查询词典 weierstrass approximation theorem

Introduces the notion of Feynman's path integrals and path integrals approach to financial modeling; Derives the path-dependent options pricing formula by making use of the Lagrange form of path integrals; Discusses Ilinski(2003)'s Gauge model which based on path integrals and fibre bundle, and its application for real-options evaluation; Summarizes the general modeling framework of options evaluation, taking advantage of the Hamilton form of path integrals; Applies the Geske-Johnson's analytical approximation in the path integrals form to the real-options evaluation for investment decisions, detailed procedure is presented under the assumption that underlying asset price dynamic follows a geometric Brownian motion, and the integral reduction for multivariate normal integrals and polynomial approximation for real-options evaluation is given.

系统论述了路径积分概念方法及其在期权估值中的应用，利用路径积分方法的Lagrange表述推导了路径依赖期权定价公式：探讨了基于路径积分和纤维丛的Gauge模型思想方法在实物期权价值评估中的应用；利用路径积分的Hamilton表述形式，总结了基于Hamilton表述的期权估值一般化框架；基于路径积分的形式框架建立了一个新的投资期权估值模型，并在具体的估值算法中给出了多重正态积分的降阶计算和期权价值的多项式逼近方法。

Then the distributed sources models of one order approximation model, twoorders approximation model, spatial frequency model and low order JA seriesexpansion model are compared with respect to the model accuracy.

随后将分布源的一阶近似模型、二阶近似模型、空间频率模型和低阶JA级数展开模型的模型精度进行了比较。

Paraxial approximation absorption boundary condition based on acoustic wave equation can obtain better absorption results by increasing paraxial approximation order of Taylor series. However, this kind of operation will increase the complexity of difference computation, and result in instability of computation process.

基于声波波动方程的旁轴近似吸收边界条件可以通过提高泰勒级数展开的旁轴近似阶数获得更好的吸收效果，但这样不仅增加了差分计算的复杂性，同时还导致计算过程不稳定。

Firstly, a two-dimension tensor product space is constructed, in which reproducing kernel exists. Secondly a multiresolution analysis is constructed in the reproducing kernel space. Then an orthonormal basis in is obtained. Thus,the reproducing kernel space can be expressed by wavelets spaces. Wavelets approximation formula and sampling formula can also be obtained in the space. Besides, the wavelets approximation formula is simple and easy for calculation. That completes the theory of multiresolution analysis in finite interval fully and provides theoretical base and algorithm for application.

首先，构造二维张量积空间，并证明该空间具有再生核；其次在再生核空间中，建立多尺度分析，获得该空间的一个标准正交基，使得再生核空间可以由小波空间来刻画，进而得到小波级数和相应的采样公式，而且给出的小波级数形式简单易于数值分析，进一步完善了有限区间上的多尺度分析方法，也为实际应用提供了良好的理论基础和算法。

According to the characteristic that the definition point of the Q matrix of wave front is always located on the extremum point on the axis of the beam, a three-dimensional formula for the rectificative factor of phase in complex ray paraxial approximation is proposed, which calculates the rectificative factor of phase directly without considering the calculation of the main directions and curvatures and the rotation of the coordinates, thus simplifying the paraxial approximation calculation by the complex ray expansion method.

根据波前Q矩阵的定义点总位于波束轴上极值点的特点，提出了三维复射线近轴近似相位校正因子计算公式。该公式不用考虑主方向和主曲率的计算和坐标旋转，直接计算相位校正因子，从而简化了复射线展开法的近轴近似计算。

The difference of results under two approximations-high order approximation and paraxial approximation are also given.

最后用计算机绘制了列阵成像系统中各观察面上的场强分布。

The concepts to be introduced include, but are not limited to, the random phase approximation, the mean field theory (aka saddle-point, or semiclassical approximation), the tunneling dynamics in imaginary time, instantons, Berry phase, coherent state path integral, renormalization group..

这些方法主要涉及如无规相近似、平均场理论(aka 鞍点或半经典理论)、虚时间中的隧道动力学、瞬子、贝里相、相干态路径积分及重整化群等概念。

A neural network is then used to represent the estimation of potentials,both the parameterized TD(0) learning formulas and algorithm are also derived for approximating the policy evaluation.By the approximation values of potentials and approximation policy iteration,a unified neuro-dynamic programming optimization approach is consequently proposed for both two criteria.

根据定义式，建立性能势在平均和折扣性能准则下统一的即时差分公式，并利用一个神经元网络来表示性能势的估计值，导出参数TD(0)学习公式和算法，进行逼近策略评估；然后，根据性能势的逼近值，通过逼近策略迭代来实现两种准则下统一的神经元动态规划(neuro-dynamic programming，NDP)优化方法。

By analysing the compute result of the quadratic approximation formula, we educe the conclusion that 3 is the best rank code for the quadratic approximation formula.

通过对最小二乘拟合公式实际计算结果的分析，得出了"拟合公式阶数取3为最佳"的结论。

Simulation results indicate that the proposed wavelet network in the paper has a good approximation capability, and has the advantages of rapid convergence rate and high approximation accuracy.

结果表明，这种新的小波网络具有良好的函数逼近能力，收效速度快且逼近精度高。

I had a lovely dog named PiPi, he was one of my best friends.

我曾经有过一只小狗，它的名字叫皮皮，它很善良，它是我最忠实的朋友。

Newly ovulated mouse oocytes were cultured in the CZB medium supplemented with different concentrations of pyruvate before treated for activation or assayed for MPF activity.

我们猜测卵母细胞在不含丙酮酸的条件下老化的更快，并且卵丘细胞可能通过消耗不含葡萄糖的CZB中的丙酮酸从而促进卵母细胞老化。