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July 15,2014
Volume 7,Issue 13
Pages -
Subject Area:Applied Statistical Mathematics,Applied Mathematics,Dynamic Programming,Graph Theory

Title: Exploration of the influence factors and the law of the factors of the second-hand housing prices in Beijing based on GWR

Authors: LIU Xiumin, HU Tao
PP: 1330-1344
Abstract: This paper applied the spatial varying coefficient regression model and the estimation method of geographical weighted regression (GWR) to analysis the spatial distribution law of the second-hand housing prices of Beijing, and researched the influence factors of the second-hand housing prices and the degree of special effects. This paper also took a non-stationary test for the spatial varying coefficient regression model and confirmed it had better performance than the ordinary linear regression model. In the end, according to the given geographic coordinates of the 20 locations, the weighted interpolation method had been used to estimate the second-hand housing prices in these places. This paper also compared the housing price between estimation results and neighborhoods. The results could guide the relevant departments to make a reasonable city planning, promote the scientific management of the secondary housing market in Beijing, and let the people understand the secondary housing prices of different regions.
Keywords: applied statistical mathematics; housing price; geographical weighted regression; spatial non-stationary

Title: Similarity analysis of music works

Authors: LI Jiahui, ZENG Fanhui, ZHAO Youxin
PP: 1322-1329
Abstract: This paper first makes a brief introduction to the application of the similarity theory in the analysis of music works. The purpose and significance, and research status for similarity analysis, specific research methods are given. This paper also collects and collates relevant music score, completes the conversion of finite length sequence string and converts wave profile string image reflected, then compares them using the contour similarity method. This research plays a positive role in the protection of intellectual property rights and inspiration on music inspired music creation.
Keywords: applied mathematics; similarity analysis; string conversion; image fluctuation; contour similarity; music works

Title: Optimal price of common demand function model goods

Authors: LIN Chengchu
PP: 1317-1321
Abstract: Selling price of a commodity is mainly based on the cost of the product and the demand of the goods. This paper studies how to determine the optimal price according to the cost of sales and demand function. As the known conditions in the cost function, according to the demand function model of commodity, we establish the profit function, and find out the optimal price formula by using the extremum theory of function. This formula has an important reference value for distributors and consumers.
Keywords: applied mathematics; demand function; mathematical model; optimal price

Title: A hybrid model based on wavelet packet denoising in stock price forecasting

Authors: CHI Bei, NIU Mingfei
PP: 1307-1316
Abstract: The purpose of this article is to use the hybrid model based on the wavelet packet denoising, back propagation (BP) model, auto regressive and moving average (ARMA) model and exponential smoothing (ES) model to examaine the effectiveness of forecasting stock price. The selection data is daily closing price of China Construction Bank during 2010-2012. Firstly, with the original data of China Construction Bank, three single models, i.e. BP model, ARMA model, ES model are set up respectively, then uses particle swarm optimization algorithm to combine the weight of models. It is found that the effectiveness in predicting the stock price of the hybrid model is better than any other single model. Then with the data after wavelet packet denoising of China Construction Bank, the same hybrid model is set up. The results show that, the model’s prediction effectiveness based on the wavelet packet denoising is more better than the unwavelet packet denoising model. Therefore, the hybrid model based on wavelet packet denoising is effective for stock price forecasting.
Keywords: applied mathematics; stock price forecasting; wavelet packet denoising; back propagation model; auto regressive and moving average model; exponential smoothing model

Title: Application of diagonal generalized RBF neural network to stock price prediction

Authors: LIU Shuanglong, MA Jinwen
PP: 1296-1306
Abstract: In this paper, the diagonal generalized radial basis function (RBF) neural network is applied to analyzeing and predicting the time series of stock prices. Specifically, the dynamic split-and-merge expectation maximization (EM) algorithm with the kurtosis and skewness criterion is utilized to determine the number of hidden units as well as the initial values of the parameters for the network design, while the synchronous least mean square error (LMS) learning algorithm is implemented for the final learning of the parameters in the network. It is demonstrated by the experiment results that the diagonal generalized RBF neural network can be successfully applied to the prediction of stock prices, which shows a good application prospect on this aspect.
Keywords: applied mathematics; radial basis function neural network; expectation maximization algorithm; stock price; time series prediction

Title: θ-difference numerical method for solving time-fractional Black-Scholes equation

Authors: ZHANG Xue, SUN Shuzhen, WU Lifei, YANG Xiaozhong
PP: 1287-1295
Abstract: It’s more practical and more actual in financial markets to use stochastic differential equation driven by fractional Brownian motion to describe the stock price. So it is very practical in the application to study the numerical computation of fractional Black-Scholes equation. This paper constructs θ-difference scheme for solving the time-fractional Black-Scholes equation. The θ-difference scheme is analyzed to be stable, convergent, existence and uniqueness of solution. Finally, this paper proves the effectiveness of θ-difference scheme for solving Black-Scholes by numerical experiments, and its calculating speed is faster.
Keywords: financial mathematics; time-fractional Black-Scholes equation; θ-difference scheme; stability; numerical experiment

Title: Continuity condition for bicubic harmonic B閦ier surfaces

Authors: NI Qian, WANG Xuhui
PP: 1282-1286
Abstract: This paper mainly studies the relationship between control points when the two corresponding bicubic harmonic B閦ier surfaces are C1 continuous. The results show that when the two bicubic harmonic B閦ier surfaces are C1 continuous at the common boundary, the two bicubic harmonic B閦ier surface patches are from the same piece of surface. Moreover, when the Cr continuity condition are satisfied at the common boundary for the two bicubic harmonic B閦ier surfaces, it implies that the two bicubic harmonic B閦ier surface patches are also derived from the same piece of surface.
Keywords: computational mathematics; bicubic harmonic B閦ier surface; continuity condition; control point

