数值函数

Initial random imperfections of composite panels are assumed to be Gaussian random fields and simulated numerically from their mean and autocovariance functions. Lindstedt-Poincare's perturbation technique is employed to solve the resulting nonlinear equation in the vibration analysis of imperfect composite panels. Monte Carlo analyses are performed for detailed numerical calculations.

层板之随机性几何缺陷以高斯随机场来描述，并利用其平均值函数及自方差函数来做数值的模拟；以Lindstedt-Poincare微扰方法来处理缺陷复合层板之非线性运动方程式，并使用蒙地卡罗法来做详细的数值分析。

The paper simply introduced the basic principle of surface nuclear magnetic resonance and computed the numerical integral of nuclear magnetic resonance kernel function which contained double Bessel functions using the method of Gauss quadrature and continued fraction expansion, and then discussed influence of conductivity to nuclear magnetic resonance′s signal.

简要介绍了地面核磁共振找水的正演理论方法，采用高斯求积并结合连分式展开的方法对核磁共振核函数中包含双重贝塞尔函数的积分核进行了数值积分，进而计算出精度较高的核函数值，在此基础之上，讨论了导电性对地面核磁共振信号的影响。

The coordinate transformation and numerical integration was executed on the discretized tetrahedral elements based on which the 3-D MT vector-finite element method was implemented. A whole computation framework for 3-D vector-finite element method with unstructured mesh was given. Based on this some typical models were tested which has demonstrated that our algorithm could distinctively avoid problems caused by the fake solution and both the accuracy and efficiency were enhanced which made our algorithm has a bright future for further application.3. According to theory of Sobolev vector space and the discretization of Helmholtz space, the error estimate which was suitable for 3-D MT vector-finite element modeling was deduced by which the procedure of adaptive technique was guaranteed.4. Based on the fully unstructured tetrahedralization and optical strategy, the 3-D magnetotelluric h-adaptive vector-finite element method was presented through combining the error estimate. With this work, the accuracy and creditableness for 3-D MT complicatedly modeling was guaranteed.5. The 3-D magnetotelluric h-adaptive vector-finite element algorithm with unstructured mesh was implemented.

针对非结构化的四面体单元，采用坐标变换和数值积分方法，实现了MT三维矢量有限单元分析，建立起基于非结构化网格的三维MT矢量有限元计算流程，并对典型模型和国际标准电磁模型进行了数值模拟，结果对比和分析表明，基于非结构化网格的三维MT矢量有限元不仅消除了节点型有限元的伪解，而且具有很高的计算精度和速度，有广阔的应用前景。3、根据Sobolev函数的向量空间和Hemlholtz空间的分解，推导出基于残差的三维大地电磁矢量有限元后验误差估计公式，为三维大地电磁自适应矢量有限元数值模拟的实现奠定了基础。4、在完全非结构化四面体单元剖分及优化基础上，结合三维大地电磁矢量有限元后验误差估计公式，提出了基于非结构化网格的三维大地电磁h-型自适应矢量有限元计算策略，保证了对复杂大地电磁模型数值计算的精度和可靠性。5、实现了基于非结构化网格的三维大地电磁h-型自适应矢量有限元计算流程，对典型模型和国际标准电磁模型进行了数值模拟。

Because we mainly involve visual fields of medical science , have placed more contents on the development in the field of medical image of visual technology and argumentation used. Second part It is the visual technology knowledge, the generalization in such respects as the basic principle , basic functions, function store and three-dimensional animation technology to OpenGL ,etc. The realization of the system using OpenGL functions finish that three-dimension demonstration. The third part It is number value that calculate knowledge, three-dimension rebuild technology is it is it is it punish to fit to go on to need, the research of interpolator technology that cant leave, So this part has quoted the Hermite function principle , define cubic Hermite function to begin, calculate the differential coefficient among them draws cubic spline again.

由于我们主要是涉及医学可视化领域，所以将更多的内容放在了可视化技术在医学影像领域的发展与应用的论述；第二部分是可视化技术方面的知识，主要对 OpenGL 的基本原理、基本功能、函数库及三维动画技术等方面的概括，在系统实现时就是通过调用 OpenGL 函数库实现三维显示的；第三部分是数值计算方面的知识，三维重建技术需要进行拟合处理，离不开插值技术的研究，所以这一部分从埃尔米特函数原理开始讨论，引入三次埃尔米特函数，进一步计算时又引用三次样条函数。

To solve above problems, a new method has been created in this paper: to construct a Hermite polynomial approximation of the objective function by FE solution using the sensitivity idea.

因此，本文提出在进行若干次电磁场数值计算之后，利用目标函数值和目标函数对设计变量的灵敏度建立目标函数的计算方法。

Integral of one variable functions, improper integral and its convergence properties.

本课程的主要内容包括：1 各种极限运算，其中包括数列极限、函数极限以及上、下极限；2 一元函数的微分学，包括微分和导数的运算法则、微分中值定理及其应用等；3 一元函数的积分和广义积分及其收敛性；4 级数及其收敛性，包括数值级数的收敛性和函数项级数的各种运算和性质；5 多元函数的微分学及其应用，其中很多方面与一元函数的微分学近似，需要注意它们之间的区别；6 多元函数的积分学，包括多重积分的性质与计算，多重积分的的应用等；7 曲线、曲面积分及其应用；8 含参变量积分的计算与性质；9 Fourier 级数及其应用，等等。

Mathieu function is the base of field theory analysis in elliptical cylinder coordinate system. So, firstly, detail investigation has been given about the problem of numerical analysis of Matheiu functions, based on the predecessor's contribution, an improved faster algorithm of numerical analysis and confirmation algorithm of Matheiu functions has been presented.

Mathieu函数是椭圆柱坐标系统下场论分析的基础，因此本文首先对Mathieu函数的数值计算问题进行了详细研究，并在前人基础上完善并进一步改进了目前被认为较为可行的数值算法，并提出了验证算法。

In chapter III,we consider the wavelet method for the approximation of the nu-merical Bergman kernel.It is very clear that the Bergman kernel plays an importantrole in the complex analysis and elliptic equations.The Bergman kernel has a closedrelation with the Riemann mapping,Green function,Neumann kernel and the Szeg〓kernel etc.

第三章研究了数值Bergman核数值逼近的小波方法，Bergman核在复分析和椭圆型方程中占有重要地位，它与Riemann映射、Green函数、Neumann函数、核等有着密切联系。

The purpose of this dissertation is to study a principle or method to describe and analyze the complex problems with high gradients arising from practical engineering. The main contents cover:1. The Bezier function was introduced to approximate high gradient functions, and a suitable coupled function was derived. Some detail numerical results show that the Bezier-based function is dominant over other combination function such as polynominal and trigonometric series, when to describe a high gradient function.

针对工程中大量存在的高梯度问题进行函数逼近的研究，引入Bezier函数对高梯度问题进行函数逼近，构成以Bezier函数为主的复合逼近函数，数值考证表明：与常规多项式插值函数的逼近及"幂／三角"复合函数的逼近相比，基于Bezier函数的逼近函数对高梯度问题的描述具有明显优势。

By usingthe dynamica l programming method, the optima l investment portfolio andconsumption policies for one kind of typica l utility function case areobtained,then we make numerica l simulation for it and get the numerica lsolution.

然后运用动态规划方法，对于一类特殊的效用函数情形，求出了最优投资组合及消费选择的显性解，并进行数值试验，得出了值函数的近似解，最后将值函数的解析解和数值解进行比较，得到了相对误差示意图。

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。