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July 15,2013
Volume 6,Issue 13
Pages -
Subject Area:History of Mathematics,Dynamic Programming,Applied Statistical Mathematics,Applied Mathematics,Algebra

Title: Stability and change of spherical trigonometry in late Qingdyhasty

Authors: TEGUS, DONG Jie
PP: 1264-1271
Abstract: In this paper, the stability and change of spherical trigonometry in late Qingdyhasty were discussed, and the results indicated the communication of the Chinese culture and the Western culture. The late Qingdyhasty scholars refused the algebraic operations and maintained the old methods, which had relationship with the requirement of the traditional system. During 30 years, some scholars held that the spherical trigonometry should be suited to the traditional system, and the fundamentals should be illustrated. However, with the educational reform, the scholars in the end of Qingdyhasty began to accept Western system. Gradually, they realized that mathematicians could cite own concepts freely on the basis of logical definitions, and the empiric evidence was not absolutely important for the trigonometry. In 1907, the structure of trigonometry changed, the spherical trigonometry got a formal basis.
Keywords: history of mathematics; trigonometry in late Qingdyhasty; algebraic trigonometry; spherical trigonometry

Title: Research on issuance ways of mortgage-backed securitization

Authors: YANG Yue, YU Bo
PP: 1255-1263
Abstract: Asset securitization is an important way to improve bank asset liability structure, and can offer financial tools for investors with high yields. According to the rapid and stable development of the domestic financial market, the large-scale asset securitization is on the way. To establish a complete and reasonable mortgage-backed securitization structuring model, this paper firstly introduced a method to estimate the repayment default rate based on distributional robust optimization. Then, a credit rating system was improved by containing an option on the mortgage market value. Finally, using the dynamic programming model to structure the mortgage-backed securities was proposed. It is supposed to make a contribution to the financial innovation of China and put forward fresh ideals.
Keywords: dynamic programming; mortgage-backed securitization; distributional robust optimization; default rate; credit rating

Title: Parallel support vector machine algorithms based on decomposition technique

Authors: LI Mingqiang, HAN Congying, HE Guoping
PP: 1249-1254
Abstract: The parallel algorithm based on decomposition technique is proposed to solve the large scale support vector machine problems. Firstly, the outline of this algorithm and the skills in parallel computing are introduced. Then a new subproblem is given and the accelerated method based on first order information is proposed to solve the new subproblem. Finally, the working set selection method without gradient computation and its feasibility is described.
Keywords: nonlinear programming; parallel decomposition algorithms; accelerated method based on first order information; support vector machine

Title: Sensitivity analysis of DEA risk assessment model

Authors: ZHOU Chi, HU Jie
PP: 1242-1248
Abstract: In this paper, considering error and change data of both positive and negative factors that affect the risk assessment synthetically, two models of sensitivity analysis of data envelopment analysis (DEA) were improved. The sensitivity analysis of coordinate preference risk assessment model based on DEA was given. Furthermore, this paper presented some sufficiency conditions which could hold the efficiency of decision making units, while positive and negative factors of decision making units were changed simultaneously. At last, the numerical example was provided to indicate the feasibility of the sensitivity analysis.
Keywords: operational research; data envelopment analysis; sensitivity analysis; risk assessment; sensitivity analysis model

Title: A parallel difference numerical method for solving the payment of dividend Black-Scholes equation

Authors: ZHANG Fan, YANG Xiaozhong
PP: 1232-1241
Abstract: This paper constructed a new Saul’yev scheme with nearly second-order accuracy for solving the payment of dividend Black-Scholes equation, and then gave the alternating segment explicit-implicit (ASE-I) scheme and alternating segment implicit-explicit (ASI-E) scheme which were analyzed to be stable, convergent and parallel. The numerical examples showed that these two schemes could improve the calculation speed rapidly, and the calculation time of the two schemes was 1/2 of the ASE-I (ASI-E) scheme and 1/5 of the Crank--Nicolson scheme. The accuracy order of the two schemes was approximate to that of the explicit-implicit scheme, thus the schemes given by this paper could be used to solve the payment of dividend Black-Scholes equation effectively.
Keywords: financial mathematics; payment of dividend Black-Scholes equation; alternating segment explicit-implicit scheme; parallel computing; numerical experiment

