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收敛的阶

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I. d. Bernoulli random variables. First, we can get the upper bound with order from Chebyshev inequality. Second, a better upper bound was gotten with the new inequalities, which can fasten the convergence rate.

并对服从两点分布的独立随机变量X1,X2,…,X进行研究,首先利用Chebyshev不等式得到随机变量偏离方差ES的上界,但它只有阶的收敛速度,然后利用新的不等式得到一个新的上界,它有更快的收敛速度,这在探讨收敛速度时有着重要的理论意义。

In Chapter 2, starting from the basic fractional ordinary differential equations,weapply a high order approximation of fractional derivative advanced by Lubich to frac-tional differential equation, construct a high numerical difference scheme to solve thefractional differential equation, present error analysis of the algorithms theoretically,and prove the consistency ,convergency and stability.

接下来的第二章中,首先从基本的分数阶常微分方程出发,对Lubich提出的一个关于分数阶导数的高阶近似,将其应用于分数阶微分方程,构造高阶数值差分格式来进行分数阶微分方程的数值求解,并在理论上给出这一算法的误差分析,证明了它的相容性,收敛性和稳定性。

And we show that random walk model converges to the stable law of Lévy-Feller advection-dispersion equation by use of a properly scaled transition to vanish-ing space and time steps,We propose an explicit finite difference approximation for Lévy-Feller advection-dispersion equation.

第三章讨论描述服从某种稳定分布反常扩散的非对称空间分数阶对流-扩散方程——Lévy-Feller对流-扩散方程,首先利用Fourier变换和Laplace变换给出方程的基本解,然后利用Grünwald-Letnikov分数阶导数移位离散算子离散方程中的Riesz-Feller分数阶导数得到离散格式,证明此格式可以解释为离散随机游走模型,并且证明了当时间和空间步长以一定的比率同时趋于0时,所提出的离散随机游走模型收敛到Lévy-Feller对流-扩散过程的稳定分布。

In Chapter 4, we consider more complex fractional nonlinear differential equation,also using the high order approximation presented by Lubich to construct correspond-ing numerical scheme and giving the error analysis of the algorithms.

在第四章中,进一步的考虑更复杂的非线性分数阶常微分方程,同样利用的是Lubich提出分数阶导数的高阶近似,构造相应的数值格式,并给出这一算法的误差分析,即相容性,收敛性和稳定性的证明。

In Chapter 3, considering fractional relaxation equation, we make use of directlythe Grunwald-Letnikov definition to discrete fractional derivative, obtain a numericalmethod of fractional relaxation equation,and give the proof of consistency ,conver-gency and stability.

第三章对于一个推广到分数阶的松驰方程,直接利用Gru¨nwald-Letnikov分数阶导数定义进行离散,得到分数阶松驰方程一个数值方法,并给出了相容性,收敛性和稳定性的证明。

Aimed at the calculation complexity of Newton iterative method for solving nonlinear equation,a new iterative method with higher convergence rate and without derivative calculation is presented in this paper.Its convergence rate p is 1.839 and it doesn't need to calculate derivative.

为解决Newton迭代法求非线性方程数值解时必须提供一阶导数值的问题,提出了一个新的迭代方法,该方法不需提供导数值而只需计算函数值,且具有p=1.839的收敛阶,因而是一个收敛速度快且不需要计算导数值的迭代方法。

This project also obtained several limit theorems for some important dependent random variables and stochastic processes, such as the Strassen law of the iterated logarithm for negatively dependent random variables, strong limit theorems for mixing random vectors in Banach spaces, sample path properties for two-parameter fractional Wiener processes, and so on.

随机环境中的随机变量与随机过程的研究在国内外相当活跃,本项目主要研究它们的极限性质,着重研究了随机风景中随机变量与随机过程的极限性质,主要取得了以下几个结果:首先对简单对称的Kesten-Spitzer随机游动在低阶矩的条件下给出了强逼近,大大减弱了前人要求任意阶矩的条件,然后对独立风景中的一般随机变量给出了强逼近的一般性结果,由此导出在风景和随机变量都只具有低阶矩的条件下的独立但不同分布、混合相依变量的强逼近,在只有弱高于二阶矩的条件下得到了重相对数律和弱收敛;给出了连续时间参数的Brown风景中Brown运动和稳定风景中稳定过程的滞后增量和连续模等精确样本轨道性质;同时给出了一些重要的相依随机变量和过程的若干极限定理,如负相关随机变量的Strassen重对数律、抽象空间上混合相依变量的一些强极限定理成立的充分必要条件、两参数分数Wiener过程的样本轨道性质等。

The convergence order of the nodal values of the finite element solution exceeds the possible global convergence order.

有限元在节点处的值的收敛阶远远超过其可能的整体收敛阶。

The chattering mode in the dynamic process of the unforced switched systems isinvestigated. The relations between the rotation directions of trajectory, the increase ordecrease the polar radius of trajectory, and the convergent chattering mode are revealed.

分析了二阶切换线性系统的收敛震颤现象与相轨迹的旋向以及相轨迹极半径增减趋势之间的关系,进而得到忽略切换延迟时二阶切换线性系统出现收敛震颤模态的充分条件。

Based on an appropriate monitoring function, a switching scheme is proposed so that after a finite number of switching, the tracking error can converge exponentially to zero if the plant relative degree is one, or a residual set whose radius is proportional to some design parameters if the plant relative degree is greater than one.

在监控函数的监测下,相关的控制信号经至多有限次切换后将停止切换,系统跟踪误差指数收敛于零(若被控系统相对阶为1),或收敛于一个正比于设计参数的残集中(若被控系统相对阶大于1)。

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They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性,但我大喊,并在他们的方向扔石头让他们过的线索,远离我,以防万一。

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在你的书包里槽2把包装纸、数量无关紧要。

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密封,遮光,置阴凉干燥处。