求解

And the energy balance equation is applied to describe the temperature field axial orientated.

对流道的径向瞬态温度场分布进行差分求解，对流道轴向的温度分布运用能量平衡方程建立数学模型，并采用松弛迭代求解；最后，考虑流动和冷却过程的温度场分布，对流道径向和轴向温度场的计算结果进行了耦合分析，解决了长期以来只能依靠经验计算热流道温度场的局限。

Not only is the method applied in this paper better to solve the iteration between unsteady convection and conduction and the boundary condition problem, but also is a developmental application on forward and backward difference of windward scheme under unsteady condition.

不仅较好地解决了对流换热和导热的迭代求解和边界条件的处理问题，还将迎风格式的向前和向后差分发展性地应用于非稳态求解过程。

The main theory results includes:(1) Using the properties of Hilbert transform, perfectly reconstruction and new type of lifting scheme, a new type of dual-tree binary coefficients complex wavelet with linear phase is achieved.(2) For linear systems that can be diagonalized by GFT and DST-II matrices, an efficient MGM method is proposed, convergence is proved.(3) We discuss the algebraic structure when Toeplitz matrix is transformed by multi-band wavelet,show that Toeplitz matrix is composed of generating function is transformed to a band and sparse matrix when wavelet applied to this matrix, based on the above results, an efficient solution of Toeplitz equations is obtained, and the computational complex is O,where N is the order of matrix.

理论成果主要包括：(1)对于对偶树二进制系数复数小波，利用Hilbert变换对性质、完全重构条件并结合新的提升格式构造研究了含参系数多进制小波构造方法，作为特例得到具有线性相位的对偶树二进制系数复数小波构造方法；(2)对于广义离散傅立叶变换与正弦变换对角化系统，提出了高效、快速的多重网格算法，理论上证明了算法的收敛性；(3)研究了Toeplitz矩阵在多进制小波变换下的代数结构，验证了多项式生成函数构成的Toeplitz系统在小波变换下的稀疏带宽性质，从而建立基于小波变换求解Toeplitz系统的快速求解方法，运算量级控制在O，其中N为系统的阶。

The basic properties of the importance measure of the basic variable effect on the failure probability are discussed in this paper. Since the saddlepoint based line sampling method is independent of the distribution types of the random variables, and has the advantages of high accuracy and efficiency, this method is employed to estimate the defined importance measure.

文中分析了所定义基本变量对失效概率影响重要性测度的基本性质，并基于鞍点线抽样在求解可靠度时不受随机变量分布形式的限制及其效率和精度较高的优点，提出了求解该重要性测度的鞍点线抽样方法。

In this paper, based on the Bessel function, an Ordinary Differential Equation was derived for time-domain Green function and its gradients in this paper. A new efficient calculation method based on solving ODE is proposed.

在探索求解精度和计算效率的矛盾中，提出了结合求解常微分方程的节点制表、节点间插值的快速计算Gre en函数的方法并据此开发了一套三维深水时域Green函数的数值计算程序。

In chapter 3, the author considers that approximate value of Bessel fuctions and transcendental equations are main ob stacle to realize computer simulation for isolated well principle. The character of Bessel functions are studied, new approximate values of Bessel function are set forth.

第3章中，针对"割离井法"微机实现的难点——贝塞尔函数的渐近计算和超越方程的合理求解，研究了贝塞尔函数的性质，提出了新的贝塞尔函数的渐近式，并采用ZEROIN法完成了超越方程的求解，最后编制出新的"割离井法"计算程序。

On the base of Lord Kelvin point-source solution, the integral of Bessel function, Poisson superimpose formula and boundary element method, we resolve it and obtain the boundary element basic solution.

受求解方法局限性的限制，目前经典渗流力学理论还无法精确求解复杂外边界油藏中生产井层部分射孔问题。

By using symmetry and boundary conditions the field and input impedance of finite wide-angle biconical antenna can be derived by modal analysis, which generally results in solving infinite linear equations.

模式匹配法利用有限长双锥天线的轴对称性求解天线电磁场边值问题，通常导致求解无限多个线性方程而得不到严格解。

In this paper we study the method of interpolation by radial basis functions in H~k(k ≥ 1) and give some error estimates. By means of such interpolation with a special kind of radial basis function, we construct a basis in H~k(k ≥ 1). Combined with the Galerkin method, this theory can be applied to solve boundary value problems for elliptic partial differential equations (such as the third boundary value problem for Poisson equation and the corresponding problem for the biharmonic equation), and some numerical experiments are also given.

本文从求解偏微分方程的角度出发，在被逼近函数u属于一般的Sobolev空间H~k(k≥1)的情形，引入了一种径向基函数插值方法，并建立了相应的误差估计；再利用这种插值性质，从一类特殊径向基函数出发构造Sobolev空间的一组基，针对Poisson方程第三类边值问题和重调和方程类似边值问题，为用无网格算法求解偏微分方程边值问题建立了相应的理论，并通过算例来验证了这一算法。

Secondly, we discuss the boundary value problem of two dimensional biharmonic equation in a rectangular field and its variational problem,discretize it by using dual tensor product of and the direct product and lining up of matrices, we get some special matrices which are the presupposition in exploring the fast computation, then solve the system of linear equations.

其次本文讨论了矩形域上二维双调和方程边值问题及其相应的变分问题，利用二元张量积小波分析和矩阵的直积、拉直技巧将变分问题离散化，从而使求解偏微分方程问题变为求解线性方程组的问题。一维情况两组基的张量积下得到的系数矩阵分别为块状七对角阵和稀疏矩阵。这些特殊结构为以后快速算法的研究打下一个基础。

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。