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January 15,2009
Volume 2,Issue 1
Pages 1-113
Subject Area:Applied Statistical Mathematics,Fuzzy Mathematics,Dynamical System,Correlation Regression Analysis,Applied Mathematics

Title: The prediction of China’s population growth

Authors: WANG Shuopeng, LIU Shuran, ZHOU Hongwei, ZHOU Shengwu
PP: 61～67
Abstract: The coordination of solving the population problem is important for economic and social sustainable development of China. In this paper, a detailed analysis of the common models used for predicting population has been presented and the shortcomings when they are applied under the practical conditions have been pointed out. Considering the age of the population, the fertility and mortality of different ages,and other factors, the total population of the year from 2010 to 2050 is predicted and good results are obtained by establishing the population discrete model and the improved queue elements model.
Keywords: applied mathematics; population forecast; population discrete model; queue elements model

Title: A note on the step-sizes of gradient-like methods for solving convex quadratic programming

Authors: HE Bingsheng, CUI Ruiyun, LI Min, SHEN Yuan, XU Minghua, YUAN Xiaoming
PP: 1～9
Abstract: When a class of gradient-projection methods for constrained convex quadratic programming is applied to the unconstrained one, it can be viewed as the steepest descent method with a reduced step-size. It is observed that the numerical performance is improved considerably via scaling the step-sizes simply by a multiplier in ［0.3, 0.99］. The further experiments indicate that the step size can vary in a range around the step size of the steepest descent method. To speed up the convergence, a certain ratio of short step size should be adopted during the iterations. While the steepest descent method is being applied, line search with high accuracy will lead to an extremely slow convergence. Thus it is unnecessary and harmful.
Keywords: operations research; unconstrained convex quadratic programming; negative gradient methods; line search accuracy

Title: Application in the prediction of stock market based on grey Markov chain model

Authors: WANG Lixia, XIA Letian
PP: 109～113
Abstract: Based on the grey prediction model and Markov chain prediction theory, grey prediction GM(1,1) model is combined with Markov chain-state transition and the theory of grey-Markov chain prediction model is expounded and applied to the prediction of stock market. Using GM(1,1) model to predict has good accuracy and regularity, but to the stock market with large random fluctuation, its accuracy is lower. Markov model can overcome this defection, so combining GM(1,1) with Markov chain model to predict stock market can improve the precision of prediction. Based on the indexes ended in the twenty months in Shenzhen Stock Exchange, the range of the index in the end of next four months is predicted, and example is given to prove its reliability in the application of the prediction of stock market.
Keywords: Markov process; Markov chain; grey system; state transition; predict; the index of market close in the end of month

Title: The neural network forecast model for graduate employment

Authors: WU Chaojian, ZHANG Tongjie
PP: 105～108
Abstract: This paper establishes the model of the graduate employment by using the BP neural network. The model uses the main factors which affect the graduate employment as the input of the neural network, and makes the graduate employment which has been known as the output of the neural network. The model is trained according to network with known data using Matlab’ procedure, and then the result is obtained. After testing the credibility of the result, it can be seen that the credibility of the model reaches 95%. It shows that the model can go along with the actual situation well. At last, this paper gives examples to show how to use the model. Also, it is used to forecast some students’ situation. The result shows the graduate employment situation and then points out how the students should be educated.
Keywords: fuzzy mathematics; BP neural network; employment; forecast; training network; credibility

Title: The generalized Hermite solutions of matrix equation AX=B and the optimal approximation problem

Authors: LIANG Maolin, MA Weixue, WANG Sanfu
PP: 100～104
Abstract: If matrix P∈n×n is satisfied with P*=P+, it can be called generalized unitary matrix. For generalized unitary matrix P, if PAP=A*, A can be called generalized Hermite matrix. Using singular value decomposition (SVD) of matrix, this paper discusses the structures of these two kinds of matrices. Given matrices X, B∈n×m, the necessary and sufficient conditions of matrix equation AX=B with generalized Hermite solutions are derived, the expression of general solution is given too. Meanwhile, the optimal approximation problem of the given matrix is considered, and the associated algorithm is given.
Keywords: numerical algebra；matrix equation; generalized unitary matrix; generalized Hermite matrix; singular value decomposition; optimal approximation

