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2017, Vol. 37 No. 3-4   Published date: 30 December 2017
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• The Central Symmetric Class Solution and Optimal Approximation to Generalized Sylvester Matrix Equations

  Zhou Fuzhao, Chen Lu

  2017, 37(3-4): 1-16. doi:

  Abstract ( 1237 )   PDF (525KB) ( 283 )   　　

  In this paper an iterative algorithm for solving the generalized Sylvester matrix equations is firstly  constructed by using the conjugate gradients and the matrix properties and the convergence of the algorithm is  proved.Furthermore,when the equation is compatible the algorithm is proved to converge to the minimal  norm solution to the problem.Then the algorithm is modified slightly to obtain the corresponding optimal approximation. Finally,numerical examples are given to verify the validity of the algorithm. 

• The Study of Numerical Solutions to a Class of  Overdetermined System of Nonlinear Equations

  Huan Xiang

  2017, 37(3-4): 17-25. doi:

  Abstract ( 1411 )   PDF (1065KB) ( 488 )   　　

  In this paper four numerical methods for solving the overdetermined system of nonlinear equations  are introduced.The Enumeration method and the Monte Carlo method are improved and combined into a  Monte Carlo-Enumeration method.These numerical methods are applied to solve the over determined system  of nonlinear equations which established at the base of the technology for positioning with the shadow of sun,advantages and disadvantages of each algorithm is analyzed according to the results of numerical experiments.At last,the computing time and accuracy of each algorithm are compared with numerical examples,the effiiency of each method and the high efficiency of Monte Carlo-Enumeration method are verified. 

• Stability and Posteriori Estimates for the Variable Step-size BDF2 Method to Parabolic Equations with Delay

  Wang Wei , Wang Wanshe

  2017, 37(3-4): 26-37. doi:

  Abstract ( 1346 )   PDF (410KB) ( 409 )   　　

  Parabolic equations with delay has been widely appeared in scientific and engineering fields.In this  paper we consider the time approximation of parabolic equations with delay.Firstly,we prove the stability of  variable step-size BDF2method for parabolic equations with delay.Then,we derive a higher order numerical  approximation by reconstruction.Finally,we obtain a posteriori estimates of variable step-size BDF2 method for the equations.

• A Fast Algorithm for Computing Products of Hermitian Toeplitz Matrices and Vectors

  Liu Zhongyun, Chen Siheng, Xu Weijin, Zhang Yulin

  2017, 37(3-4): 38-42. doi:

  Abstract ( 1515 )   PDF (209KB) ( 322 )   　　

  It is known that the product Axof a large scale Hermitian Toeplitz matrix Aand a vector xcan be computed effectively by using the Fast Fourier Transform(FFT).In this paper,based on the fact that an Her-mitian Toeplitz matrix Acan be reduced into a real Toeplitz-plus-Hankel matrix(A=T+H)by a unitarysimilarity transformation(the unitary matrix is U=1/√2(I-iJ), we develop a more efficient algorithm thatonly O(n)complex arithmetics are included for computing the product Ax by employing the DCT and DST.

• Research of Human Machine Identification for Sliding Verification Code Based on Neural Network

  Liang Xiaolin, Chen Linping

  2017, 37(3-4): 43-50. doi:

  Abstract ( 1238 )   PDF (659KB) ( 306 )   　　

  In the process of sliding verification,it is very important to distinguish whether the drill author is “machine”or“personal”.In this paper,we use the neural network algorithm and MATLAB software to make an empirical study and analysis on the characteristics of the sliding trajectory extraction left by human and machine,and establish the classification model of the neural network to predict the operator.The results show  that the BP neural network model has high prediction accuracy and provides a guarantee for network security to some extent.

• Weyl Fractional Integral andα-form Solutions to Complex Second Order Differential Equations

  Chen Zhenchao, Huang Bing

  2017, 37(3-4): 51-58. doi:

  Abstract ( 1290 )   PDF (303KB) ( 197 )   　　

  In this paper we introduce the concept ofα-form solutions to complex differential equations,andive a kind of negative powerα-form solution to the complex differential equation t² z″(t)- (bt+ c)z′(t)+βz(t)=0by employing the Weyl fractional integral,and furthermore the necessary and sufficient conditions that the equation allows a polynomial solution are concluded. 
  

  
  

• Bifurcation Continuation of a Discrete Hindmarsh-Rose Model

  Li Bo

  2017, 37(3-4): 59-63. doi:

  Abstract ( 1320 )   PDF (620KB) ( 218 )   　　

  In this paper,different kinds of bifurcation of a discrete Hindmarsh-Rose model is considered by bifurcation continuation theory,and numerical simulations are provided to explore the complex dynamics,especially the conversion between different neural behaviors. 
  

