Applied Mathematics and Computation最新文献

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Effects of an update mechanism based on combinatorial memory and high-reputation learning objects on the evolution of cooperation

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-01-23 DOI: 10.1016/j.amc.2025.129309

Qianxi Yang, Yanlong Yang

In human society, various factors influence decision-making, including memory, reputation, aspiration, etc. In recent years, research has increasingly focused on considering these factors and designing mechanisms to promote cooperation. However, few previous studies have simultaneously considered the effects of memory and reputation on cooperative evolution. Additionally, research on cooperation evolution based on memory mechanisms often focuses either on the strategy stability of the players themselves or on the strategy stability of the learning objects, but not both. Our study introduces an update mechanism based on combinatorial memory and high-reputation learning objects. This mechanism accounts for reputation and memory, where the memory effect includes the strategy stability of both the players and the learning objects. Specifically, at the stage of selecting learning objects, players prefer high-reputation individuals. We introduce a global selection weight, η, which allows players to select learning objects not only locally but also globally. At the stage of updating the strategy, each player simultaneously considers their own historical memory and the memory of their learning objects, with the parameter γ representing the memory weight of the learning objects. Monte Carlo simulations show that update rules that simultaneously consider both combinatorial memory and high-reputation learning objects are more effective in promoting cooperation than considering either factor alone. Furthermore, a small memory weight of the learning objects and a small global selection weight create an optimal environment for cooperation. Our study offers a novel approach to addressing social dilemmas and mitigating defection, emphasizing the critical roles of reputation and memory in the propagation of altruistic behavior.

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引用次数: 0

Null controllability of an ODE-heat system with coupled boundary and internal terms

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-01-22 DOI: 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.

引用次数: 0

Observer-based non-fragile control for T-S fuzzy switched systems against cyber attacks: A double-layer PDT switching method

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-01-22 DOI: 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.

引用次数: 0

Decoupled bound-preserving algorithms for compressible Darcy-Brinkman flow with advection-diffusion transport problem in fractured media

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-01-21 DOI: 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.

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引用次数: 0

k-path-edge-connectivity of the complete balanced bipartite graph

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-01-20 DOI: 10.1016/j.amc.2025.129295

Yaoping Wang, Shasha Li, Zeng Zhao

Given a graph

G = (V, E)

and a set

S \subseteq V (G)

with

| S | \geq 2

, an S-path in G is a path that connects all vertices of S. Let

ω_{G} (S)

represent the maximum number of edge-disjoint S-paths in G. The k-path-edge-connectivity

ω_{k} (G)

of G is then defined as min

{ω_{G} (S) : S \subseteq V (G) a n d | S | = k}

, where

2 \leq k \leq | V |

. Therefore,

ω_{2} (G)

is precisely the edge-connectivity

λ (G)

. In this paper, we focus on the k-path-edge-connectivity of the complete balanced bipartite graph

K_{n, n}

for all

3 \leq k \leq 2 n

. We show that if

k = n

k = n + 1

, and n is odd, then

ω_{k} (K_{n, n}) = ⌊ \frac{n k}{2 (k - 1)} ⌋ - 1

; otherwise,

ω_{k} (K_{n, n}) = ⌊ \frac{n k}{2 (k - 1)} ⌋

引用次数: 0

1-Planar graphs with no 5-cycles are 5-degenerate

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-01-20 DOI: 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.

引用次数: 0

Interval-oriented reduced-order model for uncertain control systems 面向区间的不确定控制系统降阶模型

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-01-17 DOI: 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.

降阶模型（ROM）作为控制系统设计的一个重要研究方向，在处理高维模型时可以有效地简化复杂性，提高计算效率。然而，考虑到系统模型的不完全性和传感器引起的误差所带来的不确定性，传统的概率方法依赖于大量的样本，在可用样本数量不足的情况下可能难以适用。为了解决这一问题，本文提出了一种针对不确定线性系统的面向区间的降阶模型（IROM），旨在提高不确定降阶模型在小样本条件下的精度。基于未知但有界的参数，建立了区间状态空间方程，并将其转化为区间平衡方程。利用区间李雅普诺夫方程和基于区间摄动的奇异值分解方法，得到了可控制性和可观测性矩阵的不确定性界以及Hankel奇异值。考虑不确定Hankel奇异值的密集分布，引入了一种新的区间截断准则来确定模型降阶。采用优化方法进行阶数选择后，可以得到降阶模型和输出预测。给出了两个应用实例，验证了所开发方法的准确性和有效性。

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引用次数: 0

A Fan-type condition for cycles in 1-tough and k-connected (P2 ∪ kP1)-free graphs 1-坚韧k-连通（P2 ∪ kP1）自由图中圈的一个fan型条件

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-01-17 DOI: 10.1016/j.amc.2025.129300

Zhiquan Hu, Jie Wang, Changlong Shen

For a graph G, define

μ_{k} (G) : = \min {\max_{x \in S} d_{G} (x) : S \in S_{k}}

, where

S_{k}

is the set consisting of all independent sets

{u_{1}, \dots, u_{k}}

of G such that some vertex, say

u_{i}

(

1 \leq i \leq k

), is at distance two from every other vertex in it. A graph G is called 1-tough if for each cut set

S \subseteq V (G)

G - S

has no more than

| S |

components. Recently, Shi and Shan [19] conjectured that for each integer

k \geq 4

, being 2k-connected is sufficient for 1-tough

(P_{2} \cup k P_{1})

-free graphs to be hamiltonian, which was confirmed by Xu et al. [20] and Ota and Sanka [16], respectively. In this article, we generalize the above results through the following Fan-type theorem: If G is a 1-tough and k-connected

(P_{2} \cup k P_{1})

-free graph and satisfies

μ_{k + 1} (G) \geq \frac{7 k - 6}{5}

, where

k \geq 2

is an integer, then G is hamiltonian or the Petersen graph.

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。

引用次数: 0

The outerplanar Turán number of disjoint copies of paths 外平面Turán路径不相交副本的数目

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-01-16 DOI: 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

e x_{_{O P}} (n, T)

of T represents the maximum number of edges among all n-vertex T-free outerplanar graphs. In this paper, we investigate

e x_{_{O P}} (n, r P_{s})

and determine its exact value for

r, s \geq 2

and

n \geq r s

. 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。

引用次数: 0

Calculating the C-eigenvalues of the three-dimensional piezoelectric tensors directly 直接计算三维压电张量的c特征值

IF 3.5 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation

Pub Date : 2025-01-15 DOI: 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。

引用次数: 0

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