离散的

The characteristic approximation is used to handle the convection part along the direc-tion of fluid namely characteristic direction to ensure the high stability of the method in approximating the sharp fronts and reduce the numerical diffusion; The mixed finite element spatial approximation is employed to deal with diffusion part and approximate the scalar unknown and the adjoint vector function optimally and simultaneously; In order to preserve the integral conservation of the method, we introduce the modified characteristic method.

该方法对方程的对流部分沿流体流动的方向即特征方向离散以保证格式在流动的锋线前沿逼近的高稳定性，消除数值弥散现象；对方程的扩散部分采用最低次混合有限元方法离散、同时以高精度逼近未知函数及未知函数的梯度；为保证方法的整体守恒性，在格式中引入修正项。

This section presents two kinds of characteristic schemes, one is the natural use of the usual backward Euler characteristic difference scheme ( [60] ) onto the triangular mesh, the other replaces the backward Euler's method by modified Euler formula to approximate the characteristic differential equation, so that the discretization for characteristic curve can get up to second order accuracy.

本节给出了两种三角形网格上的特征差分格式，第一种是通常的向后Euler型特征差分格式（[60]）在三角形网格上的自然运用，第二种采用§3.3、§3.4的离散思想，使用改进的Euler公式代替向后Euler公式来近似特征微分方程，使其对特征线的离散达到了二阶精度。

The control volume integration was applied to deduce the discrete expressions of the convection-diffusion equations. The staggered grid and SIMPLE algorithm were introduced to deal with coupling between pressure and velocity, and then the numerical computation expressions of such variables as fluid flow velocity and pressure were deduced. Using the backward difference method and incremental theory to discretize the governing equations for fields of chemical reaction, material structure and chemorheology, the numerical computation expressions of variables such as the monomer conversion, average molecular weight and fluid viscosity were constructed.

应用控制容积积分法导出了对流—扩散方程的离散表达式，引入交错网格技术与SIMPLE算法，实现了耦合的压力场与速度场的分离式求解，推导得到了流体的流动速度、压力等物理量的数值计算式；采用向后差分方法和增量方法，实现了化学反应场、材料结构场、化学流变场控制方程的离散，获得了反应转化率、聚合物平均相对分子质量、流体黏度等物理量的数值计算式。

It is true that the discrete version of Korn's second inequality does not hold in the standard Crouziex-Raviart 1 element space. In [24] , the strain tensor was modified, at the same time, the bilinear form changed, as a result the modified discrete version of Korn's second inequality holding in the standard Crouziex-Raviart 1 element space.

我们知道，在标准的Crouziex-Raviart 1元空间中第二Korn不等式的离散形式是不成立，Falk在[24]中修改了应变张量，相应的弹性问题的双线性型也被修改，这样，修改后的第二Korn不等式的离散形式在标准的Crouziex-Raviart 1元空间中成立。

New parameter estimation Markov recursive algorithm for continuous stochastic linear system and bilinear system is proposed.

基于小波变换的连续随机线性和双线性系统参数辨识Markov方法分析研究了连续维纳过程在小波变换下的统计特性，给出了维纳过程的离散小波变换系数所构成的离散随机过程的协方差矩阵计算和估计方法，基此提出了线性和双线性连续随机系统参数辨识的Markov估计方法及其递推算法。

It is shown that in Jameson's algorithm is not an orthogonal stream-lines coordinate system, but a local stream-lines coordinate system instead. Nevetheless, because of the finite-difference discretization in Jameson's scheme is not carried out along the direction of s and n, but along the Cartesian coordinates, the analysis on all terms of the full potential equation in Cartesian coordinates reveals that his scheme does take a back-ward difference along the streamwise exactly at all points in the supersonic flow region.

表明其所采用的坐标系不是真正的正交流线坐标系，而是局部流线坐标系；同时由于Jameson方法并不对s，n进行差分离散，而是在原笛卡尔坐标系下作差分离散，对笛卡尔坐标系下的全位势方程中的各项的分析表明，Jameson方法恰好能做到在超音速点沿真正的流线方向作后差分。

Spectral element methods for partial differencial equation is introduced in this study from viewpoint of the collocation approximation of Chebyshev polynomial. Wave Equation and its space discretization are deduced. Two time integral methods, central difference method and implicit Newmark method, are introduced, and their stability and applicability are also discussed in some details. The significance of absorbing boundary conditions in spectral element methods for Aeroacoustics is explained, and Clayton-Engquist-Majda absorbing boundary conditions is emphasized and introduced, then the discrete scheme of this boundary conditions is deduced and applied to spectral element methods for wave equation.

本文从Chebyshev多项式逼近理论出发，详细介绍了谱元方法求解偏微分方程的过程；推导了流体中的声波动方程并在空间上对其进行了谱元离散；详细讨论了两种时间积分方法──中心差分法和Newmark方法，分析了它们的稳定性条件，并从理论上对比了两种方法的优缺点和适用范围；将吸收边界条件推广应用于谱元方法求解气动声学问题中，重点介绍了Clayton-Engquist-Majda吸收边界条件的原理和公式，推导了该吸收边界条件的变分形式，并将其引入波动方程的离散形式中。

The examples indicate that the algorithm has strong pertinence and high efficiency, hi the discrete variable optimization, the problem is solved in the relative quotient method On the base of analyzing the relative quotient method, the conjugate gradient direction is used to modify the old search directions, the iterative matrix of the algorithm, and the method to resolve the discrete variable optimization, the relative conjugate difference quotient algorithm is presented.

离散变量优化算法是从相对差商法开始的，在详细分析相对差上法的基础上，用共轭梯度方向修正原有的搜索方向，并对算法的迭代矩阵进行相关的修改，最终形成一种用于求解离散变量优化问题的RCDQ法。

For PDEs with small parameters, a scheme is AP if it possesses the discreteanalogy of the continuous asymptotic limit as the small parameter goes to zero.

对于含有小参数的偏微分方程，所谓一个算法是渐近保持的指的是，当相应的数值离散在小参数趋于零的时候，仍然是渐近极限的合理数值离散。

That not only could be extended to the continuous random varia- ble,but also the theorem of maximum information measure could be extended to the continuous random variable, which unified the measurement arithmetic of information between distributed random variable and continuous ran- dom variable,and gave two validating models to the information entropy of the continuous random variable in the last.

用公理化的方法，推导出了有限分布列的离散型随机变量的信息量系，不仅将它推广到连续型随机变量，而且将信息量系的最大信息量定理推广到连续型随机变量，统一了离散型和连续型随机变量的信息度量算法。最后利用得出的结论对连续型随机变量信息熵给出两个验证性算例。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。