插值问题

Chapter 6, consider a coupled generalized KdV-Burgers equation. In section 6.2, we study the initial-boundary value problem in the semi-unbounded domain, the existence of global solutions and global attractors is proved by means of a uniform priori estimate for time. In section 6.3, the Cauchy problem by using the weighted space, the existence of the global attractors for a coupled generalized KdV-Burgers in an semi-unbounded domain is proved.

第六章，考虑了一类广义耦合的KdV-Burgers方程，在第二节中讨论了半无界区域上的初边值问题，证明了整体光滑解和整体吸引子的存在性；在第三节中讨论了Cauchy问题，利用加权函数和加权空间上的插值8不等式，证明了半无界区域上整体吸引子的存在性。

Recently, a lot of studies have been focused on the anisotropic finite element method, and there appears many relative papers(see [26,27,53,54]). However, the main attention of those were paid to the study of conforming Lagrange elements and the interpolation error analysis on the second order or fourth order elliptic boundary value problems.

近年来，各向异性有限元方法已成为有限元领域的热点问题，陆续出现了许多有关此方面的理论及应用研究成果，见[26，27，53，54]，其中大部分工作主要是针对二阶或四阶椭圆边值问题协调与非协调元的插值误差估计进行的。

Based on the Maxwell\'s equations, the boundary value problem, variation problem, interpolation function and stiffness matrix in two-dimensional magnetotelluric are derived.

从麦克斯韦方程组出发，推导出二维大地电磁测深的边值问题、变分问题、有限单元法的插值函数以及单元刚度矩阵。

The contents of this course include: the mathematical basis of FEM, the generic solution principles and expressions of elastic mechanics issue, the construction of element and its interpolation function, iso-parametric element and numerical integral, solution of linear equations, some practical issues of FEM modeling, brief introduction to typical commercial FEM packages, FEM for truss, plate blending and shell, and FEM for heat exchange and dynamics.

课程内容主要包括：有限单元法的数学基础、弹性力学问题有限单元法的一般原理和表达格式、单元和插值函数的构造、等参单元和数值积分、线性方程组解法、有限元建模的若干实际问题、典型商用有限元分析软件简介、杆件结构力学问题的有限单元法、平板弯曲问题的有限单元法、一般壳体问题的有限单元法、热传导问题的有限单元法、动力学问题的有限单元法等。

The empirical mode decomposition method is introduced to extract the trend item of gyro's drift, but the local mean estimation isn't precision and the end effects exist in the conventional EMD method. The two-tap adaptive time-varying filter and the adaptive border estimation are used to modify the EMD. After the trend extraction, the method of time series analysis is used to make the autoregressive moving average model for stationary time series.

根据陀螺漂移的特性，提出采用经验模分解的方法对其趋势项进行提取，但传统的经验模分解方法存在局部均值估值不准，插值过程存在端点效应的问题，因此，本文又引入二拍自适应滤波及自适应边界估值来对原方法加以改进；在成功提取趋势项后，通过采用时间序列的分析方法，建立了陀螺漂移平稳时间序列的自回归滑动平均模型；并得出陀螺漂移模型可近似为常值加一阶马尔可夫过程这样一个结论。

The existence and uniqueness of homogeneous elliptic polyharmonic cardinal spline interpolation are proved, the remainder formula and order of approximation in LP (1≤p≤∞)spaces are given, and the extremal problem of sobolev dass in L2 is considered.

获得Rd上齐次椭圆型Cardinal样条插值的存在唯一性，并获得Sobolev类上的函数在Lp（1≤p≤∞）尺度下的插值误差估计，以及Sobolev类在L2尺度下的一些极值问题的解；拓广了Laplace型的结果。

After analyzing of the reason of large deformation,the parametric cubic spline interpolation method was used for x, y, z respectively on Warps and wefts with accumulative bowstring length as parameter to fit the surface of mannequin.

分析了造成上述问题的曲线大挠度原因后，运用参数三次样条插值方法，采用累加玄长为参数，分别对人台经纬曲线的x、y、z进行插值计算，并拟合人台曲面。

In order to improve the numerical stability during the solving of convection-dominated convection-diffusion problems, an upwinding local radial point interpolation method is proposed based on the local radial point interpolation method and the local upwinding weight function.

为提高对流扩散问题中对流项占优时的数值稳定性，采用局部上风式权函数，在局部径向基点插值无网格法基础上构建了上风式局部径向基点插值无网格法。

The following are main contents studied: A finite element method for Navier-Stokes equation with ALE formulation is considered and by combined with theNewmark method of numerical intergration a pressure correction scheme is obtained for the solution of the FE formulation of N-S equation. Because the incompressibility condition can be satisfied approximately in this scheme, the interpolation functions of elements can be equalorder for the velocity field and pressure field. In the ALE formulation the fluid-solid interaction analysis became a three-field coupling problem of the fluid field, the solid field and the fluid dynamic mesh. The properties and charactiristices of this three-field coupling problem are deeply discussed.

研究的主要内容有：主容器中流体大晃动是一种强非线性问题，文中研究了求解ALE描述的粘性流体N-S方程的有限元方法，以有利于大晃动自由液面的跟踪和流体大晃动中非线性现象的描述；并结合Newmark数值积分法推出了求解ALE型N-S方程的压力修正解法，由于这种解法可以近似满足不可压条件，因此可以采用速度场和压力场等阶插值的有限元离散格式，从而较好地解决了普遍采用的不等阶插值解法中，速度场和压力场数值精度不一致、程序编制不便等的不足。

Solution to these problems were given, along with error analyses with and without interpolating endpoint conditions, respectively.

分别针对插值边界，不插值边界情况在两种范数下给出了问题的解析解，并且给出了逼近误差的界。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