查询词典 weak approximation theorem

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。

To reduce the error between the interpolation function regaining the sampled signal and interpolation function ha by Shannon sampling theorem, this paper suggests that the common linear interpolation is replaced by a second order approximation of the parabolic interpolation.

为减小恢复被采信号所用的内插函数与山农采样定理要求的内插函数ha之间的误差，提出了用抛物线内插--ha的二阶近似代替常规的线性内插。

The main results are as following: A A new demonstration to optical theorem is constructed B The scattering amplitude function for small particles, which is more accurate than that in classical RGB, is gained using electrostatics approximation, C Through a δ transform to the high frequent oscillation function, a concise deduction of the EG-type scattering amplitude function has been achieved.

主要结果如下： A给出了光学定理的一个新证法； B利用静场近似，得到了比经典RGB更精确的小粒子散射振幅函数； C通过一个高频振荡函数的δ变换，给出了一种EG散射振幅表达式的简明推导，并做了小角度散射简化，参照ADT，对EG近似又做了相位修正； D定义了一个新的函数—消光函数，并得到了组合散射体消光函数的平均定理。

A new type of polar decomposition—weighted polar decomposition of matrices is presented and defined. Aim at this new matrix decomposition, we prove its uniqueness theorem and obtain its uniqueness conditions, and also investigate the best approximation property of weighted unitary polar factor.

矩阵的极分解和广义极分解一直是矩阵分析研究的重要内容，本文中我们对其进行了横向扩展，提出并定义了一种新的极分解形式—矩阵的加权极分解。

In order to overcome this problem, in this paper, the surface electric current of the conducting sea surface and the first-order scattering from the conducting plate are obtained by employing Physic Optics method. The backscattering field of the time-dependant sea surface is calculated by using Kirchhoff Approximation. Meanwhile, taking the advantage of a newly developed technique that utilizes the reciprocity theorem, the difficulty in formulating the secondary scattered fields from the composite target is reduced. The dependences of the backscattered field on the parameters, such as the wind speed and the sizes of the plate are discussed.

为了克服这一问题，本文应用物理光学近似求解了导体海面表面电流及导体平板的一阶散射场，应用基尔霍夫近似给出了海面的后向散射场，同时借助互易性定理降低了求解平板和海面之间二次耦合散射场的难度，讨论了平板尺寸、风速等对后向复合散射场的影响。

Based on the above results, the problems of the electromagnetic interaction between a perfect conducting plate and 1-D/2-D conducting slightly random rough surface and the problems of the electromagnetic interaction between a dielectric spherical particle and dielectric slightly random rough surface are investigated. By using the reciprocity theorem, Small Perturbation Method and Physical Optics approximation, the solution for the composite scattering field from the composite target is derived and evaluated, and the numerical results are discussed and analyzed.

在此基础上，用互易性原理分别研究了一维、二维导体微粗糙面与其上方金属导体平板目标的复合电磁散射及介质粗糙面与其上方球形粒子的复合电磁散射，结合互易性原理和粗糙面散射微扰法及物理光学近似导出了复合散射场的计算公式并进行了数值计算，对计算结果进行了讨论和分析。

The equivalent solid sphere have same radius of the original coating shell, using reciprocity theorem, the effective conductivity of composite were obtained, it compare agree with effective medium approximation.

利用倒易定理，其结果与有效介质近似进行比较发现两者基本一

Use nationalization degree and the relationship that commercialize degree, condition of calculable market economy plays scope of optimal and state-owned economy.

利用国有化程度与市场化程度的关系，可计算市场经济条件下最佳国有经济规模。

The kinds of extractant also effected desulfurization rate .

萃取剂对脱硫率的影响也很大，乙二胺的萃取效果优于甲醇的。