逼近

An algorithm about approximating the inverse function with C\+k constrains is proposed.

提出一种带端点C\+k约束的反函数逼近算法。

Reusing iterative information ,an approximate inverse function is constructed byinverse interpolation.

重复使用迭代信息反插值构造逆函数的近似，一方面较只使用单点信息能更好地逼近隐式函数，另一方面直接得到显式近似解。

The main contents include: Some preliminary theory (introduction to Sobolev spaces and variational formulations for differential equations); finite element methods for one-dimensional elliptic problems; the construction methods for general finite elements; error estimates for interpolation operators and inverse inequalities for finite element spaces; a priori and a posteriori error estimates for the finite element method for high-dimensional elliptic problems; some typical spectral methods for partial differential equations; error analysis for the spectral approximation for some linear and nonlinear partial differential equations.

主要内容有：准备知识（Sobolev空间的基本概念和主要结果，微分方程的变分描述）；一维椭圆型方程有限元方法；一般有限元的构造；插值算子误差估计和逆不等式；高维椭圆型方程的先验、后验误差估计；求解偏微分方程的几类谱方法；线性与非线性问题谱逼近的误差分析等。

The harmonic field of electric dipole source on the uniform earth surface is converted into transient field by inverse Laplace transform,and the Bz/ t transient curve is calculated.The Hz transient curves on the stratified earth surface are obtained from cosine transform calculated by broken line approximation.

由逆拉普拉斯变换将均匀大地面上的电偶极子源谐变电磁场转换为瞬变电磁场，并计算出Bzt瞬态曲线；对分层大地面上的瞬变电磁场，采用折线逼近法计算余弦变换得出Hz瞬态曲线。

Special attention should be paid when we apply the decomposition method to two-point boundary value problems, it is necessary to solve a algebraic system;It should be noted that a modification of inverse operator should be made when dealing with singular boundary value problems;Laplace transform and Pade approximants can be coupled to enhance the efficiency of the decomposition method.

比如，在求解两点边值问题时就需要特别注意，这时需要采用待定系数法，最后会涉及到系数方程组的求解；在处理奇异边值问题时需要重新定义逆运算；不少研究人员还把分解方法与Laplace变换和Padé逼近相结合来进一步提高分解方法的精度。

The well-known spectrum assignment problem are discuussed and a general proofs for it and its generalization are gived. 3. The general conditions of invertible completions of operator pairs are acquired.

作为研究基础，引入了算子对可控性与可容许性指标及算子ε-限制，并利用算子闭值域特性、值域逼近及空间的不同分解，获得了算子谱配置问题及广义的算子谱配置问题一般性证明。

Iphigenia was the first to see the dilemma of her father, and she heard the commotion of the rebels coming to her father's tent.

伊菲革尼亚有生以来第一次看到父亲如此为难，同时耳朵里又听到了叛乱的呼声，叛军正在向她父亲的帐篷步步逼近。

Stationary NA sequences; empirical measure; large deviations principle; linear processes; functional law of the iterated logarithm; strong approximations; LPQD sequences; m-dependent random element; precise asymptotics; the central limit theorem for the sum of random number

基础科学，数学，概率论、数理统计平稳NA序列；经验测度；大偏差原理；线性过程；泛函型重对数律；强逼近； LPQD序列； m-相依随机元；精确渐近性；随机指标中心极限定理

Using RBF neural network substitutes BP network as the approximation of implicit performance function, and the response surface is formed in the sphere of hyper-pyramid at iteration step.

采用径向基函数神经网络，代替目前常用的BP网络，迭代过程中在超锥体的范围内构造响应面，逼近隐式的非线性功能函数。

Established a series of results on the Jacobi approximation, and proposed the Jacobi spectral method for singular problems, which produces the possibility of using spectral mcthod for problems in a ball.

最近，郭本瑜教授等建立了一套相当完整的Jacobi正交逼近理论，并提出了适合于一类奇异问题的Jacobi谱方注。

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。