Title: The application of corrected grey model in stock pricing prediction

Authors: SUN Xin
PP: 94～99
Abstract: With the development and improvement of China’s securities market and the process of internationalization, the stock market plays an important role in the economic life of the investment and financing. In current financial market turmoil period, a reasonable forecasting about the trend of stock prices and giving the investors an effective advice have become a top priority. To study the trend of stock prices, this paper builds the GM(1,1) model with residual amendment according to the gray system theory, and then takes use of the historical stock prices of Petro China to complete empirical analysis, and obtains a specific GM(1,1) model and the forecasted price. Meanwhile, it calculates the value of parameter a,u by the forecasted prices respectively, and gets the specific residual GM(1,1) model, and makes a residual amendment on the previous forecasted stock prices to obtain more accurate ones. Finally, it forecasts the stock prices of Petro China for next five days and finds a better buying (or selling) opportunity. The results show that the residual GM(1,1) model forecasts better in the short term, but does a very poor forecasting in the medium and long term. At the same time, it is found that the GM(1,1) model itself is a decreasing function, so the prediction of the stock prices usually shows a downward trend.
Keywords: applied mathematics; GM(1,1) model; stock pricing; prediction; corrected model

Title: Fuzzy optimization evaluation on management achievement of commercial bank

Authors: SUN Chaoqun, HUANG Jianyuan
PP: 90～93
Abstract: The commercial bank is an important part of financial market, and its management achievement impacts on the financial market even the entire national economy greatly. Therefore, it is important to choose a comprehensive evaluation method for the management achievement of commercial bank. The traditional evaluation method often assesses one or some certain indicators which are selected artificially, and then composes by weighting. Although this approach is simple and easy to operate, the subjective randomness is large. For overcoming the shortcoming in traditional method of achievement evaluation, this paper considers the management achievement of commercial banks synthetically and builds comprehensive achievement evaluation index system. Then it makes a positive analysis on four listed middle and small commercial banks in China with the fuzzy optimization model which is based on fuzzy sets theory and gets desired results.
Keywords: fuzzy mathematics；commercial bank; index system; fuzzy optimization

Title: Study on synchronization threshold of a one-way coupled delayed system

Authors: ZHANG Weiwei, ZHOU Shangbo, MAI Huanhuan, XIAO Ke
PP: 85～89
Abstract: Chaotic synchronization is always a hot topic of chaotic secure communication, but chaotic signals generated by some chaotic systems of low dimension can be deciphered without difficulty. Security will be threatened when it is used in communication. A delayed system as an infinite dimensional system can perform hyperchaotic behavior, which makes the signals hard to decipher, and new research area is developed. The paper investigates a one-way coupled time-delayed system based on the Krasovskii-Lyapunov theory, and derives the sufficient condition of the synchronization threshold of one-way coupled delayed system. Then it analyzes the references and corrects the mistakes. In the end, the result of computer simulation method proves the correctness of deduction.
Keywords: nonlinear science; chaotic synchronization; one-way coupled; time delay

Title: The exact variation speed of the unique entire solution to a singular boundary value problem for a class of second order nonlinear differential equations

Authors: FENG Huabing, ZHANG Zhijun
PP: 80～84
Abstract: By perturbation method and constructing new supersolution and subsolution, this paper derives the exact variation speed at infinity of the unique entire solution ψ to the following singular boundary value problem on the half-line u″(t)=b(t)g(u(t)), u(t)＞0, t＞0, u(0)=∞, u(∞)=0 where g∈C1［0,∞), g(0)=g′(0)=0, g is an increasing function in ［0, ∞), satisfies Keller-Osserman condition, g(s)/s is an increasing function in (0, ∞); b∈C1(0,∞) is a positive increasing function in (0,∞). The paper completes the characteristics of the unique entire solution.
Keywords: ordinary differential equation; boundary value problem; the unique entire solution; singularity; variation speed

