Current Issue

2024, Vol. 44 No. 3   Published date: 28 September 2024
Previous Issue   

• On $c$-vectors of Cluster Algebras of Rank $2$

  Ding Siyi, Fu Changjian

  2024, 44(3): 1. doi: 10.3969/j.issn.1006-8074.2024.03.001

  Abstract ( 41 )   PDF (223KB) ( 36 )   　　

  The sign-coherence property of $c$-vectors plays an important role in the structure theory of cluster algebras. However, all known proofs depend on either the invariant theory of geometry or the representation theory. In this paper we give an elementary proof for the sign-coherence property of $c$-vectors for cluster algebras of rank $2$. As an application, we prove that a cluster is determined by its associated subset of positive $c$-vectors.

• Asymptotic Dynamics of a Single-species Model with Resource-dependent Dispersal in One Dimension

  Huang Yun, Zhang Dawei

  2024, 44(3): 11. doi: 10.3969/j.issn.1006-8074.2024.03.002

  Abstract ( 37 )   PDF (194KB) ( 31 )   　　

  In this paper, we study the asymptotic dynamics of a single-species model with resource-dependent dispersal in one dimension.

  To overcome the analytical difficulties brought by the resource-dependent dispersal, we use the idea of changing variables to transform the model into a uniform dispersal one. Then the existence and uniqueness of positive stationary solution to the model can be verified by the squeezing argument, where the solution plays a crucial role in later analyses. Moreover, the asymptotic behavior of solutions to the model is obtained by the upper-lower solutions method. The result indicates that the solutions of the model converge to the corresponding positive stationary solution locally uniformly in one dimension as time goes to infinity.

• Several Classes of Two-weight or Three-weight Linear  Codes and Their Applications

  Shen Hongyan, Liu Haibo

  2024, 44(3): 25. doi: 10.3969/j.issn.1006-8074.2024.03.003

  Abstract ( 40 )   PDF (234KB) ( 25 )   　　

  Recently, linear codes with a few weights have been extensively studied due to their applications in secret sharing schemes, constant composition codes, strongly regular graphs and so on. In this paper, based on the Weil sums, several classes of two-weight or three-weight linear codes are presented by choosing a proper defining set, and their weight enumerators and complete weight enumerators are determined. Furthermore, these codes are proven to be minimal. By puncturing these linear codes, two classes of two-weight projective codes are obtained, and the parameters of the corresponding strongly regular graph are given. This paper generalizes the results of [7].

• On the Local Convergence and Dynamics of New Iterative Method with Sixth Order Convergence

  Lyu Borui, Chu Xue, Wang Haijun

  2024, 44(3): 50. doi: 10.3969/j.issn.1006-8074.2024.03.004

  Abstract ( 42 )   PDF (303KB) ( 16 )   　　

  In this paper, we construct a new sixth order iterative method for solving nonlinear equations. The local convergence and order of convergence of the new iterative method is demonstrated. In order to check the validity of the new iterative method, we

  employ several chemical engineering applications and academic test problems. Numerical results show the good numerical performance of the new iterative method. Moreover, the dynamical study of the new method also supports the theoretical results.

• Qualitative Analysis of a Diffusive Predator-prey Model with Nonlcoal Fear Effect

  Shen Zhongyuan, Zhang Xuebing, Li Shunjie

  2024, 44(3): 67. doi: 10.3969/j.issn.1006-8074.2024.03.005

  Abstract ( 33 )   PDF (1397KB) ( 19 )   　　

  In this paper, we establish a delayed predator-prey model with nonlocal fear effect. Firstly, the existence, uniqueness, and persistence of solutions of the model are studied. Then, the local stability, Turing bifurcation, and Hopf bifurcation of the constant equilibrium state are analyzed by examining the characteristic equation. The global asymptotic stability of the positive equilibrium point is investigated using the Lyapunov function method. Finally, the correctness of the theoretical analysis results is verified through numerical simulations.

• Nonadditive Skew (Anti-)commuting Maps on Operator Algebras

  Zhang Ting , Feng Liqin, Qi Xiaofei

  2024, 44(3): 83. doi: 10.3969/j.issn.1006-8074.2024.03.006

  Abstract ( 35 )   PDF (153KB) ( 19 )   　　

  In this paper, we first give the general forms of skew commuting maps and skew anti-commuting maps by the Peirce decomposition on a unital ring with a nontrivial idempotent, respectively, and then, as applications, we obtain the concrete characterizations of all nonadditive skew (anti-)commuting maps on some operator algebras.

• Gradient Estimate of Solutions to a Class of Mean Curvature Equations with Prescribed Contact Angle Boundary Problem

  Yuan Shengtong, Han Fei

  2024, 44(3): 94. doi: 10.3969/j.issn.1006-8074.2024.03.007

  Abstract ( 15 )   PDF (164KB) ( 8 )   　　

  This paper studies the prescribed contact angle boundary value problem of a certain type of mean curvature equation. Applying the maximum principle and the moving frame method and based on the location of the maximum point, the boundary gradient estimation of the solutions to the equation is obtained.

• An Adaptive Spectral Conjugate Gradient Method with Restart Strategy

  Zhou Jincheng, Jiang Meixuan, Zhong Zining, Wu Yanqiang, Shao Hu

  2024, 44(3): 106. doi: 10.3969/j.issn.1006-8074.2024.03.008

  Abstract ( 45 )   PDF (330KB) ( 29 )   　　

  As a generalization of the two-term conjugate gradient method (CGM), the spectral CGM is one of the effective methods for solving unconstrained optimization. In this paper, we enhance the JJSL conjugate parameter, initially proposed by Jiang et al. (Computational and Applied Mathematics, 2021, 40: 174), through the utilization of a convex combination technique.

  And this improvement allows for an adaptive search direction by integrating a newly constructed spectral gradient-type restart strategy. Then, we develop a new spectral CGM by employing an inexact line search to determine the step size. With the application of the weak Wolfe line search, we establish the sufficient descent property of the proposed search direction. Moreover, under general assumptions, including the employment of the strong Wolfe line search for step size calculation, we demonstrate the global convergence of our new algorithm. Finally, the given unconstrained optimization test results show that the new algorithm is effective.

• Mean Dimension for Non-autonomous Iterated Function Systems

  Meng Deyu, Zhao Cao

  2024, 44(3): 119. doi: 10.3969/j.issn.1006-8074.2024.03.009

  Abstract ( 36 )   PDF (172KB) ( 21 )   　　

  In this paper we introduce the notions of mean dimension and metric mean dimension for non-autonomous iterated function systems

  (NAIFSs for short) on countably infinite alphabets which can be regarded as generalizations of the mean dimension and the Lindenstrauss metric mean dimension for non-autonomous iterated function systems. We also show the relationship between the mean topological dimension and the metric mean dimension.