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The flow field around Taylor bubbles rising through stagnant liquids in vertical tubes is considered as potential flow, and the first order approximation of the control equation of gas-liquid interface and the rising velocity of Taylor bubbles are obtained.

应用势流理论分析了垂直管滞止液体中Taylor气泡周围的流场，得到了气液界面的控制方程和Taylor气泡上升速度的一阶近似结果。

In this paper,we discussed the existence,uniqueness,and approximation order of interpolation by bivariate quartic splines with B-Net in three direction meshes .

文[1]、[2]曾讨论了用S41（△mn（1））、S41（△mn（2））作为插值空间的插值问题，[3]讨论了三向剖分域上S31空间的B样条对偶基与拟插值。

Nonseparable biorthogonal wavelets based on Checkerboard lattice is studied, and the upper bounds of approximation order and smoothness order of the corresponding scaling function are also proved.

研究了一类基于Checkerboard格点的不可分双正交小波，并证明了其尺度函数逼近阶与光滑性的上界。

Applying the triangular element to the stationary Stokes equation, we obtain error analysis and optimal convergent order of approximation solution.

对于各向异性三角形元和各向异性四面体元，我们分别讨论了它们的各向异性插值，将它们应用于定常Stokes方程，我们研究了有限元空间不满足散度条件的各向异性非协调有限元解法，同样得到了逼近解的误差分析和最优收敛阶。

To reduce the error between the interpolation function regaining the sampled signal and interpolation function ha by Shannon sampling theorem, this paper suggests that the common linear interpolation is replaced by a second order approximation of the parabolic interpolation.

为减小恢复被采信号所用的内插函数与山农采样定理要求的内插函数ha之间的误差，提出了用抛物线内插--ha的二阶近似代替常规的线性内插。

Of course, this conversion between the old and the new CQFs can change the compactly supported, the regularity and the approximation order of the corresponding scaling function. However, for its appliction in signal processing, both the new and the old CQFs can produce identical output for a given input signal.

这种新旧CQFs转化将改变相对应的尺度函数的紧支撑性，正则性和逼近阶等，而在信号处理的过程中，对某一信号而言，用新旧两种CQFs作用可以产生同样的输出信号。

Unscented transformation is used to improve the performance of extended kalman filter in the field of automatic control because it can reach accuracy of second order linear approximation. UT compensation can make us to estimate more accurate noisy acoustic model parameters corresponding to static feature of speech and we also proposes several kinds of engineering implementations to improve the efficiency up to six times faster than usual implementation of UT compensation.

针对声学模型参数在噪声环境下非线性变化的补偿问题，现在国际上广泛使用的PMC和VTS声学模型参数补偿算法只能达到其线性展开的一阶近似，所以本文通过使用自动控制领域用来提高扩展卡尔曼滤波器性能的称作Unscented Transformation的技术，可以达到对声学模型参数非线性变化的二阶近似，得到的声学模型参数更加精确。

Secondly, the effectiveness and limitation of the classical perturbation, such as the method of multiple scales and the Poincare-Lindstedt method, are discussed in detail through a Duffing oscillator with delayed velocity feedback. It is shown that the two perturbation methods are effective only in solving the approximate solution of the first two orders. An ambiguity or paradox will be encountered when they are used to seeking for the third or higher order approximation of solution.

其次，以一具有时滞速度反馈的Duffing系统为例，研究了经典摄动法如多尺度法，Poincaré-Lindstedt法等在求解时滞微分方程级数解时的适用性和局限性问题，指出利用这些方法只能有效求得系统的前两阶近似解，而在求系统的三次以上近似解时会出现矛盾或二义性。

In this paper,based on an improved orthogonal expansion in an clement , using the new idea of Ref.[3] ,a new error expression of n-degree Hermite finite element approximation to one-dimensional 4-degrec 2-point bounded problem and 2-degree ordinary differential problem, and then optimal order superconvergence for their first derivatives is obtained.

本文针对在改进的单元正交性估计的基础上，利用文[3]提出的新想法，得到一维四阶两点边值问题和二阶常微初值问题的n次赫米特有限元u_h∈C~1的新误差估计式，以及导数误差的最佳阶超收敛，并且两者有相同的超收敛结果。

In order to reduce these shortcomings, on the basis of enriched polynomial basis functions, weighted orthogonal basis functions are used to obtain the MLS approximation by using a Schmidt orthogonalization. In the end, the improved LBIE method for elasticity fracture is proposed.

为了改善这些不足，本文在扩展的多项式基函数的基础上，利用Schmidt正交化方法构造带权的正交基函数，建立了断裂力学的改进的局部边界积分方程方法。

He knows that he's one of the mostdominant players in the NBA right now.

我知道他现在是联盟里最有统治力的球员之一了。

Using analysis method of BCG , the dissertation analyzed the management of voluntary service organizations .

利用BCG分析方法对我国的志愿服务组织管理进行了分析。