边界值问题

Some of the safe mobile codes may be rejected to execute, since there is no way to verify statically that the symbol range value of an array subscript expression in PCC.

PCC的数组边界检查存在着由于无法确定数组下标表达式符号值的范围，而造成拒绝执行一些安全的移动代码等问题。本文给出的一种数组边界检查的优化及生成算法，不仅能够比较好地解决了这一问题，同时还生成了循环不变式注解中的条件谓词。

Two problems were solved in numerical calculation, one was that a term of 1/r in Maxwell was divergence in cylindrical center where r=0, another was that the value of optical field at cylindrical center was difficult to decided when the cylindrical center set as a boundary condition in Maxwell equation, So the values of optical field need just calculate from cylindrical center to cylindrical boundary, comparing from cylindrical boundary to cylindrical boundary, near upon half CPU time and RAM saved.

计算中解决了在圆柱中心线上Maxwell方程存在发散项1/r以及用圆柱中心线作为边界条件时，中心线上光场值难确定的问题，因而光场只需从圆柱中心计算到圆柱边界，和以圆柱的两条边做为边界条件比较，节省了将近一半的计算时间和计算机存储空间。

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。

More than 30 kinds of meshfree methods are reviewed in this paper in the light of weighted residual method, and different meshfree methods can be viewed as different forms of weighted residual method and/or with different approximation functions. Various kinds of meshfree approximate schemes are presented in detail, including moving least square approximation, kernel and reproducing kernel approximation, partition of unity approximation, radial basis approximation, radial point interpolation and natural neighbor interpolation.

详尽介绍了各种无网格近似方案(包括移动最小二乘近似、核近似和重构核近似、单位分解近似、径向基函数近似、点插值近似、自然邻接点插值近似等)和无网格法中常用的各类加权余量法(伽辽金格式、配点格式、局部弱形式、加权最小二乘格式和边界积分格式等)，并讨论了数值积分方法和边界条件的处理等问题。

The main research work and its results are: 1Empirical results are analysed for the relations of fault displacement and earthquake magnitude, and difference between permanent ground deformation and maxium dynamic relative displacement on the two sides of fault; 2An analytic method is proposed for resopnse of a buried pipeline due to earthquake fault movement; 3A new shell model with an equivalent boundary and relted finite element analysis method are proposed for estimating response of a buried pipeline under large fault movement; 4By the proposed method, damage performance of water supply steel pipelines with large diameter is simulated to the real cases in Kocaeli Earthquake and Ji-Ji Earthquake, and simulating results show the real failure mode of pipes is revealed; 5Effects of overlying soil and soft/hard interlayers are analyzed on ground rupture mode and degree due to earthquake fault, and some earthquake rupture phenomena in soil layers are theoretically described for the first time; 6Pipeline response characters are discussed for the case of considering effects of soil layers on ground rupture mode; 7Research results and proposed method are applied in seismic analysis of pipline acrossing fault in the Gas Tansportation Project from West to East in China.

主要工作和成果包括：1）分析了不同断层位错形式下地表破裂位错量与震级之间的经验关系，并基于集集地震近断层记录分析了断层两侧永久地面变形和地震动相对位移幅值之间的差别，为合理地考虑地震断层位错地面变形动态影响提供了依据；2）发展了断层位错地面大变形下管线反应分析模型并给出物理概念明确、简单实用的解析分析方法；3）建立了断层位错下埋地管线反应分析的等效边界壳模型有限元方法，方法中引入了以非线性弹簧形式模拟离断层较远处管段影响的等效边界，简化了计算模型并突出了近断层处管体反应；4）利用等效边界壳模型方法，对土耳其地震和集集地震中大口径埋地管线震害进行了模拟，结果表明所提方法可以更清地解释震害所表现的管体破坏特征；5）研究了覆盖土层和软硬夹层的存在对断层位错地面破裂形式和程度的影响，首次从理论上解释了某些地震地表破裂现象；6）探讨了考虑土层对断层位错地面变形影响的管体反应特征；7）本项目成果已在西气东输工程的管道跨断层抗震问题分析中得到了应用。

And by using the initial conditions as well as the end conditions, the dynamic problem is then transferred to a second kind Volterra integral equation about the function of the axial strain with respect to time which can also be solved successfully by the interpolation method. For piezoelectric and pyroelectric hollow cylinders, by following the solving procedure for elastic hollow cylinder and by using the electric boundary conditions, the dynamic problems are transferred to two Volterra integral equations about two functions of time, one is axial strain and the other is related to electric displacement, which can also be solved efficiently and quickly by employing interpolation method. The elastodynamic solutions of hollow spheres, which are made of elastic, piezoelectric and pyroelectric materials, respectively, for spherically symmetric problems are also obtained.

对于弹性空心圆柱，通过引入一特定函数将非齐次边界条件化为齐次边界条件，然后利用正交展开技术，导出关于时间函数的方程，再结合初始条件和端部边界条件，将原问题转化为关于一个时间函数的第二类Volterra积分方程，运用插值法可给出此积分方程的解；对于压电和热释电空心圆柱，利用求解弹性空心圆柱相似的方法，再结合电学边界条件，原问题转化为关于两个时间函数（轴向应变和与电位移有关的函数）的第二类Volterra积分方程组，同样可用插值法来构造相应的递推公式高效地求解此积分方程组。

A pivotal problem to recognize of the precise position of laser facula has been solved in the process of design work: Firstly the method of background-subtraction is used to eliminate or weaken the affect of background light. Secondly the image threshold segmentation operation and morphologic operation are used to locate the sketchy position of laser facula ; Then the new method of Extracting Edge are designed based on character of laser facula , by using this method in the search area the edges of laser facula can be extracted effectively; At last the optimum picture of laser facular is selected by using the triggering function of hardware and function of software. The exact result can be obtained only by image processing to optimum picture.

在设计过程中解决了精确确定激光斑中心位置这一关键问题：首先利用减背景法，消除或减弱背景光的变化对确定激光光斑中心的影响；再对减完背景后的图片进行阈值分割和二值化处理以确定激光光斑的粗略位置；根据本文激光光斑的特征，设计了一个有效的边界提取算法，对指定区域进行提取激光光斑边界操作，精确的确定激光斑中心位置；最后利用硬件的触发功能和软件编程实现了激光光斑最佳图片的判读，只有对最佳图片进行图像处理得到结果才是准确的。

It is proved that the method using the BEM to calculate the load distributions on the contact lines of involute gear pair, in which the applied load is taken in the form of a concentrated one at a single node, is not suitable. A method in which the tractions of the BEM are made to imitate the Hertzian pressure of the gear using 8 nodes isoparametric elements is introduced.

本文解决了边界元法在空间啮合副计算中存在的系数矩阵的存储，奇异单元积分的计算、表面不连续点处面力一点多值和求解未知量的线性方程组矩阵元素的计算等问题，编制了比不采用上述处理方法的一般边界单元法节省近一半内存和计算时间的适合空间啮合副的三维边界元法计算程序。

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。

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。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。