边界值

In order to reduce the effect of imaging recognition error, the recognition location of projection is extended and refined, and the projection edge of sphere centre is implanted. So a pyramid is formed by radial line between the camera optical centre and the implanted point. A curved face is formed by the two pyramids and barbette sphere. To calculate the shape centre of the common section of the curved face, the shape centre is the coordinate of sphere centre.

为了降低图像识别误差的影响，对投影的识别位置进行拓展和细化，并对球心投影边界进行插值，摄像机光心与插值点连线射线形成了一个锥体，两摄像机的锥体分别与炮台球面相交形成曲面，计算两曲面公共部分的形心，即为球心位置。

The nonlinear stability of three-dimensional disturbances for the Blasius boundary layers is studied. We adopted here the high accuracy method of using the expansions in orthogonal functions along the normal direction and the effective algebraic mapping to deal with the problem in the infinite region. The initial solutions of two-dimensional harmonic waves are given by Landau expansion, and the mean-flow-distortion is calculated by the approximation equation.

运用Landau展开给出了二维谐波的初始解、通过求解线性PSE而得到TS波和C型亚谐扰动的初始站值、以及近似地模拟初始站的均流变形值，以此为初始条件，并结合迭代-预估校正方法来实现非线性PSE的求解和推进，详细地研究了非平行边界层三维扰动C型失稳过程。

This paper presents an IFMC CAD model that consits of a geometry model and a material model, in which the geometry space acts as a base space and the material space acts as a bundle space. In this CAD model, the geometry model is based on the non-manifold model. In addition, a half-face data sturucture, which is derived from the half-edge data structure with the non-manifold feature of IFMC taken into account, is adopted to represent the geometry and topology information of the component. For the material model of IFMC, this paper focuses on the FGM component representation firstly and present a simplex-subdivision based CAD data exchange format, in which the material information is represented as a (n-1) simplex and material distributing feature is represented by the interpolation on the simplex-subdivision. Based on those, a part-building orientation optimization algorithm and an adaptive slicing algorithm for FGM component are presented in the paper. For the IFMC material model, the IFMC material information representation is divided into a meso-scale and a macro-scale representation. In the meso-scale, a concept named parameterized periodic functional meso-structure is presented as a unique form to represent the FGM (the homogeneous materials are regarded as a special FGM), the composite and the functional meso-structure material. The model of PMS is a three-tuple that contains the space state informatation, the material parameter and the material meso-scale distribution feature. The macro-scale material information representation is similar to the FGM components by interpolation of the control parameter of the periodical functional meso-structure based on the simplex-subdivision. Through an example of manufacturing-oriented IFMC CAD data processing, it is proved that the IFMC CAD model and the material information representation and process method proposed in this paper can provide a reliable data support for IFMC digital concurrent design and manufacturing.

本文将理想材料零件CAD模型建立在以几何空间为底空间、以材料空间为丛空间的结构上，使用非流形几何模型作为理想材料零件几何拓扑模型的基础，并在半边数据结构基础上，针对理想材料零件的非流形特征局限内部边界上的特点，给出了一个半面数据结构来表述零件的几何拓扑信息；对于理想材料零件的材料模型，本文先从功能梯度材料零件的信息表述与CAD数据交换和处理入手，将材料信息表述为（n-1）维单纯形，然后通过对三维几何区域的单纯剖分，以插值的方式表述零件材料分布特征；在此基础上，根据功能梯度材料零件分层制造中对CAD数据处理的要求，给出了综合考虑零件几何特征与材料特征的生长方向优化算法和自适应切片算法；而对于文中所定义的理想材料零件，本文将其材料信息表述分解到细观和宏观两个尺度进行，首先给出了细观尺度上参数化的周期性功能细结构概念，以此来统一表述功能梯度材料（单质材料作为特殊的功能梯度材料看待）、复合材料和功能细结构材料；把周期性功能细结构模型化为一个包含空间状态信息、材料构成参数和材料细观分布特征参数的三元组，以表达零件的细观材料特征；对于零件宏观的材料变化特征，则同样在几何区域单纯剖分的基础上，通过对细观尺度上周期性功能细结构控制参数的插值来完成；通过理想材料零件CAD数据处理的算例，验证了本文中理想材料零件CAD模型及材料信息表述与处理方法完全可以为理想材料零件的数字化制造提供可靠的数据支持。

This paper presents an IFMC CAD model that consits of a geometry model and a material model, in which the geometry space acts as a base space and the material space acts as a bundle space. In this CAD model, the geometry model is based on the non-manifold model. In addition, a half-face data sturucture, which is derived from the half-edge data structure with the non-manifold feature of IFMC taken into account, is adopted to represent the geometry and topology information of the component.For the material model of IFMC, this paper focuses on the FGM component representation firstly and present a simplex-subdivision based CAD data exchange format, in which the material information is represented as a (n-1) simplex and material .distributing feature is represented by the interpolation on the simplex-subdivision. Based on those, a part-building orientation optimization algorithm and an adaptive slicing algorithm for FGM component are presented in the paper.For the IFMC material model, the IFMC material information representation is divided into a meso-scale and a macro-scale representation. In the meso-scale, a concept named parameterized periodic functional meso-structure is presented as a unique form to represent the FGM (the homogeneous materials are regarded as a special FGM), the composite and the functional meso-structure material. The model of PMS is a three-tuple that contains the space stateinformatation, the material parameter and the material meso-scale distribution feature. The macro-scale material information representation is similar to the FGM components by interpolation of the control parameter of the periodical functional meso-structure based on the simplex-subdivision.Through an example of manufacturing-oriented IFMC CAD data processing, it is proved that the IFMC CAD model and the material information representation and process method proposed in this paper can provide a reliable data support for IFMC digital concurrent design and manufacturing.

