查询词典 approximation theorem

The proof relies on regular approximation, the fixed point theorem, the embedding theorems, the semigroup theory and a series of complicated estimates.

然后，利用此结果，通过区域正则化逼近及半群理论获得各种估计，并给出了非齐次Liouville-Poisson模型的整体古典解。

Koopmans theorem is an approximation in molecular orbital theory , such as density functional theory , or Hartree-Fock theory, in which the first ionization energy of a molecule is equal to the energy of the highest occupied molecular orbital, and the electron affinity is the negative of the energy of the lowest unoccupied, i.e.

如同密度泛函理论或者Hartree－Fock理论，分子轨道理论中常用到的Koopmans 定理也是一种近似。

Secondly, using the relation between the weighted modified K-functional, the weighted modulus of smoothness ,the weighted main-part modulus of smoothness . we get the pointwise direct and inverse approximation theorem with Jacobi weight for Szdsz-Kantorovich operator. Thus some results on w = 0w(x denotes the weight function, Ditzian-Totik modulus and classic modulus are extend.

其次，引入一种改变的带权K-泛函，利用带权光滑模和带权主部光滑的关系及带权光滑模与改变带权K-泛函的等价性，关于Szász-Kantorovich算子，讨论了一阶矩不为零的算子的点态带Jacobi权逼近正定理及等价定理，推广了已有的权为零及Ditzian-Totik光滑模和古典光滑模的结果。

In this thesis,using the Bernstein polynomial approximation,Stieltjes transform method and the central limit theorem of martingale,under suitable moment conditions,we prove the CLT of LSS G_n with a generalized regular class C4 of the kernel functions for large dimensional sample covariance matrices.

在适当的矩条件下，当核函数f属于C4时，我们证明了大维随机协方差矩阵的线性谱统计量的中心极限定理。

Digital holography ; Microscopic digital holography ; Wave front reconstruction ; Fresnel approximation ; Convolution method ; Angular spectrum theorem

数字全息；显微数字全息；波前重建；菲涅耳近似；卷积法；角谱方法

In Chapter 3, by using the technique of finite dimensional approximation of Seiberg-Wittentheory, the equivariant K-theory and some other methods, we study the problem of topologicalrestriction when there are smooth groups acting on Spin 4-manifolds such as the alternatinggroup A_5, cyclic group Z_6 and symmetric group S_3 with actions of odd type, consequently weimprove Furutas 10/8 theorem under the condition of group actions.

第三章运用Seiberg-Witten理论的有限维逼近技巧和等变K-理论等工具，研究了Spin 4-流形X上分别存在光滑交错群A_5、循环群Z_6和奇型三阶对称群S_3作用时，X的拓扑限制问题，在群作用下改进了Furuta的10／8定理。

The mechanism of the least squares approximation that MFNN with finite nodes carried out on a given discrete point set is made, which, for the first time, results in an important theorem.

分析了有限规模多层前向网络用于离散点集上的最小二乘逼近的机理，首次给出了一个有关的定理。

In this thesis, we use the Min-Max criterion and Parks-McClellan algorithm to design this optimal approximation error of spectrum. Moreover, we give constraint of this optimal spectrum to get the positive spectrum. Then the positive spectrum can be factored by Spectrum Factorization Theorem and can be realized by FIR system.

我们利用最小化最大误差指标，及Parks-McClellan演算法，设计出具有最佳误差的频谱，并对此频谱做限制式上的处理，来得到正数列频谱，并将所得到之正数列频谱利用分解理论做分解，并以FIR系统实现之。

Based on approximation capability of neural networks and mean value theorem, a stable adaptive control scheme is proposed to control the implicit dynamic system with an uncertain nonlinearity.

针对一类隐含控制输入的非线性系统，引用中值定理并利用径向基神经网络的逼近能力，提出了一种稳定自适应神经网络控制方案，以实现对一类隐含控制输入未确定非线性系统的控制。

In part 3, utilizing the existing Lipschitz results and the property of Yosida approximation of monotone and continuous function, we prove the existence and uniqueness theorem of a general backward stochastic differential equation with monotone and continuous coefficient.

第三部分在系数仅满足单调连续这样一个新条件下，我们综合运用单调连续函数的Yosida逼近的性质以及Lipschitz条件下的已有结果，证明了一般形式的倒向随机微分方程解的存在唯一性。

"Second Life is remarkably easy to work with, and is very popular,"

"第二次生命是显着容易的工作，并且很受欢迎，"

For example, we usually assume that materials are homogeneous and isotropic and free of internal defects or flaws.

为了得到适合有限元分析的模型，我们必须经过如图2所示的简化步骤。