一种新型的数据安全存储系统模型

目前电子数据的安全存储主要依赖加密技术,数据通常只用一个密钥进行加密,并且密钥的管理过于集中,无法应对内部人员的密钥泄漏问题。设计了一种数据存储系统模型,包括访问控制子模型,用于数据的安全存储。一份完整的数据被分割成数份后加密存储在多个存储服务器上,一个或多个服务受到攻击时,攻击者无法从这些数据分片还原出完整的数据明文,从而达到安全存储的目的。最后将分析该模型的安全性能以及存储效率。     

A class of boundary value problems for third-order differential equation with a turning point

A class of boundary value problems for a third-order differential equation with a turning point is considered. Using the method of multiple scales and others, the uniformly valid asymptotic expansion of solution for the boundary value problem is constructed.     

The superiority of bayes estimators in a multivariate linear model with respect to normal-inverse Wishart prior

In this paper, the multivariate linear model Y = X B +e, e ～ Nm×k(0, Im ?Σ) is considered from the Bayes perspective. Under the normal-inverse Wishart prior for(B, Σ), the Bayes estimators are derived. The superiority of the Bayes estimators of B and Σ over the least squares estimators under the criteria of Bayes mean squared error(BMSE) and Bayes mean squared error matrix(BMSEM) is shown. In addition, the Pitman Closeness(PC) criterion is also included to investigate the superiority of the Bayes estimator of B.     

On restricted edge-connectivity of replacement product graphs

This paper considers the edge-connectivity and the restricted edge-connectivity of replacement product graphs, gives some bounds on edge-connectivity and restricted edge-connectivity of replacement product graphs and determines the exact values for some special graphs. In particular, the authors further confirm that under certain conditions, the replacement product of two Cayley graphs is also a Cayley graph, and give a necessary and sufficient condition for such Cayley graphs to have maximum restricted edge-connectivity. Based on these results, we construct a Cayley graph with degree d whose restricted edge-connectivity is equal to d + s for given odd integer d and integer s with d 5 and 1 s d- 3, which answers a problem proposed ten years ago.     

财经类院校数学建模的内容与方法探索

通过财经院校十年教学建模的实践,总结了数学建模的内容与方法.论述了将数学建模与课堂教学和大学生第二课堂相结合,与实验教学和实践教学相结合,在提高大学生综合素质,培养创新能力和应用能力等方面发挥重要作用.     

基于广义Beta回归的不良贷款回收率模型

依据国内最大的违约损失率数据库-LossMet rics~(TAI),利用广义beta回归模型对时间跨度为2001-2008年的不良贷款回收率分布进行了研究。采用极大似然和OLS估计方法,针对全样本和回收率为(0.1)开区间的非极端回收样本给出包含宏观、贷款和债务人异质因子的多变量广义beta回归模型的拟合参数和各个因素对回收率均值、方差的影响分析,并在多种变换方式下研究了只含宏观因子的单变量模型。结果表明,宏观因子的影响在单、多变量模型中都十分显著;不良贷款的有效抵质押和债务人的经营状况对模型的拟合也有明显影响;各因素对全样本和非极端回收样本的拟合结果差异性显著,同一因素对回收率均值、方差的影响大为不同。应用所得广义beta回归模型可进一步讨论回收率的区间估计、在险价值(VaR)等问题,给不良贷款风险管理提供极大帮助。     

Analysis of a class of dynamic programming models for multi-stage uncertain systems

Uncertainty theory is a new branch of mathematics concerned with the analysis of subjective indeterminacy. This paper deals with the optimal control problem for a multi-stage dynamic system in an indeterminate environment. Firstly, we formulate a practical uncertain control model based on the critical value criterion and present recursion equations for this model based on Bellman’s Principle. A special linear model is shown to illustrate how the recursion equations operate to obtain the analytical solution. Furthermore, we demonstrate a hybrid intelligent algorithm to evaluate and approximate the optimal solutions of more general cases. Finally, a discrete version of the production-inventory problem is discussed and numerically analyzed to illuminate the effectiveness of the methodology.