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2016, Vol. 36 No. 4   Published date: 30 December 2016
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• The New Criteria of Generalized Nekrasov Matrices

  Su Anbing, Liu Jianzhou, Ding Biwen

  2016, 36(4): 1-7. doi:

  Abstract ( 1918 )   PDF (265KB) ( 389 )   　　

  Generalized Nekrasov matrices have wide applications in economic mathematics,control theory and numerical algebra.In this paper,we consider the criteria of generalized Nekrasov matrices.Firstly,by applying inequality techniques and constructing positive diagonal matrix factors,we obtain several new criteria of generalized Nekrasov matrices based on the matrix elements, which extend some of the recent results.Then we give corresponding numerical examples to illustrate the effectiveness of the derived results.

• Flag-transitive Non-symmetric 2-designs with at Most 20 Points

  Liu Yan, Zhou Shenglin

  2016, 36(4): 8-17. doi:

  Abstract ( 1980 )   PDF (356KB) ( 346 )   　　

  In this paper,we study the classification of flag-transitive nonsymmetric 2-(v,k,λ)designs with v ≤20.We prove that if(r,λ)=1then there are exactly 18non-isomorphic designs.

• BZ Derivations to the Lie Algebra of 4×4 Antisymmetric Matrices Over a Commutative Ring

  Liu Weili, Zhang Meili, Lu Huimin, Xie Jun

  2016, 36(4): 18-22. doi:

  Abstract ( 2159 )   PDF (202KB) ( 648 )   　　

  Let Rbe a 2-torsion free commutative ring with identity.In this paper the decomposition of an arbitrary BZ derivation to the Lie algebra L4(R)of all 4×4antisymmetric matrices over Rand a sufficient and necessary condition for a BZ derivation to be an inner derivation are given.

• A Conjugate Gradient Iterative Algorithm for Hermitian Solutions of Matrix Equations with Constraints

  Yue Xiaorong, Zhou Fuzhao

  2016, 36(4): 23-28. doi:

  Abstract ( 1959 )   PDF (234KB) ( 219 )   　　

  In this paper,we give a conjugate gradient iterative algorithm for Hermitian solutions of matrix equations under submatrix constraints.First,we transform the equations into two lower-order equations,then we construct a gradient iterative algorithm by conjugate gradients for lower-order equations to obtain the solutions and the optimal approximation of the matrix equations.Finally some numerical examples are given to verify the effectiveness of this method.

• An Inexact Regularized Newton Method for Monotone and Nonlinear Equations and its Local Convergence

  Li Weifei

  2016, 36(4): 29-35. doi:

  Abstract ( 1991 )   PDF (566KB) ( 402 )   　　

  This paper presents an inexact regularized Newton method for monotone and nonlinear equations. Under relatively weak local error bound conditions,we show that the proposed method converges quadratically.This method is a generalization of the exact regularized Newton method proposed by Fan and Yuan[4].

• Non-adjacent Vertices Neighborhood Union Condition for Fractional(g,f,m)-deleted Graphs

  Zhong Jiemei , Gao Wei

  2016, 36(4): 36-43. doi:

  Abstract ( 1943 )   PDF (299KB) ( 295 )   　　

   A graph G is called a fractional(g,f,m)-deleted graph if the resulting graph admits a fractional(g,f)-factor after any medges are deleted.In this paper,we prove that if Gis a graph of order n,1≤a ≤g(x)≤f(x)-Δ≤b-Δ for any x∈V(G),δ(G)≥(b-Δ)(b+1)/a+2m,n≥(a+b)(2(a+b)+2m-1)/(a+Δ), and|NG(x1)∪NG(x2)|≥(b-Δ)n/(a+b) for any non-adjacent vertices x1 and x2,then G is a fractional(g,f,m)-deleted graph.The result is tight on the neighborhood union condition in some sense

• A Logarithmic Criterion for L¹ -convergence of a Bisexual Branching Process in a Random Environment

  Zhou Yuanzheng, Wang Yuejiao, Qiu Yumei

  2016, 36(4): 44-49. doi:

  Abstract ( 1964 )   PDF (251KB) ( 492 )   　　

  In this paper,the L¹-convergence of a bisexual branching process in a random environment normalized by the upper bound of the conditional mean growth rate is investigated.A necessary and sufficient condition for theL¹-convergence of the logarithmic criterion is given.

• Several Properties of the OROD Method for Solving the Sylvester Equation AXB+CX=D

  Deng Jianping

  2016, 36(4): 50-56. doi:

  Abstract ( 1961 )   PDF (536KB) ( 398 )   　　

  This paper presents several properties of the OROD iterative method(orthogonal residual method and the orthogonal direction method)for solving the Sylvester equation AXB+CX= D.It is showed that the corresponding error sequence decreases monotonely.The minimization property of the method is precisely characterized.A numerical example is presented in the end.

