基于GPEM主旋律分析的系统序参量识别方法研究

针对系统的演化与发展,引入基于目标规划评价模型(GPEM)的主旋律分析方法,识别引导与支配系统发展的序参量.通过分析主旋律与序参量间的关系,认为在GPEM中的价值参数结构是二者的共同体现,且主旋律分析是序参量识别的前提与基础.应用基于GPEM的主旋律分析方法对系统所属群体进行相关计算,可以获得群体发展的主旋律,同时可以获得群体成员在各主旋律下的排名向量,进而认为与理想排名向量相似系数最高的主旋律在群体发展过程中发挥着关键性作用,则该主旋律对应的价值参数结构即为序参量.通过观察该主旋律所集聚成员在理想排名向量中的位置,来判断与分析序参量的特征.     

基于三阶和四阶龙格库塔法的GM(1,1)模型优化及应用

为提高GM(1,1)模型的预测精度,提出了应用三阶和四阶龙格库塔法对GM(1,1)模型的建模过程进行优化.给出了优化模型,并讨论了两种优化模型中发展系数的变化对其精度的影响.实例表明,基于三阶和四阶龙格库塔法所建立的GM(1,1)模型,可以有效地提高模型的预测精度和适用性.     

A New Expression for Higher Order Accelerations and Poles Under the One Parameter Planar Hyperbolic Homothetic Motions

The one parameter planar hyperbolic homothetic motion was introduced in Ersoy and Akyigit (Adv Appl Clifford Algebras 21:297–313, 2011). We give a formula for higher order accelerations and poles under this motion. In the case of the homothetic rate \({h\equiv 1}\) we obtain the higher order accelerations and poles under one parameter planar hyperbolic motion which was given by Sahin and Yüce (Math Probl Eng 2014, 2014). Also, the higher order velocities and accelerations are analyzed by taking the angle of the rotation instead of the parameter of the motion.     

Numerical Method for Singularly Perturbed Third Order Ordinary Differential Equations of Convection-Diffusion Type

In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of convection-diffusion type of third order Ordinary Differential Equations (ODEs) in which the SPBVP is reduced into a weakly coupled system of two ODEs subject to suitable initial and boundary conditions. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. In order to get a numerical solution for the derivative of the solution, the domain is divided into two regions namely inner region and outer region. The shooting method is applied to the inner region while standard finite difference scheme (FD) is applied for the outer region. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples. The method is easy to implement and suitable for parallel computing.     

How to Solve Nonlinear Equations When a Third Order Method is Not Applicable

In this paper, we use a one-parametric family of second-order iterations to solve a nonlinear operator equation in a Banach space. A Kantorovich-type convergence theorem is proved, so that the first Fréchet derivative of the operator satisfies a Lipschitz condition. We also give an explicit error bound.Supported in part by the University of La Rioja (grants: API-98/A25 and API-98/B12)and DGES (grant: PB96-0120-C03-02).     

一种新的求解双曲型守恒律的三阶中心差分格式

本文提出了一种求解双曲型守恒律新的三阶中心差分格式，主要是引入了一种推广的三阶重构，并证明了这种重构在网格边界无振荡．所提的格式保持了中心差分格式简单的优点，不需用Riemann解算器，避免了进行特征解耦．数值试验结果表明本文格式是高精度、高分辨率的。     

一类三阶奇摄动特征值问题

将带有边界条件的三阶非齐次线性方程的可解性条件应用到退化特征值问题上,得出了奇摄动问题的解的渐近表示式.     

一类改进的Logistic模型参数估计方法及其应用

根据实测数据估计Logistic模型参数时,对已有的数据不满足直接利用三点法、四点法应用条件的问题,提出一类改进的三点法、四点法,即迭代逼近算法.以底部耗氧型结冰湖的溶解氧浓度分布为例,建立冰盖下溶解氧浓度垂直分布的Logistic模型,采用迭代逼近算法估计该模型的参数值.结果表明:改进的三点法、四点法的判定系数都较高,均可用于Logistic模型的参数估计,但改进的四点法整体优于改进的三点法.算法进一步完善了Logistic模型的参数估计方法.     