Title: Growth in private car ownership and control issues

Authors: ZHANG Yuansi, XU Yunlong, SHI Yuwen, ZHANG Xingyong
PP: 73～79
Abstract: According to the estimation from China Association of Automobile Manufacturers, by the end of 2006, China’s private car ownership was about 26.5 million, accounting for 60% of the national car ownership approximately. The number of private cars directly affects national economic development and environmental issues. According to data, it forecast the private car ownership of this area in 2010, using computer simulation method of BP artificial neural network and the multiple regression model, it got the relationship of car ownership, per capita GDP and total retail sales of consumer goods for the entire society, and made a scientific forecasting for car ownership. Through the method of simulation hypothesis testing, it explained the feasibility of multiple regression model. The results of the two forecasting were identical.
Keywords: applied mathematics；BP artificial neural network model; multiple regression analysis model; upper optimal model

Title: The parameter estimation method of multi-dimensional linear regression

Authors: WU Shixun, ZHAO Dongfang, JIN Xiuyun
PP: 68～72
Abstract: Multiple linear regression model is used to show the dependent relationship between a kind of phenomenon and a variety of other phenomena. There are a lot of ways to estimate the parameters, such as the least square estimation method, the maximum likelihood estimation and so on. According to the Gauss-Markov theorem, through the analysis of parameter estimation value from the least square estimation method, this paper uses matrix decomposition method to get another estimation method, and gets the same estimator as the least square method from the minimum variance of the estimation. Moreover, the variance is the smallest of all the linear estimation.
Keywords: probability theory and mathematical statistics; least square method; parameter estimation; linear

Title: A strong law of large numbers for random variable functions

Authors: WU Xinxing, GUO Mingle
PP: 54～60
Abstract: Strong laws of large numbers for random variable sequences play an important role in probability theory. This paper discusses the strong laws of large numbers for random variable functions, and proves a strong law of large numbers for random variable functions by the analytical method. Furthermore, as a deduction, it obtains a strong law of large numbers for non-homogeneous Markov chain functions. The results in this paper extend some strong laws of large numbers for classical random variable sequences and non-homogeneous Markov chain functions in former literatures.
Keywords: probability theory and mathematical statistics; random variable functions; strong law of large numbers; non-homogeneous Markov chain functions

Title: Packing dimension of product sets for homogeneous Moran sets

Authors: HUANG Jinghua
PP: 48～53
Abstract: It is important to research the dimension of product sets in fractal geometry. The paper discusses the Packing dimension of product sets for homogeneous Moran sets. Let (I, {nk}k≥1, {ck}k≥1) denote the Moran collection determined by the closed interval I, the positive integer series {nk}k≥1, and a positive real series {ck}k≥1. Use the homogeneous structure of Moran sets and a special method of natrual covering to estimate the Packing dimension formula for E×F, where E, F∈ is satisfied with some conditions. And the Packing dimension of E×F is strictly less than the sum of Packing dimensions for E, F.
Keywords: fractal geometry; homogeneous Moran sets; homogeneous Cantor sets; partial homogeneous Cantor sets; Packing dimension

Title: An elementary deriving method of M-mand Haar wavelet filter

Authors: ZHANG Kun, ZHANG Wei, CUI Li
PP: 40～47
Abstract: M-mand Haar wavelet is one of the most basic M-mand wavelets, and wavelet filter is the basis of wavelet’s construction. Based on multiresolution analysis and the necessary and sufficient condition of symmetric and antisymmetric orthogonal wavelets, this paper defines coefficient symmetry to construct the coefficient of filter, and then derives the M-mand Haar wavelet filter. This elementary method is simple and intuitive, and some universal results are gained. This method can be used to construct wavelet filter according to the different requirements, so it can be expanded to construct some other similar wavelet filters.
Keywords: basic mathematics; M-mand Haar wavelet filter; elementary method; multiresolution analysis

