近似方法

We use the Taylor series expansion method to get the second-order approximate expression of the confidence region of the parameters, and then according to the principle of minimizing the volume of the confidence region, this paper carries out experimental design for the regression model, and then fixes the point range in the domain of definition of design variable for the model function so as to select the designing point, which can minimize the volume of the confidence region.

文章首先计算指数族非线性模型的回归参数β在1-α置信水平下的置信域的体积，为了便于计算，需把置信域投影到切空间中去，投影后的置信域是一个椭球体，用Taylor展开方法对此椭球体的体积进行二阶近似，推出原参数置信域的体积的近似表达式，然后对回归模型进行试验设计，根据置信域体积最小准则，在模型函数的设计变量的定义域上确定点列，选取使置信域体积达到最小的设计点。

We have also introduced a method of approximate description of three order systems, using a kind of bang-bang control to approximate the extremal control.

同时利用bang-bang控制来近似极端控制的方法，给出了三阶反稳定系统可控区域的近似描述。

In order to solve the problem,starting from the analysis of the simplest plane wave numerical theory,we derived the formula of relative phase velocity and group velocity under the condition of arbitrary high-order finite-difference approximation,and gave the computational method for acquiring the optimum Courant number,and then analyzed the anisotropic effects due to finite difference approximation.

针对此，从最简单的平面波数值理论分析出发，推导了任意高阶有限差分近似条件下相对相速度和相对群速度的计算公式，给出了求解最佳Courant数的计算方法，分析了差分近似造成的各向异性效应。

Calculus can be used to find approximate solutions to equations, in methods such as Newton's method , fixed point iteration , and linear approximation .

积分可以用来寻找近似解方程，在方法，如牛顿法，不动点迭代和线性近似。

One position control system is introduced as the objective controlled by FOC. Based on Mittag-Leffler function, the fractional order control system with full memory length is adopted as evaluation criterion, and an approximation performance function of discretization methods is proposed. Analyzing the time domain error and approximation performance, the investigation to various discretization methods is carried out comparatively in detail.

引入一个位置控制系统作为分数阶控制对象，将Mittag-Leffler函数的全记忆长度分数阶控制系统作为评估基准，提出了一种离散算法的近似性能函数，通过时域误差分析以及近似性能分析，对比研究了分数阶微积分算子的数字实现方法。

The first, look like each detail picture of direction of picture and each layers to carry on DCT towards get of again, then will imbed to look like the son diagram DCT transformation through two value watermark pictures of the false random row preface behind of the part of the high part of frequency and the detail son diagram energy concentration.

本论文中提出的第一种算法是一种基于离散余弦变换和离散小波变换相结合的脆弱水印方法，即：先对图像进行离散小波变换，再对得到的近似图像和各层各方向的细节图像进行离散余弦变换，然后将经过伪随机排序的二值水印图像嵌入到近似子图DCT变换后的高频部分和细节子图能量集中的部分。

However, the solutions of the Cauchy problem of the nonlinear hyperbolic system generally develop singularities in finite time even if the initial data are small and smooth.For this reason, solutions must be found in the space of discontinuous functions. Therefore, one can not directly use the classical analytic techniques that predominate in the theory of partial differential equations of other types. Instead, we construct approximate solutions via the singular perturbation methods. By using the compactness of the approximate solutions, we can obtain the existence of the solutions of original system.

然而一般而言，即使是在初值很小且光滑的情况下，非线性双曲型守恒律的Cauchy问题的解在有限时间内也会出现奇异性，为此，我们必须在不连续函数空间中寻找上述问题的解，因此对这类问题的研究，我们也不可能直接利用在其它类型的偏微分方程中占主导地位的解析方法来解决问题，而是通过奇异扰动法构造近似解，由近似解的紧性得到原问题解的存在性。

Algorithm for determining the lower limit of the iterated times in IFSP;2. Stratigraphical division and lower limit of the Quaternary in Hunan;3. At present, the approximate solution of Voigt and Reuss's upper limit or lower limit and the calculating formula of Hashin and Shtrikman's upper limit or lower limit are accurate.

计算复合材料有效弹性模量上、下限的方法中，Voigt和Reuss的上、下限近似解及Hashin和Shtrikman的上、下限计算公式较为精确，但Voigt-Reuss近似解通常忽略了各向异性非均匀体的研究，是一个不全面的结果。

While the new components having the same numbers with these original physical vectors are introduced and the new components are combined with those original physical components to form a new symplectic space, the ray problem of wave propagation in geometrical optics is converted into the problem of Lagrange submanifold in the symplectic space.

本论文的工作作为国家自然科学基金地震波传播与成像项目（NO.40174032）的一部分，得到如下结果：论文分析了利用Maslov方法求解非均匀介质中波动方程高频近似解的基本原理和求解过程，构造了介质系数只在一个方向变化时波动方程高频近似解的通用计算公式。

The results are the following: When calculating the motion mass, it is better to use idler's equivalent mass instead of the rotating part mass and serial idler's rotating inertias and equivalent mass are calculated. The accurate analysis result for the deflection curve length of the belt shows: The error calculated by the approximate parabola length is lower than 10〓. Thus the approximate method is accurate enough for calculation. The relations between the running resistances coefficient and the belt velocity are studied by experiment, which are the bases for calculating the linear coefficient values between them.

得出：在计算参与运动质量时对托辊应采用托辊的等效质量而不是目前采用的托辊旋转部分质量，并计算出了系列的托辊转动惯量和等效质量；对输送带的挠曲线长度进行了精确的分析，结果表明：采用近似的抛物线长度计算方法其误差在10〓以下，因而得到在计算输送带挠曲线长度时采用近似的抛物线具有足够的精度；对输送机运行阻力系数与带速间的关系进行的实验研究，得出阻力系数与带速线性关糸的系数值。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。