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By using the estimate for trigonometric sums and the esitimate for general Kloostermann sums, we study the asymptotic properties of N, and give a sharper asymptotic formula.

本文的主要目的是利用三角和估计及广义Kloostermann和估计研究了N的渐近性质,并得到一个较精确的渐近公式。

Our main results are as follows: we have given a non-trivial estimate for a class of rational exponential sums,and the best possible upper bound for a class of characters sums with exponential functions.

我们的主要结果是:给出了一类有理指数和的非平凡估计,以及一类特征和的最佳上界。

It provides global estimate for the parameters and local linear smoother for the functional coefficient s in the models respectively.

为了检验特殊的参数化模型是否已经足够描述实际数据的动态结构,提出了一个Boot st rap 检验方法。

In this paper we present an estimate for bounds of module of eigenvalues of the iteration matrix M^(-1)N for a kind of Baily-Crabtree diagonally dominant matrix M.

该文对一类Baily-Crabtree型对角占优矩阵M,给出了迭代矩阵M^(-1)N的特征值模的上下界估计。

Firstly, the existence and uniqueness of the solution for neutral stochastic functional differential equations with infinite delay under the uniformly Lipschitz condition, linear grown condition and contractive condition can be directly derived; And the moment estimate of the solution and the estimate for error between the approximate solution and the accurate solution can be both given; If the uniformly Lipschitz condition is replaced by the local Lipschitz condition, the existence and uniqueness theorem can be gained; Meanwhile, the existence and uniqueness of the global solution in the interval 0,+∞ can also be obtained; Secondly, L~p-exponential estimate of the solution for neutral stochastic functional differential equations with infinite delay can be studied; At length, the theorem of the local solution about neutral stochastic functional differential equations with infinite delay only under the local Lipschitz condition and the contractive condition can be established.

首先,在一致Lipschitz条件,线性增长条件和压缩性条件下,直接得到了具无限时滞中立型随机泛函微分方程解的存在惟一性,并给出了解的矩估计,近似解与精确解之间的误差估计;将一致Lipschitz条件替换为局部Lipschitz条件,也得到了具无限时滞中立型随机泛函微分方程解的存在惟—性,同时,也给出了在整个区间0,+∞上具无限时滞中立型随机泛函微分方程解的存在惟一性定理;其次,也讨论了具无限时滞中立型随机泛函微分方程解的L~p指数估计;最后,在局部Lipschitz条件和压缩性条件下,建立了具无限时滞中立型随机泛函微分方程局部解的存在惟一性定理。

The model is applied to predict the total amount of Chinese population,and the results show that nonparametric regression model is better than linear regression model,at the same time,the situation orthogonal sequence estimate is superior to k-near neighbour estimate for the dynamic relation between the total amount of Chinese population and nation...

并应用此模型对我国1952—2003年的人口总量和GDP总量进行了预测分析。结果表明:非参数回归模型优于线性回归模型,同时正交序列估计效果也优于k-近邻估计。

In.Chapters7-8, when the conditions for the exponential estimate are not satisfied, a local asymptotic estimate and a tail asymptotic estimate for the distributions of ladder height and supremum for the random walk are derived and non-exponential asymptotic forms for solutions of defectiverenewal equations are obtained.

在第七、八章中,首先给出了随机游动阶梯高度及极大值的局部估计和尾估计以及一瑕疵更新方程解的渐近估计,然后将结果应用到风险理论中,得到了一些新结论。

Unbiasedness is the property of an estimator, that is, the procedure that can produce an estimate for a specific sample, not an estimate.

估计量是一种方法,该方法使得给定一个样本,我们可以得到一组估计值。

The numerical results show that our method is effective. For the noncharacteristic Cauchy problem for 2-D and 3-D heat equation, we give the explicit H\"{o}lder type stability estimates by using weighted energy method. Especially,H\"{o}lder type stability estimate for discrete solutions of the heat equation is obtained through a fully discrete method. The numerical results are presented.

对于二维和三维的热传导方程的非特征Cauchy 问题,我们利用权函数方法,给出了一个显式的H\&{o}lder 型的稳定性估计,特别的,对于二维的非特征Cauchy问题,我们利用充分离散的方法,对二维问题的离散形式同样给出了H\&{o}lder 型的稳定性估计,同时,我们也给出了数值例子来说明我们的估计。

In the first part, first of all, we have a priori estimate for solution of the reaction-diffusion equation with initial condition and Dirichret boundary conditions. Then, we construct a semidiscrete Legendre pseudospectral scheme, and have a priori estimate for approximate solution. We discuss the asymptotic stability of approximate solution. At last, we get a error estimation on large time for solution of the semidiscrete system.

首先,对此类方程初边值问题的解进行了先验估计;然后建立方程半离散的Legendre拟谱格式,并对近似解进行了先验估计,讨论了近似解的渐近稳定性;最后,得到了半离散系统解的长时间误差估计。

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