Current Issue

2018, Vol. 38 No. 3-4   Published date: 30 December 2018
Previous Issue    Next Issue

• Clustering Analysis for the Delayed Flocking Model with Multi-topology Structures

  Huang Yao , Liu Yicheng

  2018, 38(3-4): 1-11. doi:

  Abstract ( 1314 )   PDF (552KB) ( 301 )   　　

  Flocking behavior is a common phenomenon in nature. The research of flocking theory has been widely applied in economy, military and management. This paper studies the group behavior of two models with time delays under different topology structures, and obtains necessary and sufficient conditions. For the Cucker-Smale type model with directed graphs, we get the necessary and sufficient conditions of time delay .For another model with competitive relationship between individuals under bipartite graph, we also explore the influence of time delay on group behavior, and get the necessary and sufficient conditions. Finally, we verify the correctness of the conclusion by numerical simulation. 

• Strongly M-α-symmetric Rings and Their Extensions

  Geng Yanli, Geng Daohong

  2018, 38(3-4): 12-17. doi:

  Abstract ( 1270 )   PDF (248KB) ( 223 )   　　

  Let M be a monoid andα an endomorphism of a ring R. We investigate the properties of M-symmetric rings with endomorphisms on R by introducing the concept of strongly M-α-symmetric ring. Using the classical method in ring theory, we prove that(1)R is a strongly right M-α-symmetric ring if and only if R is a strongly left M-α-symmetric ring;(2)Letαbe an automorphism of R. If R is a right Ore ring, hen R is a strongly M-α-symmetric ring if and only if Q is a strongly M-a-symmetric ring, where Q is the classical right quotient ring of the R.
  

  
  

• Improvement and Application of Shortest Path Algorithm Based on Point Cut Set

  Wu Man , Bai Mingli , Zeng Yongxin, Jiang Feng , Li Yebin

  2018, 38(3-4): 18-32. doi:

  Abstract ( 1355 )   PDF (2595KB) ( 397 )   　　

  By introducing the concept of cut point and point cut set, which are the important part of graph theory, this paper combines the algorithm of finding cut point and point cut set with the classical Dijkstra algorithm to form an improved parallel algorithm. The application of the improved parallel algorithm is also given. It provides a theoretical basis for finding the shortest path of undirected graph, and improves the routing algorithm in the routing protocol OSPF, which reduces the time complexity of the algorithm.

• Existence of Traveling Wave Solutions for a Class of Cooperative Lotka-Volterra System

  Liu Hui , Hu Haijun

  2018, 38(3-4): 33-42. doi:

  Abstract ( 1285 )   PDF (370KB) ( 356 )   　　

  Focusing on the effect of global climate change on species persistence,we consider a cooperative  Lotka-Volterra system with intrinsic growth rate,which depends on climate change.By constructing the appropriate upper and lower solutions,and combining the method of monotone iteration,we prove that when  two species are weakly cooperative,there exist a pair of monotone traveling wave solutions in the reaction-diffusion system. 

• General Solution to the Two Species Lotka—Volterra Equation with Constant Coefficients

  Zhu Shuyang, Zhu Yan

  2018, 38(3-4): 43-49. doi:

  Abstract ( 1515 )   PDF (270KB) ( 383 )   　　

  The two species Lotka—Volterra equation has important applications. The analytical solution of the  equation can be obtained by using the integral method and the adjustment coefficient method. First ,a linear  transform is carried out and unknown parameters are embedded in the transform. Then the first equation is substituted into the second equation. The analytic solutions of the new equation is obtained by integrating method and parameter adjustment method. Finally, the general solution of the population of two species Lotka—Volterra equation is derived. 

• A New Preconditioning Technique for Hermitian Toeplitz Systems

  Liu Zhongyun, Xu Weijin, Chen Siheng, Zhang Yulin

  2018, 38(3-4): 50-58. doi:

  Abstract ( 1342 )   PDF (341KB) ( 370 )   　　

  In this paper we give a preconditioned conjugate gradient method(PCG)to solve the Hermitian To-eplitz system Ax=b.Based on the fact that an Hermitian Toeplitz matrix Acan be reduced into a real Toeplitzmatrix plus a Hankel matrix(i.e.,UAU*=T+H)by a unitary similarity transformation(this unitary matrix  is U=(I-iJ)/ √2),we first reduce the system Ax=b to a real linear systems(T+H)[x1,x2]=[b1,b2]. Then we propose a new preconditioner for solving those two systems.In particular,our solver only involveseal arithmetics when the discrete sine transform(DST)and discrete cosine transform(DCT)are used.The  spectral properties of the preconditioned matrix are analyzed,and the computational complexity is discussed. Numerical experiments show that our preconditioner performs well for solving the Hermitian Toeplitz systems.

