边界值

By analyzing the characteristics of the boundary pixels to formulate a boundary pixel extraction operator, the operator need only calculate up to 4 pixels neighborhood pixels, is efficient, fast, he can direct the use of binary images are extracted as the boundary pixel, are single-pixel wide border.

通过分析边界象素的特征，归纳出一个边界象素提取算子，该算子最多只需要计算象素的4邻域象素，运算量小，速度快，运用他能直接提取出二值图象的边界象素，得到单象素宽的边界。

At first, preprocessing with the image pyramid and diffusion-filtering technology; then abstracting the boundary-outline information; carrying on the logarithmic coordinate transformation of the abstracted boundary-outline information to get bar chart of the logarithmic coordinate; calculating the value of Cs to get all the phase match points; calculating the value of the degree of approximation to judge the shape matching.

本发明涉及一种基于Shape Context的人脸形状匹配方法，首先采用图像金字塔及扩散滤波技术进行预处理；再利用Canny边缘检测算法和轮廓提取算法提取边界轮廓信息；对提取的边界信息进行对数极坐标变换，得到对数极坐标直方图；通过计算Cs值，获得所有相匹配点；计算相近似度值，进行形状匹配判断。

In the last chap-ter,the natural integral equation and natural boundary element method forharmonic problem on exterior elliptic domain are introduced.Then,based onthis,the natural boundary reduction method for a kind of exterior problem ofanisotropic constant coefficients elliptic equation is discussed, the natural inte-gral equation and its solving method on circular boundary and elliptic bound-ary are obtained.These results can be directly applied in coupled methodand DDM for exterior boundary value problem.

最后，讨论了椭圆外区域调和问题的自然积分算子即D-N算子及自然边界元方法，并基于此研究了一类各向异性常系数椭圆型方程外问题的自然边界归化方法，首次得到其在圆周边界及椭圆边界上的自然积分方程及其求解方法，并将这些结果直接应用于外边值问题的耦合算法。

Studied present measuring methods" advantages and disadvantages, and presented the necessity and importance of researching propellant transient heat transfer.2.according to 130 and aeronautic 90 rocket projectiles" structure, analysed and acquired physical and mathematical models for propellant transient heat transfer, also designed propellant temperature field simulation units for test.3.acquired discrete transient heat balance equation and temperature calculation program, and gave contrasting curves between experimental temperature values and program calculating temperature values as well as maximum errors and average square root errors between them.4.by programs based on the first class boundary condition, worked out temperature distribution in propellant temperature field simulation units at different time, analysed temperature field distribution law and main elements affecting heat transfer, acquired propellant mass weighted average temperature and one at the half position of propellant maximum thickness as well as maximum errors and average square root errors between them.5.established transient heat transfer mathematical model and temperature calculation program for the third class boundary condition, drew contrasting curves between temperature experimental values and calculation values and gave maximum errors and average square root errors between them, got temperature distribution in the simulation unit at different time and main elements affecting heat conduction, figured out propellant mass weighted average temperature and one at the half position of propellant maximum thickness as well as maximum errors and average square root errors between them.

分析了现有测试方法的优缺点，提出了研究推进剂瞬态导热的必要性和重要性。 2。根据130和航90两种火箭弹的结构，分析得到了推进剂传热的物理模型和数学模型，设计了推进剂温度场模拟实验装置。 3。得到了离散形式的瞬态热平衡方程和温度场计算程序，给出了实验温度与程序计算温度值的对比曲线及其最大偏差与均方差。 4。利用程序求出了第一类边界条件下、不同时刻推进剂温度场模拟装置中的温度分布，分析了温度场的分布规律和影响传热的主要因素，求出了推进剂质量加权平均温度和最大肉厚1／2处的温度时间曲线并给出了两者之间的最大偏差与均方差。 5。建立了第三类边界条件下的瞬态导热数学模型和温度计算程序，求出了温度实测值与计算值的对比曲线并给出了两者之间的最大偏差与均方差，得到了不同时刻温度场模拟装置的温度分布与影响导热的主要因素，求出了推进剂质量加权平均温度和最大肉厚1／2处温度及两者之间的最大偏差与均方差，讨论并确定了能代表130和航90推进剂温度的特征点的位置。

We present a new direct boundary integral equation in terms of the boundary magnetic field only.

文中提出了一个新的直接边界积分公式，仅仅由边界上的已知磁场值确定空间点的磁场值。

LBIE, based on the local boundary equation, adopts the traditional moving least squares approximation which depends on only the values of the nodes in the domain of the problem or along its boundary. The whole process of integration is carried on over a local domain or its local boundary centered at the node in question. The local boundary equation can be rewritten to represent the values of the unknown function at the point of interest, and the essential boundary conditions can be directly and easily enforced by using the Green formula and the characters of the Dirac function.

