近似公式

An approximate formula for calculating the ultimate load on a foundation was derived by using the generalized limit equilibrium method.

应用广义极限平衡法获得了地基极限荷载的近似计算公式。

A general formula for computing the OTF of a defocused optical system is derived from the Kirchoff diffraction integration under an approximate condition which is weaker than the Fresnel condition.

本文从基尔霍夫衍射积分公式出发，在弱于菲涅耳条件的近似下，以高斯像面的像差量及系统的离焦量为参变量，导出了便于计算离焦光学系统的OTF的普遍算式。

In some areas,the liquid limit and plastic limit has approximate lineal relevant formula , expressed formula as like this ω P=a+bω L.

液塑限试验是土工试验的重要项目之一，塑限试验一般用手工操作、人为因素大、效率低，但局部地区塑限与液限却有如ωP＝a＋ bωL 的近似线性相关公式。

We thus see that Eq.(7. 44) can only be an approximate solution at best.

于是，我们看到，公式(7.44)至多也只能是一个近似解。

In addition, these equations only approximate the true expected value s.

除此之外，这些公式仅近似真正的预期值。

A method for the generation of Weierstrass fractal surface is presented,based on Helmholtz equation,with the Kirchhoff approximation,the calculus formula of light scattered field on the 1-D Weierstrass fractal suface is deduced.

采用Weierstrass分形函数模拟实际粗糙表面，从简谐光波满足的亥姆荷兹方程出发，利用基尔霍夫近似推导出一维Weierstrass分形粗糙表面的光散射场的积分公式，考虑遮蔽效应后数值计算并分析了表面散射光强的角分布特性。

The uniformly valid asymptotic expansion of the solution to a class of time delay differential equations with damping term and general forcing term was obtained and a simple analytic approximate expression for the resonance solution was given.

对于一类带阻尼和一般力的时滞微分方程问题求得一致有效渐近展开式，给出了共振解筒洁的近似解析表达公式。

Finishing calculation of mean value, standard deviation, skewness, kurtosis of Beta distribution.(2) Fitting parameters of many kinds of typical distribution and using residual deviation to evaluate fitting precision.(3) Using Beta distribution as an agreed indication distribution applied to many kinds of practical photoelectric measurement distributions.(4) Deriving theory formula of Bayes point estimation about Beta distribution parameters and mean value and standard deviation on the condition of mean square error loss function and supposed the prior distribution is uniform distribution.(5) Generating MCMC sample from post distribution by the method of Gibbs sample algorithm. Calculating bayes point estimation from sample on the condition of mean square error loss function. Calculating confidence interval by an approximate method to complete interval estimation.

本文的主要工作有：(1)解决了Beta分布参数a和b的精确计算以及均值、标准差、偏度、峰度的计算问题；(2)拟合出10余种典型分布的Beta分布的两个参数，并且采用剩余标准差评价该Beta分布的拟合精度；(3)对多种典型的光学与光电测量系统的测量分布进行了Beta分布统示表示；(4)在假设先验分布为均匀分布前提下，得到参数a和b以及均值μ和标准差σ在均方误差损失函数下的贝叶斯点估计理论计算公式；(5)利用直接抽样的Gibbs抽样算法，从后验分布中产生MCMC样本，从样本直接计算均方误差损失函数下的贝叶斯点估计，并使用一种近似方法计算其置信区间，完成区间估计。

Recent measurements on CO2-laser-assisted electron-atom collisions have shown large inconsistencies with the Kroll-Watson formula.We use Born approximation theory to carry out a detailed study of the problem.

最近的CO2激光辅助电子-原子碰撞的测量结果与K-W公式存在着非常大的差异，用玻恩近似理论对此进行了详细的研究。

And the formulae for estimatingthe edge-toughness of Cartesian product and Kronecker product of some special graphs are presented.

证明了一类r-正则r=κ′连通非完全图G的边坚韧度近似等于r/21+(1/│V│-1并且提供了估计一些特殊图类的笛卡儿积和Kronecker积的边坚韧度的公式。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。