• On the Norms of r-circulant Matrices with Jacobsthal and Jacobsthal-Lucas Numbers

  2018, 38(3-4): 59-68. doi:

  Abstract ( 1369 )   PDF (366KB) ( 280 )   　　

  In this paper we study the norms of r-circulant matricesA = Cr(J0,J1, …,Jn-1) and B =Cr(D0,D1,…,Dn-1)where Jnand Dnare Jacobsthal and Jacobsthal-Lucas numbers,and give some boundsfor the spectral norms of Kronecker and Hadamard products ofthe r-matrices Aand B. 

• A Kind of Generalized Inverse Eigen-pairs Problem for Fixed-Free Mass-Spring System

  Huang Xiantong

  2018, 38(3-4): 69-84. doi:

  Abstract ( 1187 )   PDF (589KB) ( 205 )   　　

  This paper discusses the problem for constructing a kind of fixed-free mass-spring system by solving a kind of generalized inverse eigen-pairs problem. The conditions of solvability and the expression of solution are derived. The numerical algorithms and some numerical examples are given.

• The Perturbed BFGS Method for the Unconstrained Optimization with the Armijo Line Search

  Yan Jiaojiao

  2018, 38(3-4): 85-92. doi:

  Abstract ( 1247 )   PDF (310KB) ( 239 )   　　

  A perturbed BFGS method was proposed in[3]to solve the unconstrained optimization and was proved to be globally convergent when the Wolfe line search is used.In this paper,we show that the perturbed BFGS method also possesses global convergence for nonconvex problems with the relatively weaker Armijo line search.Numerical results show that this method with the Armijo search is also promising. 

• A New Perturbed BFGS Method for Unconstrained Optimization Problems

  Chen Fei

  2018, 38(3-4): 93-100. doi:

  Abstract ( 1178 )   PDF (299KB) ( 225 )   　　

   Based on the idea of constrained optimization and the BFGS method in unconstrained optimization,this paper presents a new perturbed BFGS method for the unconstrained optimization.We prove that the proposed method has global convergence for nonconvex optimization problems.Numerical results show that this method is efficient. 
  

  
  

• Combined Forecasting of Improved Multidimensional Grey Model and Support Vector Machine

  Liang Zhixun, Yuan Quan, Zeng Xiangyan

  2018, 38(3-4): 101-110. doi:

  Abstract ( 1263 )   PDF (562KB) ( 350 )   　　

  Support vector machine improves the generalization ability through the principle of structural risk  minimization.It is mostly used to solve the classification problem and regression problem of small samples.However,when used for prediction,a single model has certain limitations.In this paper,an improved multi-dimensional gray model and a support vector machine combined forecasting model are proposed.The combined forecasting model realizes the complementary advantages of different models,and can avoid the limitations of  the single model,increase the stability of the model.The experimental simulation results show that the proposed combined forecast.The prediction effect of the model is significantly better than the support vector machine and the innovation-based prioritization method,the prediction accuracy of the combined prediction  model is higher than that of the single prediction model. 
  

  
  

• A Note on the Harmonic Mean Limit Theorem of Stochastic Transition Probability of Finite Nonhomogeneous Markov Chains

  Li Shilin, Yang Weiguo

  2018, 38(3-4): 111-113. doi:

  Abstract ( 1267 )   PDF (151KB) ( 256 )   　　

  This note points out that the result about the harmonic mean limit of stochastic transition probability of finite non-homogeneous Markov chain is a corollary of the strong limit theorem for any random adaptive  sequence. 

• The Evaluation Model of Football Striker Athletes in Higher Vocational Colleges Based on Analytic Hierarchy Process

  Duan Zhenhua, Hu Peiyong , Dai Liutong

  2018, 38(3-4): 114-122. doi:

  Abstract ( 1195 )   PDF (620KB) ( 478 )   　　

  The evaluation model of selecting football striker athletes in higher vocational colleges is established  by using document literature,expert consultation and other methods to screen out the evaluation indicators of  excellent striker athletes by combining the specific data under the indicators of football striker athletes.Analytic Hierarchy Process(AHP)is also used to evaluate athletes comprehensively so that the selection of football athletes is more scientific and operable. 

• A Theorem Related to Matrix Exponential Function and Its Teaching Method

  Zheng Yan

  2018, 38(3-4): 123-128. doi:

  Abstract ( 1364 )   PDF (226KB) ( 506 )   　　

  This paper introduces a very useful theorem for calculating matrix exponential function,and discusses its introduction and treatment in teaching.