它以局部边界积分方程为基础，采用移动最小二乘近似函数，从而只需要分布在问题域内及其边界上的节点的信息值，无需划分单元；整个积分是在以节点为中心的局部域及其边界上实现，所以不需要背景积分网格；借助于格林公式及Dirac函数的性质，将局部边界积分方程转化为所考虑点的未知函数的边界积分表达式，便于直接施加本质边界条件。

In this dissertation, we construct the Bariev model with nine kinds of boundary fields by the matrices K_± defining the boundaries. And then the Lax operator is given in the form ofmatrix, as well as the basic quantities, e.g., the R -matrix, the monodromy matrices and the transfer matrices are defined. By using the expression of the local Lax operator of the model,the action of the monodromy matrices T, T~(-1), U_ on the pseudo-vacuum state is given outin detail. Furthermore, the main fundamental commutation relations are obtained through the reflection equations, the recursive n-particle state as well as the one-particle exact solution is given and the Bethe ansatz equations are found accordingly. Finally, we list the nesting boundary K matrices, which play a crucial role for obtaining the n-particle solution and finding the Bethe ansatz equations, the eigenvalues of the transfer matrices and the energy spectrum of the system by means of the nested algebraic Bethe ansatz method.

在这篇文章中，我们利用边界K_±矩阵构造出了具有九种边界场的Bariev模型，同时给出了该模型L算子的具体矩阵表示形式，并定义了R矩阵，monodromy矩阵以及转移矩阵；接着利用L算子的矩阵形式，给出了其对应monodromy矩阵T、逆矩阵T~(-1)作用到真空态上的值，并利用Yang-Baxter关系及反射方程得到了双行monodromy矩阵U作用到真空态上的值；然后利用反射方程通过复杂的计算得到了一系列重要的基本对易关系式，并给出了模型的递推的多粒子波函数、单粒子解及Bethe ansat方程；最后给出了模型的嵌套的边界K矩阵的具体形式，从而为运用嵌套Bethe ansatz方法求解该模型的多粒子解、Bethe ansatz方程以及系统的能谱打下了很好的基础。

The Neumann boundary value prob-lem is firstly reduced into the equivalent natural boundary integral equation withthe kernel possessing 2nd-order singularity,and then the corresponding variationalproblem on the boundary is obtained.By applying Quak trigonometric wavelet basisBjsee(1.2.3as boundary elements and the method of expanding kernel functionto its Galerkin discretization,we obtain simple computational formulae of the en-tries in the stiffness matrix.

首先，我们将Neumann边值问题归化为等价的带有2阶强奇性核的自然边界积分方程，然后化为边界上相应的变分形式，以Hermite插值Quak三角小波基Bj见(1.2.3作为边界元并利用积分核函数展开法将其离散，得到了十分简单的刚度矩阵系数的计算公式，而且刚度矩阵具有十分简单的形式，它是分块循环对角阵。

In recent years, Feng Kang has advanced a more natural and direct redu-ction, i. e. the reduction via Green's formula and Green's function.

近年来冯康又提出一种更自然而直接的归化，即从Green公式及Green函数出发将微分方程边值问题化为边界上的含有广义函数意义下发散积分有限部分的奇异积分方程，这种归化在各种边界归化中占有特殊地位，被称为正则边界归化，本文将这一理论应用于重调和椭圆边值问题，研究了其正则归化的性质，并通过利用Green函数、Fourier分析及复变函数论方法等不同途径求出了在上半平面、单位圆内部、单位圆外部三种区域的Poisson积分公式及正则积分方程，其离散化可用于实际计算。

Only with such characteristics, the movement equations can be expressed as matrices, and the idea of transforming the movement equations to the simplest form through a nonlinear transformation can be realized;(2) The form of Zi =Yi + YTH2i Y + Y7H3i Y(2)+ Y(2)T H4i Y(2)+ YTH5i Y(3) is adhibited in the nonlinear transformation, so that the multivalued problem caused by the nonlinear transformation is avoided, and the higher order transformation can be taken next;(3) The fourth order nonlinear transformation matrices H21,H31,H41 and H51 are derived, by which the original movement equations of electric power system is transformed to Jodan form in Z space;(4) By use of the fourth order nonlinear transformation, the approximate expression of the stability boundary is obtained, in Z space it is Z1= 0,in Y space it is Y1 + YTH21 Y + YTH31 Y(2)-i- Y(2) TH41 Y(2)+YTH51 Y(3)= 0;(5) The criterion used in this paper to judge whether the system critical unstable is simple and quick;(6) The method used in this paper is a direct method, and no need to construct an energy function.

正是由 于电力系统的运动方程具有这样的特性，才能写成矩阵的形式，通过非线性变换将电力系统的运动方程变换为最简单的线性形式的思想才能得以实现；（2）将通常运用于电力系统暂态稳定性分析的Normal Form变换的形式由 Yi＝ Zi＋ ZTh2riZ变形为 Zi＝ Yi＋YTH2iY＋YTH3iY（2）＋Y（2）TH4iY（2）＋YTH5iY（3），从而使得在对持续故障轨线实施同样的非线性变换以确定临界切除时间时，避免了非线性变换带来的多值性的问题，而只有在没有多值性问题的困扰下，才能采用较高阶的变换：（3）推导出了将原始电力系统系统的运动方程变换到Z空间的约当形式的非线性变换矩阵H21、H31、H41、HS1：（4）在运用四阶了「线性变换的情况下，给出了受扰动后系统的稳定边界的近似的解析表达，在Z空间为Z1=0，在y空间为： Y1+YTH21Y+YTH31Y(2)+Y(2)TH41Y(2)+YTH51Y(3)=0 （5）确定临界失稳的判据简单、快捷：对于一个复杂的电力系统，其稳定边界是相当复杂的一个高维曲面，即便是已知系统稳定边界的解析表达，要求出系统持续故障轨线何时与这一高维曲面相交，在数学上几乎是不可能实现的。

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。