• Initial Boundary Value Problem to a Generalized Kawahara Equation on a Bounded Interval or a Half-line

  Lu Meihong, Mi Cailian, Yang Han

  2016, 36(4): 57-71. doi:

  Abstract ( 2134 )   PDF (552KB) ( 378 )   　　

  In this paper,we study the initial-boundary value problem to a generalized Kawahara equation on a bounded interval or a half-line.The energy integral method,the inequality technique and the embedding theorem are used to establish a prior estimate of the solution,and the existence and uniqueness of the global regular solution on a bounded interval are showed by the principle of contraction mapping.It is proved that the L2-norm of the solution has exponential decay when the time tends to infinity. Furthermore,under a stronger condition on the initial boundary values,the existence of a global regular solution on a bounded interval which is independent of the length of the bounded domain,and the existence of a unique global regular solution on a half

  -line are derived.

• The Survey and Analysis on the Aged People’s Life Quality in Changsha City First Social Welfare House

  Su Hui, Zhu Enwen, Qing Qingping

  2016, 36(4): 72-80. doi:

  Abstract ( 1994 )   PDF (297KB) ( 229 )   　　

  In this paper,we investigate the aged people’s life quality by aquestionnaire survey on 100aged people lived in Changsha city first social welfare house.The classifications of K-means clustering upon the indexes of physiology,psychology,social relations and environments,and upon the self-assessment scores of life quality,respectively,show that the life quality of those aged people is slightly higher than the basic level. The single factor variance analysis indicates that the life quality is of statistical significance at difference of genders, marital status and pensions,but of non-statistical significance at difference of ages and education.And the correlation analysis demonstrates that the life quality of the aged people is positively correlated to the indexes of physiology, psychology,social relations and environments.It is found by stepwise regression that the main factors affecting the life quality of the aged people are the pension,the social relations,and the environment. The results of this study suggest that we should develop targeted measures based on the current situation and affecting factors to improve the life quality of the aged people in the welfare house.

• Investigation and Analysis on WeChat Payments Among College Students in Changsha City

  Chen Jing, Gu Xiaoxiao, Zhu Enwen

  2016, 36(4): 81-91. doi:

  Abstract ( 2113 )   PDF (2110KB) ( 980 )   　　

  With the rise of e-commerce in the internet era,the online shopping has become a new consumer trend.With the rapid development of WeChat in the past few years,WeChat payments have greatly changed the pattern of Alipay or other third-party payment  platform monopoly market.In nowdays,college students as one of the main groups of WeChat payment and third-party payment will affect the future of WeChat＇s development to a large extent.A sampling survey via distributing questionnaire to college students in Changsha city is carried.Sample data are analyzed with the statistical software SPSS and Excel,and some suggestions are

  given based on the results from the data.

• Sample Learning Based on λ -increasing Function

  Li Jingjing, Tian Dagang

  2016, 36(4): 92-105. doi:

  Abstract ( 1942 )   PDF (451KB) ( 607 )   　　

  How to determine the structure of a neural network is often an aporia in theoretical research and practical application.Based on the recent research of Vugar E.Ismailov,this paper study the learning method of sample points in neural network.The results show that with theλ -strictly increasing function,any specified sample set can be learnt by using only two neurons in hidden layer.The differences between using the usual Sigmoid function andλ -strictly increasing function as active function in the hidden layer are presented as well.

• Application of Copula Function in Financial Market

  Dong Zhiqian, Li Xingye

  2016, 36(4): 106-115. doi:

  Abstract ( 2129 )   PDF (4470KB) ( 766 )   　　

  The paper studies the correlation between the stock market and the real estate stock(Vanke)and the tail dependence by establishing a copula model.Marginal distributions of the stock market and the real estate stock are estimated by the non-parametric kernel density estimation method.An optimal copula model is constructed by making use of the bivariate distribution histogram,quantile-quantile(Q-Q)plot,square Euclidean distance.Parameters in the model are estimated by the maximum likelihood estimation(MLE)method.Q-Q plot is applied on the test data without distribution function.The results show that the Binary t-copula model can fit the joint distribution of market and Vanke better than other models,the market and Vanke stock have a strong positive correlation,and the tail dependence under extreme cases is lower than the positive correlation under general cases.

• Application of GM (1,1)Model Based on Least Square Method in Vegetable Yield Forecast in China

  Wang Jie, Wang Bo

  2016, 36(4): 116-124. doi:

  Abstract ( 1960 )   PDF (660KB) ( 471 )   　　

  Since 2011the production and output of vegetable in China have exceeded that of grain and become the largest agricultural product so that its production affects the stability of the national market.Owing to the production of vegetable being affected by many factors,the available data of the production have three shortages: large volatility,small sample size and poor information. In order to predict the vegetable yield in China in a short term,we apply a GM(1,1)model based on least square method and the gray system prediction theory, where the least square method is used to weaken the large fluctuation of data and to reduce the randomness. The predicting model is established with the vegetable production data of 2009to 2014and is showed with the data of 2014to have good forecasting accuracy.The forecasting results show that the production of vegetable will continue to increase in the next three years,which can provide some references for other related prediction, for facilitating the macro-regulation to the future vegetable market to maintain market balance and avoid risks of price fluctuation.

• Parallel Algorithm to the Inverse of Cyclic Toeplitz Matrices

  Xu Wenhua

  2016, 36(4): 125-128. doi:

  Abstract ( 2005 )   PDF (166KB) ( 715 )   　　

  Toeplitz Matrices and theirs related equations have a wide application in mathematics,engineering and scientific calculation.This paper introduces the parallel algorithm to the inverse of cyclic Toeplitz Matrices.