高阶导数的一个极限表达式

通过对二阶微分问题的求解与推广,给出求解高阶导数的极限表达式．这也是差分法的一个推广．     

高阶特征线性及其与semi-Lagrangian方法的比较

特征线性与semi-Lagrangian方法都是处理流体方程时间离散的两种有效的方法．它们比经典的半隐格式，如Backward-Euler／Adams-Bashforth方法有更好的稳定性．本提出一种基于高阶空间离散的特征线法，通过稳定性，精度和计算复杂性与semi-Lagrangian方法进行比较，分析了高阶特征线法的有效性和适用性，并从数值试验上对分析结果进行验证．     

A Pseudo-Pareto Distribution and Concomitants of Its Order Statistics

Pareto distributions are very flexible probability models with various forms and kinds. In this paper, a new bivariate Pseudo-Pareto distribution and its properties are presented and discussed. Main variables, order statistics and concomitants of this distribution are studied and their importance for risk and reliability analysis is explained. Joint and marginal distributions, complementing cumulative distributions and hazard functions of the variables are derived. Numerical illustrations, graphical displays and interpretations for the obtained distributions and derived functions are provided. An implementation example on defaultable bonds is performed.     

含双参数的三阶非线性两点边值问题的套层解

对含双参数且有套层解的一类三阶非线性微分方程的边值问题的渐近解做了估计 ,得到了任意次近似的一致有效的渐近展开式 .     

A Parameter Selection Method for Wavelet Shrinkage Denoising

Thresholding estimators in an orthonormal wavelet basis are well established tools for Gaussian noise removal. However, the universal threshold choice, suggested by Donoho and Johnstone, sometimes leads to over-smoothed approximations.For the denoising problem this paper uses the deterministic approach proposed by Chambolle et al., which handles it as a variational problem, whose solution can be formulated in terms of wavelet shrinkage. This allows us to use wavelet shrinkage successfully for more general denoising problems and to propose a new criterion for the choice of the shrinkage parameter, which we call H-curve criterion. It is based on the plot, for different parameter values, of the B ₁ ¹(L ₁)-norm of the computed solution versus the L ₂-norm of the residual, considered in logarithmic scale. Extensive numerical experimentation shows that this new choice of shrinkage parameter yields good results both for Gaussian and other kinds of noise.     

基于等距节点积分公式的牛顿迭代法及其收敛阶

利用等距节点的数值积分公式构造牛顿迭代法的变形格式.我们证明了利用4等分5个节点的Newton-Cotes公式构造的变形牛顿迭代法收敛阶为3,并进一步证明了对于最常用的3等分4节点、5等分6节点、6等分7节点、7等分8节点积分公式,所得到的变形牛顿迭代法收敛阶都是3.最后,本文猜想,利用任意等分的积分公式构造变形牛顿迭代法,所得的迭代格式收敛阶都是3.     

一类带小参数的二维反应扩散型方程组的数值方法

本文讨论了一类带小参数的二维反应扩散型方程组的数值方法，基于奇摄动理论，Ｇｒｅｅｎ函数、分裂方法和半群理论，建立这种类型方程组的计算格式，在误差分析中，运用了不等距步长的可行等距度，并将Ｌｏｒｅｎｚ的技巧用于估计解的性状，最后，得到了不安ｌ１「Ω」模意义下以Ｏ（ｈ＋ｌ＋△ｔ）的速度一致收敛。     

高阶Bernoulli数的递推公式及其应用

给出了高阶Bernoulli数的一个递推公式和Nrlund数的一个计算公式,推广了Namias[4],Deeba和Rodriguez[5],Tuenter[6]的结果.