Title: The recognition for English letters using Hopfield network

Authors: HAN Jichao, LIU Wuyin, LI Qian, GUO Sicong
PP: 33～39
Abstract: This article uses Hopfield network as content addressed storage to conduct pattern recognition of English letters image. Every letter is considered as an image and raw date is extracted from it, the extracted raw data is taken as the data of network studying, the correct weight is calculated and a network model is established. Then the English letter image which needs to be recognized is substituted into the network and the recognition is carried out. This article analyzes how the Hopfield network is used to identify the capital English letters, demonstrates the effectiveness and practicality of Hopfield network in the pattern recognition and its fault-tolerant ability, and also gives the realization of Matlab software in process of pattern recognition.
Keywords: applied mathematics; Hopfield network; content addressed storage; pattern recognition

Title: Hyperbolicity and Riemann invariants of a multi-class traffic flow Lighthill-Whitham-Richards model

Authors: YANG Jianwei, WANG Ke, WANG Hongli
PP: 25～32
Abstract: With the further development of society, the study on traffic flow becomes more and more important. This paper studies a traffic flow multi-class Lighthill-Whitham-Richards model (MCLWR) based on the theory of one-order hyperbolic conservation laws. Mathematic proof of the hypertonicity for this model is given using two different cases. Furthermore, the Riemann invariants for the multi-class traffic flow LWR model are studied by using characteristic line method, and the physical interpret of the Riemann invariants are also pointed out. The information in transfer is obtained, that is, the total density and the relative density hold the same. Finally, the coherence between MCLWR model and LWR model is shown when the multi-class vehicle flow almost run at the same velocity.
Keywords: applied mathematics; hyperbolicity; hyperbolic conservation laws; multi-class traffic flow Lighthill-Whitham-Richards model; Riemann invariants

Title: Analysis and research on the extreme value of multivariable functions

Authors: GUO Changyu, XU Ling, YANG Shu, YI Hui, ZHENG Xuean
PP: 15～24
Abstract: This article mainly discusses how to discriminate the extreme value of multivariable functions, especially binary functions in case that the Hessian criterion fails. First, it enumerates some discriminant criterions for the extreme value of binary functions and makes a brief introduction to the corresponding geometric meaning for the extreme value, and introduces some necessary conditions for discriminating the extreme value of binary functions from the geometric aspect when discriminance fails. After that, analytically using the Taylor formula, it reduces the expansion to one-variable function and makes a specific discussion. By using the theory of quadric surface geometrically, it is also discussed in detail. And then, for binary function, by applying the inertia theory of polynomials, it has obtained an elegant result for extreme value discrimination in a special condition. At last, it gives a simple generalization of the multivariable case.
Keywords: calculus; extreme value of function; Taylor formula; the inertia theory of polynomials

Title: Location-allocation problem for community service centers bases on Floyd algorithm

Authors: MEI Suo, MAO Hongzhen, ZHAO Dongfang
PP: 10～14
Abstract: This paper discussed how to choose the location of community service centers to facilitate the district residents better. To solve this problem, first of all, it made appropriate assumptions and established a single objective programming model. And in order to get the model data, it used the distance matrix to denote the distance of each district. Then by the software Matlab, via Floyd algorithm, it concluded the minimum adjoining matrix. After that, by substituting the minimum adjoining matrix, it used Lingo 9.0 to solve the programming model and obtained the available options for the corresponding area residents to choose various service centers. Finally, through two examples (multiple service centers for single community and multiple service centers for multiple communities), the paper verified that the programming model is available.
Keywords: operations research and cybernetics; Floyd algorithm; single objective programming model; the minimum adjoin matrix

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