查询词典 approximate differentiability

Finally, to explain the advantage and shortcoming of nonparametric analysis and parametric analysis, and introduce some main shapes of nonpametric regression model: Fourier series, kernel estimators, and spline smoothing. In the meantime, we give the approximate theory and approximate distribution theory of these methods.

阐述了非参数回归分析和参数回归分析的优缺点，介绍了非参数回归模型的几种主要形式：富氏级数，核估计量和样条平滑，给出了这些方法的逼近理论和逼近分布情况。

Base on the fact that a hard-edge aperture function can be expanded into a finite sum of complex Gaussian functions, the approximate analytical expressions for the propagation characters of Hermite-Guassian beams passing through double rectangular apertured are derived. The approximate analysis uses Collins formula. At last, Matlab illustrates some numerical examples.

基于硬边孔函数能拓展成一组有限复高斯函数的和，研究厄米－高斯光束通过双矩孔的传输特性，用Collins公式分析，用Matlab进行一些数值模拟。

Isomap is one of the representative techniques of nonlinear dimensionality reduction.It extends classical multidimensional scaling by considering approximate geodesic distance. However,Isomap is sensitive to noise because the approximate geodesic distance is constructed on the basis of Euclidean distance. In this paper,a kernel-induced distance metric defined in the feature space is introduced instead of the Euclidean distance to evaluate the geodesic distance and construct the corresponding neighborhood graph.

采用核方法在特征空间推导出一类异于欧氏距离的新度量，代替等度规特征映射中的对噪声敏感的欧式距离，用新度量构造测地距离和相应的最小近邻图，提高Isomap算法的抗噪声能力。

If average values before or after catastrophe point when the pressure at both ends reduces exceed the threshold value, judging that there is leak and positioning: calculating approximate wavelet transformation coefficient of pressure data at both ends, initializing searching interval, calculating a signal time delay value corresponding to approximate wavelet transformation coefficient in the searching interval from maximal scale N; converting the time delay value under scale N to that under N-1 by geometric proportion relation; updating the searching interval, repeating above processes until the scale is 0 and positioning based on the time delay value.

若两端压力下降突变点前后的均值变化均超过阈值，判定有泄漏并进行定位：计算两端压力数据的近似小波变换系数，初始化搜索区间，从最大尺度N开始在搜索区间内计算对应近似小波变换系数的信号时延值，利用等比关系将尺度N下的时延估计值转换为N-1下时延估计值，以该值更新搜索区间，重复以上过程至尺度为0，以此时延估计值进行定位。

In the method, the symmetric positive semidefinite matrices are updated to approximate the Hessian matrices of the elemental objective functions and their sum to approximate the Hessian matrix of the objective function.

算法用对称半正定矩阵作为元素目标函数的Hessian阵的近似，使得其和仍然保持目标函数的Hessian阵的某种稀疏性。

First of all,we have given some of the basic concepts of differential equations, described the constant coefficient linear ordinary differential equation solution, for a class of second-order variable coefficient linear ordinary differential equation initial value problem, an approximate solution, the method is first unknown function of a definition for N sub-interval, and then in between each district within a constant coefficient ordinary differential equations similar to the replacement, the solution has been the problem as similar to the original analytical solution, and then gives a detailed second-order change order coefficient of linear homogeneous ordinary differential equation solution examples, the examples of the approximate method proposed in this paper is valid.

首先给出了微分方程的一些基本概念，讲述了常系数线性常微分方程的解法，针对一类二阶变系数线性常微分方程初值问题，提出了一个近似解法，本方法是先对未知函数的一个定义区间作N等分，然后在每一个小区间内用一个常系数常微分方程近似替换，所得到的解作为原问题的近似解析解，随后详细给出了一个求二阶变系数齐次线性常微分方程的解的实例，该实例说明本文提出的近似方法是有效的。

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。

As CMAC neural network could not be used to approximate the multi-valued mapping of an inverse hysteresis directly, an inverse hysteretic operator was proposed to transform the multi-valued mapping into a one-to-one mapping which could enable neural networks to approximate the behavior of an inverse hysteresis.

由于CMAC神经网络不能够直接逼近滞回逆这种具有记忆性的多映射现象，通过引入一个滞回逆算子，将多映射的滞回逆转换成一一映射，然后运用CMAC神经网络控制器来逼近这个一一映射，从而建立一个基于CMAC神经网络的滞回逆模型。

We will demonstrate the specification of reference prior distribution on the random covariance matrix. We will consider the approximate uniform shrinkage prior and approximate Jeffreys' prior. Both are formulated based on the approximated likelihood function. Under generalized linear mixed models, we show that the posterior mode under Jeffrey's prior is asymptotically closer to the REML estimate than the mode under uniform shrinkage prior does.

在广义线性混合模式下，我们证明了在样本数很大时，随机效应之变异数成份的后验众数和REML估计值会近似相等，同时也建立了后验众数和REML估计值的近似关系式，并提出了比较二种后验众数与REML估计值之间远近的准则。

In this paper,some approximate optimal solutions and an augmented Lagrangian function in nonlinear programming were introduced,duality map and duality problems based on the augmented Lagrangian function were established, relationship between the approximate optimal solutions of augmented Lagrangian function and primal problem was discussed.

介绍了几种近似最优解和增广拉格朗日函数，建立了基于增广拉格朗日函数的对偶映射和相应的对偶问题，讨论了增广拉格朗日函数的几种近似解和原问题的几种近似解的关系，得到的结果推广了一些已有的结论。

Chimborazo and Cotopaxi, took me by the hand.

越过琴博腊索山和科托帕克西山。

This car is in a good condition.

这辆车的状况很好。