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2016, Vol. 36 No. 3   Published date: 30 September 2016
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• Moment Exponential Stability Analysis for a Class of Impulsive Stochastic Neural Networks

  Liu Xinge, Wang Fengxian, Tang Meilan

  2016, 36(3): 1-4. doi:

  Abstract ( 1284 )   PDF (181KB) ( 332 )   　　

  Based on the mathematical induction,a novel sufficient condition on exponential stability in mean square and a new moment exponential stability condition are proposed for a class of impulsive stochastic neural networks,which are with less conservatism.

• Relations Between Several Ideals of a Ring and Its Quotient Ring

  Guan Zhengxiong, Wang Yao

  2016, 36(3): 5-11. doi:

  Abstract ( 1252 )   PDF (268KB) ( 167 )   　　

  In this note,we investigate the relationships between ideals of a ring Rand its quotient ring R/I.We show that if I ⊆K ⊆ Rand I△R,then Kis a 2-primal ideal(strongly prime ideal,left T-nilpotent ideal, radically-symmetric ideal)of Rif and only if K/Iis a 2-primal ideal(strongly prime ideal,left T-nilpotent ideal,radically-symmetric ideal)of R/I.

• Lower Bounds of the Life Span of Classical Solutions to a System of Nonlinear Wave Equations with Weighted Function in Two Space Dimensions

  Wang Husheng, Sun Haixia, Mi Cailian

  2016, 36(3): 12-24. doi:

  Abstract ( 1304 )   PDF (462KB) ( 166 )   　　

  This paper concerns the Cauchy problem of a nonlinear wave equation system with weighted function.Lower bounds to the life span of classical solutions with small initial values are derived,which generalizes the known results.

• Noise Supress Exponential Growth for Cohen-Grossberg Neural Networks

  Juanjun Wang, Qiao Lin, Hui Su

  2016, 36(3): 25-36. doi:

  Abstract ( 1231 )   PDF (437KB) ( 221 )   　　

  In this letter,we will show that noise can make a given Cohen-Grossberg neural networks whose solution may grows exponentially become the new stochastic Cohen-Grossberg neural networks whose solution will grow at most polynomially.In other words,we reveal that the noise can suppress the exponential growth for Cohen-Grossberg neural networks.

• An Existence Theorem on Elliptic Partial Differential Equation with Square Integrable Leading Coefficients

  Li Yang

  2016, 36(3): 37-41. doi:

  Abstract ( 1233 )   PDF (215KB) ( 204 )   　　

  In this paper we give the existence of weak solutions to a second order elliptic partial differential equation with square integrable regularity of leading coefficients.Specifically,we consider the elliptic equation - ∂ _j(a_ij(x) ∂_iu)=f⁰ + ∂_ifⁱ inΩ,u =0on the boundary,with a_ij =a_ji，a_ij uniform elliptic,and a_ij ∈L²(Ω).First,we approximate a_ijby a^(m)_ij which belongs to L∞(Ω),and then prove the existence theorem by applying the well known results concerning solvability of elliptic partial differential equation together with the standard energy method.

• Characteristic Analysis and Detection of Abnormal Data in High Frequency Monitoring Data

  Li Ting, Kong Wenjia, Zhou Juan, Zheng Zhoushun

  2016, 36(3): 42-53. doi:

  Abstract ( 1394 )   PDF (1227KB) ( 411 )   　　

  In this paper,by analyzing 60000high-frequency monitoring data of 10equipments in a thermal power plants,we find that abnormal data has two characteristics:outlier or abnormal segment.A denoising method based on the first-order forward difference and the frequency distribution to detect the outlier and abnormal data in the high-frequency is proposed.In this method the threshold of abnormal data is determined by the risk probability and the frequency distribution of absolute value of the first-order forward difference, and the maximum number of the outliers included in the abnormal segment is obtained according to the performance of the device and the sampling frequency. The judgment rule for detecting abnormal data is then given with the threshold and the maximum number of the outliers.The method is applied to 6000data of a thermal power plant pre-pump motor for showing its effectiveness.