本文将理想材料零件CAD模型建立在以几何空间为底空间、以材料空间为丛空间的结构上，使用非流形几何模型作为理想材料零件几何拓扑模型的基础，并在半边数据结构基础上，针对理想材料零件的非流形特征局限内部边界上的特点，给出了一个半面数据结构来表述零件的几何拓扑信息；对于理想材料零件的材料模型，本文先从功能梯度材料零件的信息表述与CAD数据交换和处理入手，将材料信息表述为(n-1)维单纯形，然后通过对三维几何区域的单纯剖分，以插值的方式表述零件材料分布特征；在此基础上，根据功能梯度材料零件分层制造中对CAD数据处理的要求，给出了综合考虑零件几何特征与材料特征的生长方向优化算法和自适应切片算法；而对于文中所定义的理想材料零件，本文将其材料信息表述分解到细观和宏观两个尺度进行，首先给出了细观尺度上参数化的周期性功能细结构概念，以此来统一表述功能梯度材料(单质材料作为特殊的功能梯度材料看待)、复合材料和功能细结构材料；把周期性功能细结构模型化为一个包含空间状态信息、材料构成参数和材料细观分布特征参数的三元组，以表达零件的细观材料特征；对于零件宏观的材料变化特征，则同样在几何区域单纯剖分的基础上，通过对细观尺度上周期性功能细结构控制参数的插值来完成；通过理想材料零件CAD数据处理的算例，验证了本文中理想材料零件CAD模型及材料信息表述与处理方法完全可以为理想材料零件的数字化制造提供可靠的数据支持。

The boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function uses Cauchy integral formula as the foundation . The singularity of the Cauchy

广义解析函数的Riemann-Hilbert边值问题的边界元方法是以Cauchy公式为基础，Cauchy核具有奇性，这是所面临的困难，可以设法利用Cauchy主值积分来解决，最后给出问题的解。

Furthermore, it can be changed into singular integral equations with Cauchy kernel by introducing Sherman transformation. Then , the numerical example of the elastic welding problem with symmetric cracks is given, and the stress intensity factors can be obtained.

通过应用平面弹性复变方法，把满足已知边界条件的弹性平衡问题转化为解析函数的边值问题，再通过引入Sherman变换，把边值问题化为Cauchy核的奇异积分方程组。

This paper provides a method of variable integrity testing to detect the faults of software By checking the definition domain of the variable itself and the restriction condition of consistency between variables, we only need to determine the bound of each output data, rather than the exact value Although the output of testing case cannot be easily caught, this method can improve the efficiency of detecting faults Furthermore, the checking point is not limited to the final output place, but spreads over the reference places in the program code to key variables just like those at the checkpoints under debugging As a consequence, the testing becomes more precise

由于软件测试用例的输出部分很难确定，而通过测试变量自身的定义域和变量间的一致性约束关系，只需要确定输出值的范围而不用知道其确切的值，就可以提高了错误检测的效率同时，检测的范围不局限于程序最后的输出结果，而是散布在程序中的各个有意义的变量，正如调试过程中设置断点观察的那些变量，使得检测错误更加精准1 引言软件测试的本质在于针对要测试的内容确定一组测试用例[1] 测试用例分为输入和输出两部分功能测试和结构测试等基本的软件测试方法，都比较关心测试用例的输入部分定义域的确定，而对测试用例的输出部分考虑得较少例如，边界测试和等价类测试[2 ] 只考虑测试用

The domain variables are interpolated by classical fundamental solutions and thus allowing for the transfer of the domain integration to the boundary.

其中，域内场函数用基本解插值，边界上的场函数用移动最小二乘法插值。

The generalized pivotal model is drawn by Fiducial inference, by which the generalized p-value is defined directly. Then the hypotheses test problem is solved and this test is proved to be valid at the boundary.

首先用Fiducial方法得到广义枢轴向量，由此直接定义广义p-值，并证明了由此广义p-值所给出的检验在边界上具有频率性质。

Based on the exergy transfer equations, exergy transferring in the steady heat conduction process are calculated for the infinite plate at the first type boundary condition, and two results are compared when conductivity is stable and changed with temperature in this paper.

利用一维稳态传递方程，对平壁在第一类边界条件下的一维稳态导热过程的传递做了数值计算，并就导热系数为定值与变值的两种计算结果进行了比较。

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。