Title: Congruent infinity and its application in the limits of functions

Authors: CHEN Siyuan
PP: 1277-1281
Abstract: In this paper, a new concept of congruent infinity is raised. Furthermore, its natures, related conclusions and some applications of congruent infinity are discussed by using some conclusions of equivalence, and some application examples are given. This research provides a new thinking for computing limits.
Keywords: mathematical analysis; equivalent infinity; congruent infinity; limit; asymptote

Title: A two-stage dynamic programming model under backordering and an emergent supplier

Authors: YOU Junyan, WANG Yiju, ZHANG Wenhua
PP: 1266-1276
Abstract: In this paper, under the conditions of backordering and existing an emergent supplier, we study the optimal ordering strategy of two-stage newsboy model of related demands. Through benefit analysis, we establish a dynamic programming model, and give an algorithm to solve the retailer’s optimal ordering policy. Finally, the effectiveness of the algorithm is verified by combining with a numerical example. The sensitivity analysis shows that the correlation coefficient of two stage demands and the backordering rate have important influence for retailer’s order decision and profit.
Keywords: dynamic programming; supply chain management; partial backordering; emergent supplier; related demands

Title: Immune genetic algorithm for solving nonlinear constrained interval-valued programming

Authors: ZHANG Mingxing, ZHANG Zhuhong
PP: 1260-1265
Abstract: This work investigates the transformation of nonlinear constrained interval-valued programming (IVP) based on the concepts of interval order and possibility, and develops one immune genetic algorithm for the transformed IVP. In the design of algorithm, some high-quality individuals produced by the basic genetic algorithm are admitted to participate in evolution, and meanwhile the current population is divided into elitist and non-selected subpopulations by means of interval-constraint dominance. Such subpopulation search for high-quality and diverse individuals is along with different directions, relying upon immune operators and individual detection. Comparatively numerical experiments show that the proposed method is available and effective for IVP problems.
Keywords: optimization; nonlinear constrained interval-valued programming; interval possibility; immune genetic algorithms; interval arithmetic; interval order

Title: Nonexistence of solutions for singular nonlinear differential inequalities

Authors: LI Xiaohong
PP: 1252-1259
Abstract: We study the nonexistence of the solutions for the coercive and anticoercive nonlinear elliptic differential inequalities by using the test function method. On the base of many previous researches and combining with the present results, we construct the suitable function. By various computing skills and the estimation method, we obtain an a priori estimate for a solution. Then, the nonexistence of a solution is proved by contradiction.
Keywords: partial differential equation; nonlinear differential inequality; test function method; singularities; strongly-p-coercive; weakly-p-coercive

Title: Law of the single logarithm for the self-normalized sums for arrays

Authors: KE Chunmei, CHEN Lianglu
PP: 1246-1251
Abstract: By the self-normalized moderate deviations, the law of the single logarithm for the self-normalized sums for arrays is obtained, which generalizes the well-known results. As the application, the law of the single logarithm for the t-statistics of arrays is derived.
Keywords: limit theory; self-normalized sum; law of the single logarithm; array; moderate deviation

Title: Prediction of weighted Markov chain on sunspot number by Matlab program

Authors: CHEN Chu, MA Yingjun, CHEN Yan, ZHAO Dongfang
PP: 1240-1245
Abstract: Firstly, as the sunspot cycle is 11 years, the number of sunspot from 1900 to 2010 are divided into 6 levels by the optimal partition method to set up a weighted Markov chain prediction model with 12 years as one step. Secondly, after being tested, the model is affirmed with a high accuracy to predict the sunspot numbers in the next 11 yeaes. Finally, the model is used to predict sunspot numbers from 2011 to 2021. The process is achieved by Matlab program. The result displays that the sunspot numbers of 2011 and 2012 are in a higher value section. In 2013 and 2014, it reduces to a median section, drops down to the lowest section in 2015 and remains the lowest section from 2016 to 2021. Thus, the grade of the 11-year sunspot numbers has been through one cycle, suggesting it is feasible to forecast the sunspot numbers by the weighted Markov chain.
Keywords: probability theory and mathematical statistics; weighted Markov chain; sunspot number; sunspot cycle; Matlab program

Title: Extending cycles and Hamilton cycle

Authors: XIE Yingtai
PP: 1236-1239
Abstract: In this paper, the relations between degree sums of two vertices and extending cycles in graphs have been discussed. A similar result is obtained in a new direction. Then, this paper studies the condition for a cycle extending to a cycle including all vertices of a path or an another cycle. By extending a cycle to Hamilton cycle, the following well known Fan-theorem “Let G be a 2-connected graph, if d(u,v)=2!襪ax（d(u),d(v)）≥2 then G is Hamiltonian” has been proved simply.
Keywords: graph theory; joints; extending cycle; Hamilton path; Hamilton cycle

Title: A note on Erdös-Sòs conjecture

Authors: YANG Guobin, ZHANG Xiaodong
PP: 1224-1235
Abstract: Firstly, we introduce some of existing results about Erd\0￶s-Sﾨﾰs conjecture. Then, let T be a tree with 9 vertices. We classify the conjecture into different cases according to ﾦﾤ(T), the maximum degree of tree T, and prove that if the average degree of graph G exceeds 7, then G contains T. Thus, Erd\0￶s-Sﾨﾰs conjecture is true for some special cases.
Keywords: graph theory; Erdös-Sòs conjecture; tree; the maximum degree

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