• Option Pricing to a Continuous Dividend Payment Model Driven by an Asymmetric Jump-diffusion

  Liu Dongyan, Fan Sujun, Wang Bing

  2016, 36(3): 48-53. doi:

  Abstract ( 1326 )   PDF (238KB) ( 159 )   　　

  Assuming that the stock company pays dividend continuously and the pricing process is an asymmetric jump-diffusion process,this paper establishes an European call option pricing model and solves it with the insurance actuary pricing method.

• A Compound Markov Binomial Model with Random Dividends and Stochastic Premium Income

  Fang Shizu, Qin Lihua

  2016, 36(3): 54-65. doi:

  Abstract ( 1316 )   PDF (420KB) ( 225 )   　　

  Consider a compound Markov binomial model with random dividends and stochastic premium Income. The recursive formulas for the expected discounted penalty function are derived,and the existence and uniqueness of the solutions to the recursive equations are proved.As applications,some examples concerning the quantities related to ruin are presented.

• Forecasting Stock Risks Based on a Physical Bubble Breakage Model

  Tian Zhikun

  2016, 36(3): 66-76. doi:

  Abstract ( 1303 )   PDF (1394KB) ( 191 )   　　

   Since stock market bubbles are payed close attention by investors,it is meaningful to figure out the breakage time of the stock market bubble for investors to manage risks.In this paper by regarding the stock market bubbles as physical bubbles and taking into account the fluctuations of stock market,a model to depict the stock market bubbles is build.Parameters in the model are estimated by the least square method and genetic algorithm.Empirical analysis with our model on the Shanghai securities composite indexes of three time intervals shows that the errors between the predicted breakage time and the real breakage time of stock market bubbles are small,and furthermore,the time of the bubble breakage forecasted is more likely after the real breakage time.The model is used to forecast the Shanghai securities composite indexes from January,2014 to June,2015,and it is found that the predicted breakage time is almost the same to the real breakage time, which demonstrates that our bubble model has good effects in depicting the risks in stock market.

• Optimal Portfolio Selection Problem with Liability and Return Rate Modulated by Markov Chain under Partial Information

  Zhou Yue

  2016, 36(3): 77-82. doi:

  Abstract ( 1236 )   PDF (242KB) ( 267 )   　　

  It is well-known that a financial model with deterministic coefficients are only good for a relative short period of time and cannot respond to changing conditions.The information available to the investor is the filtration generated by the asset price processes only.The investor can in general not directly observe the mean return rate processes and the volatility process of the asset price process.A simplified continuous time financial market with one risk-free asset(bond)and one risk asset(stock)were assumed.When the liability process is modeled by a linear-diffusion model and the mean return rates is modulated by a finite state continuous-time Markov chain,we estimate the mean return rates of stock under the Woham filter.By using the stochastic linear-quadratic control technique,the closed form solutions of the optimal portfolio strategy and the maximal expected exponential utility are obtained under the partial information.

• Research and Application of Multiple Attribute Decision Making Method with Interval Fuzzy Numbers

  Zhou Yicheng, Yao Jian

  2016, 36(3): 83-92. doi:

  Abstract ( 1293 )   PDF (965KB) ( 451 )   　　

  In this paper some approaches are used to improve the multiple attribute decision making method. Firstly,direct and feasible interval hesitate fuzzy numbers are converted into intuitionistic fuzzy numbers,and overlapping intervals are employed to reduce numbers of attribute value elements,then the weights of attributes are determined by optimization,and finally,the mechanism of interval hesitate numbers and the applicability of real problems are taking into account to give evaluation on a regional enterprise.