  
  

• A Hybrid Partheno Genetic Algorithm for Solving Vehicle Transportation Problems

  He Yifan, Zhang Hongyan

  2017, 37(3-4): 64-77. doi:

  Abstract ( 1302 )   PDF (2034KB) ( 290 )   　　

  In this paper we employ the Hybrid Partheno Genetic Algorithm(HPGA)to solve a vehicle transportation problem.The constrained optimization problem is transformed into an unconstrained optimization  problem by applying apenalty function,and the HPGA uses the serial number coding method to carry on the  computation.When generating the initial population,the vehicle serial number is inserted in the quasi-chro-mosome to generate the subpaths that meet the constraints as much as possible,and the subpaths are splicednto a complete transportation path to reduce the calculation amount of the penalty function.The elitist strategy  is embedded in the selection operation,which guarantees the global convergence of the algorithm.Parental  crossover operations are eliminated and each chromosome independently changes gene to produce new individual,to avoid premature convergence phenomenon.Neighborhood search are introduced so that HPGA can focus on some designated areas of search,to speed up the algorithm in the optimal solution near the optimization speed.Finally,the classical vehicle routing problem is used as the test model of HPGA,and the numerical ex-periments are carried out by Christofides and Eilon＇s standard VRP test.And by comparing to other algorithms it is verified that the HPGA has smaller calculation,faster convergence speed and does not produce premature convergence.
  

  
  

• Prediction of Consumption Peak of Electrolytic Copper in China Based on a Grey Verhulst-BP Neural Network

  Huang Xiaofeng, Liao Lipei , Zhu Hao

  2017, 37(3-4): 78-92. doi:

  Abstract ( 1289 )   PDF (1368KB) ( 280 )   　　

  This paper selects the typical industry data of copper and copper consumption in China in the years 1999-2015and applies the adaptive-Lasso method to analyze and identify the key industries that affect the consumption of copper in China.Based on the analysis,a combined model of grey Verhulst and BP neural net-work is constructed,and the consumption of copper in China is predicted by this model.The peak of copper consumption in China will arrive in the years 2020-2026,with a peak range of 990×10⁴-1300×10⁴ tons.And we suggest that the copper smelting production capacity should be controlled within 1280×10⁴-1690× 10⁴tons,and the new smelting investment should be suppressed so as to avoid overcapacity. 

• Study of Influence Factors of Private Car Ownership Based on Regression Analysis

  Ge Guangjin

  2017, 37(3-4): 93-97. doi:

  Abstract ( 1352 )   PDF (226KB) ( 424 )   　　

  To understand the influence factors of private car ownership in Hebei province,data of private car from 2005to 2015is collected.Private car ownership is chosed as an explained variable,five explanatory variables are selected by least squares regression.It is found that the main influencing factors of private car ownership in Hebei province are the highway mileage,density of urban population and urban per capita disposable income.Some suggestions are put forward according to the influencing factors. 

• Comparison of Price-to-Earning Ratios Between China＇s Listed Banks and Security Companies

  Lu Xiner, Rao Haiqing

  2017, 37(3-4): 98-109. doi:

  Abstract ( 1243 )   PDF (1083KB) ( 242 )   　　

  Price-to-earning(P/E)ratio is an important basis for investment valuation.It is observed that  the P/E ratios of China＇s listed banks and security companies are significantly different,though they are both  financial enterprises.This paper studies the impact of macroeconomic variables on P/E ratios.Empirical analysis with the market open data shows that the monthly average P/E ratio of the listed banking industry is negatively correlated with China＇s accumulated value of fiscal revenue and positively correlated with China＇s accumulated value of fiscal expenditure,while the monthly average P/E ratio of the listed security companies is negatively correlated with the supply growth rate of narrow money.

• Simple Proof to Three Euler-type Combinatorial Identities

  Ding Ding

  2017, 37(3-4): 110-114. doi:

  Abstract ( 1164 )   PDF (206KB) ( 308 )   　　

  In this paper we present some simple proofs to three combinatorial identities of double zeta values.

• A Mathematical Model for Parameter-Calibration and Imaging of CT System

  Yang Yunxia

  2017, 37(3-4): 115-121. doi:

  Abstract ( 1359 )   PDF (3704KB) ( 718 )   　　

  Abstract In this paper,firstly,by fitting the CT scan received information with the MATLAB software,a  series of images about the parameter-calibration and imaging of a CT system are obtained.And then,based on the received information and the obtained images,a mathematical model is established for the parameter-calibration and imaging of the CT system.

• The Analysis of Teachers’Transformation in Applied Universities Based on the Incentive Theory

  Xiao Haiyan

  2017, 37(3-4): 122-128. doi:

  Abstract ( 1084 )   PDF (257KB) ( 151 )   　　

  As the subject of application-oriented university,the behavior of teachers is influenced by thetransformation incentive mechanism.Universities regulate teachers＇behavior through incentive mechanism,and  teachers obtain income and avoid risks through their own efforts.In application-oriented universities,wemust construct a double-qualified teachers team which can meet the demand of talent cultivation.Therefore, it is necessary for university teacher to become a double-qualified teacher.Based on the previous studies,we  try to use the principal-agent theory,regarding university administrator as the principal and the agent for the  teacher,to analyse the principal-agent relationship between university administrators and teachers.We will  establish a principal-agent model of multi principals and multi agents how the university administrator effectively encourage teacher transforming to a double-qualified teacher.It can improve the transition rate.