边界值

Based on Pontryagin maximum principle, the lunar soft landing problem is transformed into a two-point boundary value problem in mathematics. In consideration of the bound condition and transversality condition, the resulted two-point boundary value problem is converted into a parameter optimization problem aiming at the initial values of conjugate variables and the terminal time, then it is solved by the nonlinear programming.

首先，从庞德里亚金极大值原理出发，将有限推力作用下月球软着陆问题转化为数学上的两点边值问题；在考虑边界条件及横截条件的前提下，将该两点边值问题转化为针对共轭变量初值和末时刻的优化问题；然后应用非线性规划方法求解所形成的参数优化问题。

Boolean sum projection, P〓P〓, interpolates to a primitive function f along lines; it is a transfinite interpolant.

布尔和曲面投影算子，即Pu〓Pw，沿着曲面片的边界曲线插值被逼函数f，因而这是一种超限插值。

For getting the major characteristic edges without confusions by undesired structures like muscle edges, we integrate a star-like edge detection filter named "Asterisk Filter" with the Canny Edge Detection in the image preprocessing. In addition, we also propose a new contour tracking method named "One-Pixel Rolling Ball Contour Tracking" for getting the boundary information in a binary image which is a link-list data structure. Instead of using a regression curvature estimator, PCA is used for better curvature estimation from a discrete bony contour.

为了从影像上取得骨头特徵边缘，将不重要的肌肉视为杂讯滤除，我们引用一种星形滤波器－Asterisk Filter，搭配Canny边缘检测法，做为这类影像的前处理；另外，为了将骨头的边缘精确地追踪出来，我们提出滚球边界追踪法，来对二值化影像进行边缘追踪，藉此获得边缘的串列资料结构；我们采用以主成分分析(Principle Component Analysis，简称PCA)取代原本以回归方法来计算的曲率，以取得更佳的曲率估测值，其可提高计算之参数的准确性。

An example of these maximal monotone operators is the subdifferential of a closed convex function.

这种多值极大单调算子的一个特殊例子是闭凸函数的下微分算子，所以本文考虑的多值随机微分方程包含了在凸区域内具有反射边界的随机微分方程。

For solving the boundary case of 〓 interpolation subdivision given in forth chapter, we give convergence and smoothing conditions and a C〓 continuous four point interpolation scheme using the curve triple subdivision methods from chapter three.

另外本文在第三章给出了曲线三分法细分算法的收敛和光滑条件，并给出了C〓连续的三分法四点插值算法，它解决了我们第四章给出的〓插值算法在边界上会遇到的问题。

These surfaces not only inherit the most properties of Coons surfaces,but also can adjust their shape through changing the values of parameters.The effect of two parameters λ1 and λ2 on the interior concavity and convexity of the generated surfaces is also discussed.

这些曲面不仅具有Coons曲面的良好边界插值性质，还可以通过调整参数λ的值来改变曲面内部的形状，并讨论了参数λ1，λ2对曲面内部凹凸的影响。

Then it uses the star-shaped interpolation method to interpolate the level lines layer by layer, from the boundary of the impainting region into it.

其次用星型插值的方法，从破损区域边界处出发，由外向内、一环一环地对水平线进行插值，把水平线逐步地延伸进去，让修复区域逐步缝合起来。

Making use of this model I have a taste in Yan Shan Reservoir watershed in He Nan Province: I start on the information of the surface in this area, give every grid cell the proper parameters by distilling them from the map of how the people use soil and the map of soil type in this area; In order to get the topographical information, I add numerical value to a abundant of contour lines and points in topographical map, use the software Arc View of GIS to create Digital Elevation Models automatically, get every volume of the reservoir from the water level 99m to 117m. By using a special module of the software, I distill triumphantly the grid cells elevation value, slope value, flow direction, flow accumulation, watershed, stream network, isochrones and so on.

本文在分布式水文模型的基础上，对河南省燕山水库流域洪水入库计算模拟方面作了一些研究：从燕山水库流域的下垫信息开始着手，依据流域的土地使用类型图、土壤分布图确定每个栅格单元的土壤特性和土地利用方式，进行下垫信息的参数化，得到单元模型所需的参数值；为了提取地形信息，本文通过对流域地形图海量数据加载高程值，利用GIS软件自动生成流域内的数字高程模型，提取了流域水文模型所需要的库容曲线；通过栅格自动划分，提取栅格单元的高程、坡度、栅格流向、流域边界、虚拟河网、流量积累、等时流线面积分布等分布式水文模型的流域特征。

Influences of the conditions, such as seed value of randomizer, the form parameter of statistical distributing function m, cell number, stress strain state, if there are weak areas in the center of specimens, limit conditions, random evaluating method of material factor on the elastic-plastic failure process of rock specimen are discussed.

分别研究随机数发生器种子值、统计分布函数的形态参数m、单元数目、应力应变状态、试样中心有无弱区、边界条件、材料参数随机赋值方式等条件对岩石试样弹塑性破裂过程的影响。

The improved model possesses band-pass filer characteristic, diffuses processing stability and satisfies the max-min principle. The simulation results show that the median filter is only proper for outlies noise and removes the thin line and corners of image. The linear filter extends or blurs the boundary of image. The anisotropic diffusion removes random noise effectively, but it brings about illusive edge and back diffusion for outlies noise. The improved model that possesses both median filter characteristics and anisotropic diffusion capability is proper for various mixed noise and can sufficiently protect the detailed characteristic such as corner, thin line and edge.

研究结果表明：中值滤波作为一种经典的非线性滤波方法仅适合于&飞点&噪声的滤波并引起图像的角点、线条损失，线性滤波扩大或使图像边界范围模糊；传统的各向异性扩散能对随机噪声有效地压制，但对&飞点&噪声会产生虚假的边缘甚至反扩散，而改进模型既具有中值滤波的特性又具有传统各向异性扩散的性能，适合于平滑不同强度与形状的混合噪声，并对角点、线条、边缘等细节信息提供足够保护。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。