• Research on the Fuzzy Membership Function Determination Based on Probability Statistics

  Ma Wanyuan, Geng Xiuli

  2016, 36(3): 93-100. doi:

  Abstract ( 1219 )   PDF (682KB) ( 706 )   　　

  The key of using fuzzy mathematics to solve practical problems is to establish realistic membership function.The commonly used method to compute the fuzzy membership function is fuzzy statistic method, which relies on a large number of survey data and analysis on the function graph,and the calculation with heavy workload and complex process limits the practical application of fuzzy technology.A method for determining the fuzzy membership function based on probability statistics is proposed from the view of statistics.The proposed method is relatively simple and can adapt to much more cases of fuzzy membership function determination. Finally,a real world case is given and membership function curves derived from two methods are compared to verify the proposed method having higher accuracy.

• Comprehensive Risk Evaluation of Haze for Economic and Social Development in Yangtze River Delta District

  Jiang Mianfeng, Ye Chunming

  2016, 36(3): 101-111. doi:

  Abstract ( 1151 )   PDF (694KB) ( 216 )   　　

  The aim of the paper is to make a comprehensive risk evaluation of potential hazard from Haze weather.We constructed the evaluation system of indicating factors which consists of 21indicators in 3categories on the basis of disaster systemic theory.We combined the Analytical Hierarchy Process(AHP)and the entropy approach to determine these indicators’weight.With the indicator system and its weights in hand,we calculate the correlation coefficient of comprehensive risk of haze pollution of three provinces in in Yangtze River delta district.The results indicated that the security risk level of Shanghai Jiangsu and Zhejiang isⅣ,Ⅱand Ⅰrespectively.The evaluation result based on matter-element extension model was accord with the result of traditional comprehensive index evaluation method,which proved that this model was reliable.In addition,we classified evaluation index in terms of weight,security level and improve difficulty,and find key index to reduce the risk level quickly.

• Empirical Analysis on the Relationship Between Housing Price Volatility and Main Economic Factors:Based on an ECM Model

  Zhang Hui, Rao Haiqin

  2016, 36(3): 112-118. doi:

  Abstract ( 1296 )   PDF (2228KB) ( 262 )   　　

  The most cost of real estate prices is produced in the process of the development and construction of the house,but housing price volatility is influenced by many factors.In recent years,with the growing amount of total GDP and the per capita disposable income,the rapid expansion of urban population,China’s real estate market has developed rapidly,the housing price is up all the way.This paper investigates the relationship between housing price and various economic factors.Based on the annual data 2000-2014average price of China＇s real estate and the main economic factors GDP,the urban residents living disposable income,more than 5 years lending rate,money supply M1and the exchange rate against the U.S.dollar,this paper establishes a vector autoregression(VAR)model and modifies through a variety of statistical analysis.According to the modified ECM model,we get a conclusion:the housing price can economically function back to ROE in the long term. The short-term America subprime crisis could make the housing price play apositive influence on the ROE.

• An Automated Assessment Algorithm for Subjective Tests

  Zhu Shihua, Chen Ming

  2016, 36(3): 119-122. doi:

  Abstract ( 1364 )   PDF (175KB) ( 282 )   　　

  In this paper,by improving the Single Similar Degree algorithm,a weighted Single Similar Degree algorithm is developed for automated assessment of subjective tests in the online exam system,which mainly considers the importance of the key words in the reference answer and gives each of the key words a certain weight.The improved algorithm has more accuracy for the assessment.

• The Exploration of Quality Assurance System for the Teaching of Mathematics and Statistics under the Construction of World-class(first-rate)Disciplines and Universities:Based on the Practice at Sun Yat-sen University

  Cheng Yuehua

  2016, 36(3): 123-128. doi:

  Abstract ( 1183 )   PDF (222KB) ( 212 )   　　

   Under the new currency of constructing world-class disciplines and universities in the country, mathematics and statistics,as the undergraduate public basic courses of many disciplines and majors in the higher education,have had new tasks and become more important.In order to establish a better foundation for the relevant disciplines,as well as to achieve the goal of constructing world-class disciplines and universities, strengthening the quality assurance system of the public teaching for mathematics and statistics is crucial.This is also in regard to the potential tendency of the fusion of different disciplines,and the real needs from the development of those disciplines.