viscosity is needed. Through several numerical results for a double-gyre wind forcing benchmark, we show that with the nonlinear filter we obtain accurate results with very coarse meshes, thereby drastically reducing the computational time (speed up ranging from 30 to 300).</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142528991","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 : 2024-10-17DOI: 10.1016/j.amc.2024.129134
Yuanhua Wang , Ying Wang , Haitao Li , Wenke Zang
The symmetric property in n-player games is explored in this paper. First of all, some algebraically verifiable conditions are provided respectively for the totally symmetric, weakly symmetric and anonymous games, which are based on the construction of permutation matrix, and some interesting properties are revealed. Then we investigate how network structures affect the symmetry in a networked game. Some sufficient conditions are proposed and several nice properties are preserved when traditional networked games are extended to generalized networked games, in which the resulting network structure is more complex than a classical network graph.
本文探讨了 n 人博弈中的对称属性。首先，本文基于排列矩阵的构造，分别为完全对称博弈、弱对称博弈和匿名博弈提供了一些可验证的代数条件，并揭示了一些有趣的性质。然后，我们研究了网络结构如何影响网络博弈的对称性。当传统网络博弈扩展到广义网络博弈时，我们提出了一些充分条件，并保留了一些很好的性质，在广义网络博弈中，所产生的网络结构比经典网络图更复杂。
{"title":"Matrix expressions of symmetric n-player games","authors":"Yuanhua Wang , Ying Wang , Haitao Li , Wenke Zang","doi":"10.1016/j.amc.2024.129134","DOIUrl":"10.1016/j.amc.2024.129134","url":null,"abstract":"<div><div>The symmetric property in <em>n</em>-player games is explored in this paper. First of all, some algebraically verifiable conditions are provided respectively for the totally symmetric, weakly symmetric and anonymous games, which are based on the construction of permutation matrix, and some interesting properties are revealed. Then we investigate how network structures affect the symmetry in a networked game. Some sufficient conditions are proposed and several nice properties are preserved when traditional networked games are extended to generalized networked games, in which the resulting network structure is more complex than a classical network graph.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445334","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 : 2024-10-17DOI: 10.1016/j.amc.2024.129131
Dhanya Roy , Sandi Klavžar , Aparna Lakshmanan S
The general position problem in graphs is to find the largest possible set of vertices with the property that no three of them lie on a common shortest path. The mutual-visibility problem in graphs is to find the maximum number of vertices that can be selected such that every pair of vertices in the collection has a shortest path between them with no vertex from the collection as an internal vertex. Here, the general position problem and the mutual-visibility problem are investigated in double graphs and in Mycielskian graphs. Sharp general bounds are proved, in particular involving the total and the outer mutual-visibility number of base graphs. Several exact values are also determined, in particular the mutual-visibility number of the double graphs and of the Mycielskian of cycles.
{"title":"Mutual-visibility and general position in double graphs and in Mycielskians","authors":"Dhanya Roy , Sandi Klavžar , Aparna Lakshmanan S","doi":"10.1016/j.amc.2024.129131","DOIUrl":"10.1016/j.amc.2024.129131","url":null,"abstract":"<div><div>The general position problem in graphs is to find the largest possible set of vertices with the property that no three of them lie on a common shortest path. The mutual-visibility problem in graphs is to find the maximum number of vertices that can be selected such that every pair of vertices in the collection has a shortest path between them with no vertex from the collection as an internal vertex. Here, the general position problem and the mutual-visibility problem are investigated in double graphs and in Mycielskian graphs. Sharp general bounds are proved, in particular involving the total and the outer mutual-visibility number of base graphs. Several exact values are also determined, in particular the mutual-visibility number of the double graphs and of the Mycielskian of cycles.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445335","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}
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