插值函数

In the PIM, the interpolation function has the Delta function property, so the essential boundary conditions can be simply imposed.

在该方法中，插值函数具有Delta函数性质，可以方便地施加边界条件。

Secondly,the one-step and multistep methods of the precise integration algorithms arederived by means of the integration of functional matrix by parts and interpolation function,and some recursion schemes suitable for precise integration are obtained.

然后，以函数矩阵的分部积分法和插值函数为工具，推导出精细积分的单步法和多步法，给出了多种精细积分的递推格式。

The semi-analytic formula was taken as an interpolation function near crack tip notch and the degree of freedom near the notch tip were transformed into a set of generalized coordinates by means of series expansion formulas of displacement field.

该方法将半解析函数作为插值函数，将缺口尖端附近的自由度通过位移场的扩展公式转化为一组广义坐标。

The mass conservative interpolation function is based on the stream function.

根据流函数可构造质量守恒的插值函数。

Paper puts forward the method of read DICOM field in term of sequence, reduces the time of read DICOM file in order to mend the arithmetic efficiency of read DICOM file information. Paper introduces two concept, slope and shift, reduces the linear interpolation function of VOI LUT (Value of Interest Look Up Table), and uses the way of make real number operation into integer operation to simplification the linear map function, thereby makes the image zoom speed up. Paper depicts the class and function of image measure and label particular at last, and analyses actualize step of the operation of measure and label.

论文提出严格按照顺序读取DICOM字段的做法，尽量减少访问DICOM文件的时间以加快读取DICOM文件信息的算法效率；论文中引入斜率和偏移量这两个概念，简化了VOI LUT转换的线性插值函数，并采用将实数乘除转化为整数运算的方法简化线性映射函数，从而加快了图像缩放的速度；论文最后详细描述了图像测量和标注用到的类和函数，并分析了具体的测量和标注操作的实现步骤。

From the minimum potential energy principle, the shape discrimination is transformed into the solution of minimum characteristic value.

将轧后板带离散为若干纵向条元，用三次样条插值函数和正弦函数构造挠度模式，根据最小势能原理，将板形判别——失稳判别——归结为最小特征值的求解。

Secondly, point out that meshless method is different from finite element method in handling boundary condition and numerical integral because the approximation function of meshless method is not inserted function, it have itself special methods. Deduces meshless Galerkin essential equation of parabolic partial differential equation with the method ofweighted residuals------Galerkin. Furthermore, discusses the main factors which may effectthe calculation precision and give some suggestion with which can get the best result.

其次，由于无网格法的近似函数不是插值函数，所以无网格Galerkin法在处理边界条件和对区域积分时是不同于有限元的，它有其独特的处理方法，从加权残量法——Galerkin出发，推导出抛物型偏微分方程无网格Galerkin法的基本方程，并对影响无网格Galerkin法的主要因素进行探讨，给出了取得最佳效果的相应建议。

At last ,the piecewise linear interpolation function is applied to deal with complicated constraints conditions for solving the objective function .The simulation results on the three gorges cascaded hydropower system long term optimal dispatch under the flood and dry power price and comparison with other algorithms show that it is greatly efficient to solve engineering optimal problems with complicated constraints.

针对模型中复杂的约束条件，采用分段线性插值函数实现了对目标函数的求解，并通过对丰枯电价下三峡梯级水电系统长期优化调度问题的计算及与其它算法的对比，验证了该算法可运用在解决具有复杂约束条件的工程优化问题中。

Moreover, we analyze explicitly selection of weighted function, reversibility of A matrix, confirm of radius of influencing domain and characteristic of interpolating function and so on.

并对移动最小二乘法的权函数的选取、A矩阵的可逆性、影响域半径的确定以及插值函数的性质等关键性问题都进行了详细的分析。

The second, according to mapping function of blank and product sections, and to many interpolating functions along model-cavity vertical surface, paper has built mathematics model, fluid surface function of special-shaped product plastic deformation and velocity field, gotten basis theory for metal forming prediction, for example empty drawing metal pipe thickness homogeneity and special-shaped product fluid regular, die parameter optimization and integration research of die CAD/CAM.

根据拔制坯料和制品截面映射函数和模腔纵向多种插值函数（直线型、凸型、凹型和三次多项式型），建立了相似异型材、圆形坯料——异型材和异型材——异型材三维金属拔制塑性成形的数学模型和异型材塑性成形的流面方程及流动场方程，为预报金属成形规律（如：空拔管壁均化、异型材流动规律），模腔参数优化及其CAD／CAM一体化研究提供了理论基础。

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。