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2017, Vol. 37 No. 1   Published date: 30 March 2017
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• The Shifted Sine Preconditioner for Real Symmetric Positive

  Liu Zhongyun , Wu Nianci , Qin Xiaorong, Zhang Yulin

  2017, 37(1): 1-6. doi:

  Abstract ( 1267 )   PDF (692KB) ( 240 )   　　

  This paper studies the solution of real symmetric positive definite Toeplitz matrices by the preconditioned conjugate gradient method.Based on the fact that the real symmetric Toeplitz matrix admits a triangular transform splitting(TTS),we propose the shifted Sine preconditioner TS,the spectral properties of the preconditioned matrix are analyzed,and the arithmetic complexity is discussed.The numerical experiments show that our preconditioner is more effective than T.Chan＇s preconditioner[2].

• Oscillation of Solutions for a Class of Nonlinear Neutral Differential Equations

  Long Cheng, Liu Yi, Xie Yongqin

  2017, 37(1): 7-15. doi:

  Abstract ( 1378 )   PDF (331KB) ( 206 )   　　

  In this paper we study the oscillation of certain third-order nonlinear neutral differential equation with distributed delay by using non-classical Riccati transformation and integral averaging.We establish some new sufficient conditions which ensure that every solution of this equation oscillates or converges to zero.Our results essentially improve and complement the known results in the literatures recently.

• Analysis on Effects of Opening Residential Area on Road Capacity with Jackson Queueing Networks

  Peng Yi, Zhou Huanyu, Zhou Meilin, Li Jian

  2017, 37(1): 16-24. doi:

  Abstract ( 1360 )   PDF (1541KB) ( 270 )   　　

  In this paper,by applying the discrete event dynamic system modeling method a Jackson queueing network model is established to study the effects of opening residential area on road capacity with two examples. The road traffic states in surrounding area are deeply analyzed by using some performance measures of Jackson queueing networks.Based on our results,some suggestions about whether or not to open residential area according to the environment of surroundings,road traffic flow,road capacity,convenience to the transportation of citizens and the safety are provided.

• The Decay Parameter of Stopped M^X/M³/1 Queueing Model

  Li Yanyun

  2017, 37(1): 25-31. doi:

  Abstract ( 1223 )   PDF (272KB) ( 177 )   　　

  In this paper,we discuss the stopped M^X/M³/1queueing model,which stops when the system hits the states 0,1,2.The exact value of decay parameter for such model is obtained.It is determined by the generating function of the Q -matrix.
  

  
  

• Posteriori Error Estimates for the Variable BDF₂ Method for Parabolic Equations

  Zhao Xinyang, Wang Wansheng

  2017, 37(1): 32-37. doi:

  Abstract ( 1327 )   PDF (227KB) ( 234 )   　　

  In this paper the posteriori error estimates to the variable BDF2method for linear parabolic equations are given by reconstructing numerical solutions via interpolation to the equations.

• Solving a Class of Matrix Equations by Sparse Approximate Inverse Preconditioning

  Deng Miao, Zhou Fuzhao

  2017, 37(1): 38-43. doi:

  Abstract ( 1269 )   PDF (231KB) ( 584 )   　　

  In this paper a F-norm minimization based sparse approximate inverse preconditioning for solving a class of matrix equations is given.Firstly,the effective preconditioner is find by the F-norm minimization based sparse approximate inverse preconditioning technique,then a algorithm is given by applying the obtained preconditioner in the orthogonal projection iteration method and the convergence of the algorithm is showed. Finally,a numerical example is presented to verify the effectiveness of the algorithm.

• A Generalization of The Generalized Entropy Ergodic Theorem for Nonhomogeneous Markov Chains

  Sun Pengfei, Yang Weiguo

  2017, 37(1): 44-49. doi:

  Abstract ( 1213 )   PDF (243KB) ( 260 )   　　

  In this paper we give a generalization to the generalized entropy ergodic theorem for nonhomogeneous Markov chains given by Wang and Yang in[4].

• Improvements of Two Kinds of Stability Theorems

  Yang Mo, Fan Yingfei

  2017, 37(1): 50-56. doi:

  Abstract ( 1271 )   PDF (488KB) ( 371 )   　　

  In this paper,two kinds of stability theorems are improved.By the property of the Kfunction,the property of the function’s derivative in original Markin stability theorem is extended from the finite time to the infinite time,and this brings the new method to get the stability of the solution of the nonautonomous differential equation.By the supplement of the integral convergence theorem ,the new theorem is further improved and promoted,and a new determination method about uniform stability is obtained.

• A New Auxiliary Function-based Integral Inequality

  Liu Hua , Qiu Sai-Bing

  2017, 37(1): 57-60. doi:

  Abstract ( 1355 )   PDF (166KB) ( 214 )   　　

  Integral inequality is an important tool to study the stability of delayed systems.In this paper,a general auxiliary function and a energy function are constructed.Based on the orthogonality of functions,a new integral inequality is derived,which extends the Jensen integral inequality.

• Neural Network Weight-Threshold Optimization Method Based on LASSO

  Huo Jianguang, Ren Guizheng, Yang yang

  2017, 37(1): 61-66. doi:

  Abstract ( 1337 )   PDF (1725KB) ( 207 )   　　

  Based on the LASSO method and neural network,we establish a LASSO-BP algorithm.Compared with the BP neural network algorithm and the RBF algorithm,it has the advantages of time-consuming, strong anti-interference ability and  better effects on classification.Its effectiveness is verified by numerical experiments.