Title: A technique for constructing preconditioned diagonally dominant matrices

Authors: WANG Xuezhong
PP: 1227-1231
Abstract: Most iterative methods converge when the coefficient matrix of linear systems is a strictly diagonally dominant matrix. When coefficient matrix is not diagonally dominant matrix, preconditioned techniques can be employed. This paper presented a method to establish appropriate preconditioned matrices P and Q when coefficient matrix was an H-matrix, in order to transform a non-diagonally dominant matrix into a diagonally dominant matrix. Numerical example also showed the effectiveness of this method.
Keywords: computational mathematics; iterative method; H-matrix; preconditioned matrix; diagonally dominant matrix

Title: Parametic estimation of linear model based on uniformly distributed covariate

Authors: LIU Dongmei, WU Xiaoping, ZHAO Xuejing
PP: 1221-1226
Abstract: This paper focused on parametric estimation of linear model for interval-censored covariates. By using two approximation methods (discretization method and large sample normal approximation) of the interval-censored covariates, the results of the parametric estimation with the maximum likelihood estimation (MLE) method was obtained. Furthermore, the performance of the proposed methods was illustrated by numerical simulations comparison analysis. The results showed that, in the linear model with an interval censor-data covariates, a higher accuracy of estimation of unknown parameters could be obtained by using the discretization method, and the error was small when comparing with the traditional methods. In addition, a good estimation of parameter could also be obtained in the case of large sample, and the result was satisfactory.
Keywords: applied statistical mathematics; interval-censored covariates; regression model; maximum likelihood estimation

Title: Estimation on indirect economic loss from the earthquake in Japan based on SARIMA model

Authors: LIANG Qijun, WANG Binhui
PP: 1215-1220
Abstract: In the past, the study on indirect economic loss from earthquake mostly focused on the social economy related type loss, which resulted in the incomprehensive estimation of indirect economic loss. This paper gave quantitative analysis on part of resources related type loss of indirect economic loss from earthquake in Japan, i.e. indirect economic loss from the increase of foreign exchange reserves through canonical analysis and SARIMA model. An exploratory conclusion was obtained: the rate of economic growth of Japan had slowed down 13.06% because of the indirect economic loss from the change of foreign exchange reserves from March 2011 to February 2012.
Keywords: applied statistical mathematics; delay degree of economic development; SARIMA model; indirect economic loss; foreign exchange reserves

Title: Application of nonparametric additive model in real estate bubble measurement

Authors: WEI Chaoqiao, HUANG Xuejun
PP: 1209-1214
Abstract: This paper carefully explored the nonlinear relationship between the real estate bubble and the various factors that impacted it. From the nonparametric additive model perspective, we established the nonparametric model of speculation degree. Then, we measured the bubble measuremewt coefficient in real estate under non parameter conditions, and thus we compared and identified the harm extent of bubble. Using the nonparametric additive speculation degree model, this paper empirically analysed the quarterly data of Wuhan city from the year 2001 to 2012. In the last, this paper gave some advice to curb real estate bubble from the four stakeholders’perspective: the government, the developers, the consumers and the financial institutions.
Keywords: applied mathematics; real estate bubble; degree of speculation; nonparametric regression； additive model

Title: Internet diffusion research and model comparison bassed on Logistic, Gompertz and Bass models

