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It is proved that any continuous time-invariant operator with fading memory can be approximated by a Volterra series.

任何具有衰减记忆的连续时不变非线性算子，都可以由Volterra级数任意逼近。

A human model using polynomial convolution surface is presented which is modeled by articulated skeletons convolved with some kernel function. The convolution surface and curve correspondence theorem under orthogonal projection is presented. The human contour is approximated with a convolution curve and 3D human pose can be estimated using a nonlinear optimization algorithm.

首先建立了一种新颖的多项式密度卷积曲面人体模型，该模型由连接体线骨架与某种卷积核卷积而成，整个曲面是一张连续曲面，调节多项式和半径参数可以让人体任意变形；给出了正交投影下卷积曲面和曲线对应的概念和相关定理，为二维的图像轮廓和三维人体模型之间建立对应关系；根据正交投影下卷积曲面与曲线对应定理，用卷积曲线去逼近人体的图像轮廓曲线，从而估计和恢复出三维人体运动姿态。

State variables at left end of time interval and costate at right end of time interval were taken as independent mixed variables, and the state and costate variables inside the time interval were approximated by Lagrange interpolation. Nonlinear optimal control problems were replaced by nonlinear equations through dual variable principle, and the symplectic algorithm for solving nonlinear optimal control problems can be obtained at the same time.

以时间区段一端状态和另一端协态作为混合独立变量，在时间区段内采用拉格朗日插值近似状态变量与协态变量，然后利用对偶变量变分原理并将非线性最优控制问题转化为非线性方程组的求解，最终得到求解非线性动力学系统最优控制问题的保辛数值方法。

State variables at left end of time interval and costate at right end of time interval were taken as independent mixed variables,and the state and costate variables inside the time interval were approximated by Lagrange interpolation.

以时间区段一端状态和另一端协态作为混合独立变量，在时间区段内采用拉格朗日插值近似状态变量与协态变量，然后利用对偶变量变分原理并将非线性最优控制问题转化为非线性方程组的求解，最终得到求解非线性动力学系统最优控制问题的保辛数值方法。

The Cholesky decomposition of cross spectral density matrix was approximated and reduced, and then the modified spectral representation method is efficient and requires less computer memory, which is suitable for simulating spatial wind fields of long span bridges.

针对现有Deodatis方法模拟大跨度桥梁空间脉动风场中存在的计算量问题，通过对谱分解矩阵引入插值近似，减少谱分解的次数，从而提高该谐波合成法的计算效率，并节省内存花费，实现了对三维空间脉动风场的有效模拟。

The nonlinear equation of β obtained is subsequently approximated by a cubic equation from which β is solved directly.

利用这一极值原理，得到一个关于β的非线性方程，近似简化后成三次方程，直接求解。

Several important relations are studied between the girth condition and the ACE (approximated cycle extrinsic message degree) spectrum of the QC-LDPC (quasi-cyclic low-density parity-check) codes, where the PCM (parity-check matrices) are defined by the base-matrix and expanded by the cyclic permutation matrices.

研究了基于置换阵的QC-LDPC码圈长分布、ACE分布与对应的基矩阵结构之间的关系。

His deion of the event approximated to the truth.

他对事件的描述接近事实。

Apparently, the approximate controllability doesn"t hold for generally linear parabolic equations with bounded control. It doesn"t hold for the semilinear heat equations presented there,either. Then, it is proved by analyzing its" solutions that no matter how long the time T is , there are targets that can"t be approximated by the solution of heat equation with Dirichlet boundary conditions;If a given target satisying certain conditions can be reached by the solution of heat equation .

本文先针对两个具体的半线性热方程系统证明了控制加约束后系统是不能控的；然后通过分析方程的解，对带位势及Dirichlet边界条件的热方程系统，无论时间多大，都存在不能控的目标；文中还证明了满足一定条件的目标可达。

In this study, we find that there are two problems when applying the techniques of discretization to obtain an approximated probability density function of the project completion time in stochastic activity networks. Namely, first, there exists neither exact data structure nor systematic scheme for the computer programming when applying the techniques of discretization; and second, error may arise from assuming independency between sub-paths in the activity network.

本研究发现在运用文献中的散式计算技术，求算随机性专案完成时间的机分配函时，存在个问题：第一，文献中既未提供明确的资结构也没有系统化的架构，足以将其转为计算机程式；第二，因为文献中的散式计算技术，皆假设随机性专案网中的各条子径彼此独，而造成明显的误差。

If you were not , and OS X just booted normally, have no fear.

如果你没有，和OS X刚刚启动通常，没有恐惧。

I only want to preserve our all .

我只想保存好我们的一切