• Study of Correlations Between the Cash Flow of High-value Payment System in the People’s Bank of China and the CPI

  Lin Qiao , Zhu Enwen , Chen Li

  2017, 37(1): 67-72. doi:

  Abstract ( 1311 )   PDF (409KB) ( 192 )   　　

  The high-value payment system (HVPS)provides fast,efficient and secure payment services for enterprises and financial markets and prevents payment risks.This paper investigates the correlations between the cash flow changes of the People＇s Bank of China(PBS)in Hunan province and the economic index CPI in Hunan province by building a regression model.The results show that there is a highly positive correlation between the cash flow changes and the CPI.By using the regression model,we can predict the CPI and provide an effective method for the local government to make economic decisions.

• A Bidding Model Under Non-cooperation Mode Based on Least Squares

  Zhou Shuaihu, Ni Nianyong, Wang Cong

  2017, 37(1): 73-80. doi:

  Abstract ( 1209 )   PDF (278KB) ( 204 )   　　

  The Least Squares Optimization Model with constraints is used to study the bidding problem of two adjacent batches of goods with dynamic float ratio under non-cooperative mode,where the average price of each type of goods and the optimal bidding of each batch are adopted.The model is applied in a real bidding invitation of national grid capacitor project.The results show that the bidding model presents satisfactory performance and has good viability.Some suggestion on the formula of benchmark price B =A_l×(1-a)is given in the end.

• An Ant Colony Optimization Algorithm for Multi-criteria Degree-constrained Minimum Spanning Tree

  Wei Xin, Ma Liang, Zhang Huizhen

  2017, 37(1): 81-89. doi:

  Abstract ( 1253 )   PDF (772KB) ( 256 )   　　

  Both multi-criteria minimum spanning tree problem and degree-constrained minimum spanning tree problem are NP-hard problems in network optimization.They always have many important applications in practice.To solve the minimum spanning tree problem by considering both the multi-criteria and degreeconstraints, this paper proposes an algorithm (coded in Delphi)which is based on the ideas of ant colony optimization. The computational numerical experiments show the efficiency and effectiveness of the algorithm for the multi-criteria degree-constrained minimum spanning tree problem.

• Solving Vehicle Routing Problems with the Greedy Randomized Adaptive Bat Algorithm

  Sun Qi , Zhang Huizhen

  2017, 37(1): 90-99. doi:

  Abstract ( 1232 )   PDF (778KB) ( 462 )   　　

  The Vehicle Routing Problem(VRP)is a worth researching NP-Hard problem in logistic and supply chain.The Bat Algorithm (BA)is a new intelligent optimization algorithm having broad application prospect. But it can’t use to solve discrete problem directly,and just like most intelligent optimization algorithms, it may easily fall into local optimum and its convergence rate is very slow in the late stage of the algorithm.In this paper,in view of the specific characteristics of the VRP,we redefine the coding mode and use GRASP to generate the initial population of BA to improve the algorithm,and then apply it to solve the VRP.

• Study on Water Level Regulation Based on Gauss-like Mixed Model

  Zhou Lin, Tang Yijing, Dai Binxiang, Liu Xiaoqun

  2017, 37(1): 100-111. doi:

  Abstract ( 1229 )   PDF (2793KB) ( 166 )   　　

  Function fitting is an important data mining technique.In this paper,the modified Gauss type mixed model is applied to the study of the changing pattern of the water level in order to make accurate prediction of the water level.Firstly,we make a pretreatment of the ten years data of the water level and establish a Gauss-like mixed model which satisfies the smallest loss function via curve fit.Then,we construct an overdetermined linear equations and use the least square method to obtain the corresponding weight.Finally,we get a weighted model and examine the rationality of the model and make some improvements.

• Investigation and Analysis on the Life Quality of Orphans in the First Social Welfare Institute of Changsha

  Dong Manxin, Zhang Shidi

  2017, 37(1): 112-121. doi:

  Abstract ( 1416 )   PDF (1467KB) ( 375 )   　　

  With the improvement of people′s living standard,clinical studies on the quality of life and psychological research have drawn more and more attentions.The quality of life is a comprehensive evaluation of a personal life.However compared with the investigations and studies on the life quality of adults,there are very few investigations and studies on the life quality of teenagers and young children,especially on that of the disabled orphans in orphanages.In this paper,a survey on the life quality of orphans in the first social welfare institute of Changsha is carried out.Some scales suitable for evaluating life quality of disabled children are adopted. A normal children group is taken as a contrast group.Scoring and processing of the obtained data are firstly taken with the EXCEL,and the principal component analysis is then made with the software SPSS.Upon the survey and analysis,problems concerning the life quality of orphans are put forward,and suggestions for solving the problems are given.

• An Empirical Analysis on the Impact of China′s Import and Export Trade on Taxation

  Li Junjun, Wang Liwen, Fang Qiulian

  2017, 37(1): 122-128. doi:

  Abstract ( 1324 )   PDF (1589KB) ( 335 )   　　

  Based on the time series data of GDP import and export,and tax from 1978to 2014,this paper analyzes the impact of import and export trade on taxation by establishing the error correction model and utilizing the impulse response and variance decomposition.The empirical results show that the short-term effect of import and export trade on tax is smaller than the short-term effect of GDP on tax,but the long term effect is stronger has the characteristics of strong than GDP has the characteristics of strong;the effect of import and export trade on tax revenue increases over time significantly,which matches China′s economic development at the present stage.