Authors: WU Ling, JIA Huaijing
PP: 1204-1208
Abstract: As the technology diffusion followed the law of the S-shaped curve, the China’s internet diffusion curve fitting result showed that the internet saturation penetration rate in the future was 61%. From 2013 to 2014, China’s internet would be in a stage of rapid growth. In 2025, China’s internet penetration would gradually tend to a stable level (61.07%). In addition, Logistic curve fitting results had the excessive optimistic tendencies after losting the diffusion data of the first stage. Furthermore, three fitting results of China’s internet diffusion based on the Logistic, Gompertz and Bass models were compared and it was found that Logistic model was the optimal forecasting model.
Keywords: applied mathematics; technology diffusion; internet; Logistic model；Bass model; Gompertz model

Title: Research on one Chemostat model with predator-prey populations

Authors: RONG Shaohong, ZHANG Juan
PP: 1198-1203
Abstract: Chemostat model is a kind of important biology model and plays a key role in the biological and ecological study. In this paper, the Chemostat model of the predator and prey populations with the Holling III reaction function was constructed. Through qualitative analysis on this model using the stability theory and method, the feasible equilibrium point of the model was obtained. In addition, the global stability of equilibrium point was proved through Liyapunov function and Jacobi matrix. Model analysis results showed the conditions that the predator and prey population was permanently survival, prey population was survial with predator population’s extinction and predator population was survial with prey population’s extinction.
Keywords: ordinary differential equation; Chemostat model; global stability; equilibrium point; predator-prey

Title: VaR estimate of g-h distribution and extreme value theory

Authors: DING Fang, YAN Dingqi
PP: 1192-1197
Abstract: In order to solve the problem of spike and fat-tail of financial assets sequence data, we gave the estimate value based on the g-h distribution of risk at value (VaR) on the basis of some features of the g-h distribution, and compared with the estimate of the value based on the extreme value theory. The analysis showed that the estimate value of VaR based on the g-h distribution could describe the changes in the rate of return on assets more accurately.
Keywords: probability theory and mathematical statistics; risk at value; g-h distribution; extreme value theory

Title: Analysis on function of multidimensional random variable using conditional distribution

Authors: CHEN Bihong
PP: 1187-1191
Abstract: Using the distribution function of the random variable to analysis the function of multidimensional random variable is an old method. In this paper, a new analysis method was put out. This method used the concept of conditional distribution instead of distribution function. Furthermore, it was easy for this new method to study and understand. Some difficult problems could be resolved easily. In addition, this method was proved to be available by example analysis.
Keywords: probability theory; random variable; function of multidimensional random variable; local inverse function

Title: Determination on reducibility of integral coefficient polynomial based on homomorphic Euclidean ring ZP［x］

Authors: DENG Congzheng, LUO Yongchao
PP: 1182-1186
Abstract: It is extremely difficult to determine the reducibility of integral coefficient polynomial because of the complexity of their degree and coefficients. Euclidean ring is a unique factorization ring. Based on homomorphic mapping and homomorphism of polynomial rings with Euclidean rings ZP［x］ over finite field, we gave a new method for determining the reducibility of integral coefficient polynomial. In addition, we obtained a number of conditions and methods for the reducibility irreducibility and their factorization of the integral coefficient polynomial, which provided a new reference for the factorization. In comparison with traditional discriminating methods, this method was more convenient and faster.
Keywords: algebra; homomorphic principle; reducibility; integral coefficient polynomial; Euclidean ring

Title: Reliability of special three-dimension systems

Authors: LI Ning, SUN Ge, ZHAO Xian
PP: 1177-1181
Abstract: Three-dimension systems can be used to monitor space environment. Consecutive-(r1,r2,r3)-out -of-(m,n,w):F systems is a typical three-dimension system. It consists of m譶譿 components. The system fails if and only a three-dimension (r1,r2,r3) area exists, and all components failed in this area. In this paper, for Consecutive-(2, 2, 2)-out-of-(m, n, w):F system, the state space and transition probability matrix was constructed and analytical expression of reliability was proposed by using finite Markov chain imbedding approach. Numerical example showed that the new method was effective.
Keywords: Markov process; reliability; quality control and reliability management; three-dimension system

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