插值问题

Two technologies, spectral channelization and spectral analysis with zero crossing that could be both applied to multi-signals, are also introduced.

前面提到的插值算法也能用于多信号测频，但算法的基础是先进行谱峰的搜索，如果多信号同时到达，言普峰搜索存在的问题是有可能出现信号的错峰不能被正确判别的问题。

State variables at left end of time interval and costate at right end of time interval were taken as independent mixed variables, and the state and costate variables inside the time interval were approximated by Lagrange interpolation. Nonlinear optimal control problems were replaced by nonlinear equations through dual variable principle, and the symplectic algorithm for solving nonlinear optimal control problems can be obtained at the same time.

以时间区段一端状态和另一端协态作为混合独立变量，在时间区段内采用拉格朗日插值近似状态变量与协态变量，然后利用对偶变量变分原理并将非线性最优控制问题转化为非线性方程组的求解，最终得到求解非线性动力学系统最优控制问题的保辛数值方法。

State variables at left end of time interval and costate at right end of time interval were taken as independent mixed variables,and the state and costate variables inside the time interval were approximated by Lagrange interpolation.

以时间区段一端状态和另一端协态作为混合独立变量，在时间区段内采用拉格朗日插值近似状态变量与协态变量，然后利用对偶变量变分原理并将非线性最优控制问题转化为非线性方程组的求解，最终得到求解非线性动力学系统最优控制问题的保辛数值方法。

In this chapter we discussed the existence,uniqueness and approximation degree of binary cubic splines with C~2 connectivity for type-Ⅱtriangulations on rectangular domain,and we also gave a analysis of approximation of the interpolation splines.

本文还研究了二元三次样条函数在曲面重建中的应用问题，在TYPE-Ⅱ型剖分下，对于三次样条插值曲面的C~1-拼接问题，许多学者在这方面展开了大量的研究

The design of interpolation filter is one of the important problems for all digital implementation of receiver.

插值滤波器的设计问题是接收机全数字化实现的核心问题之一。

Based on the elliptic curve cryptosystem, a multi-key sharing scheme in which the Lagrange interpolation polynomial is used and the cheaters can be detected is presented.

文章利用拉格朗日插值的思想，提出了一种基于椭圆曲线的可防欺诈的动态多密钥共享方案；方案中每个参与者的子密钥可以不受限制的重复使用，因此在更新主密钥的时候，无需更改参与者的子密钥，从而减少了可信中心与参与者之间的通信量；方案可灵活地增删参与者，且安全性是基于椭圆曲线离散对数问题的难解性，因而其安全性比在有限域上更高；方案实现过程中解决了检验子密钥真伪的问题。

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。

We constructed a finite volume scheme of fifth order Hermite type with high accuracy for twopoint boundary value problems, choosing trial and test spaces as the fifthorder finite element space of Hermite type and the piecewise linear function space respectively. We didn't use higher derivatives as interpolation conditions, which is the same as the thirdorder finite element of Hermite type, but the scheme obtained had higher accuracy.

构造求解两点边值问题的一种Hermite型五次元高精度有限体积法，其中试探函数空间取Hermite型五次有限元空间，与Hermite型三次元相同，未引入更高阶导数作为插值条件，检验函数空间取分段线性函数空间，这样构造的格式求解精度更高。

This thesis investigates the profile extraction and shape optimization on the result of topology optimization of planar compliant mechanisms. The main context includes the following work:(1) summarizing and analyzing the recent research status, some harvest and unsolved problems;(2) analyzing the conceptual design of planar path-generating compliant mechanisms and its mathematical model and tools;(3) Modifying the method of density contour as the method of profile extraction, and developing a method to optimize the density function in the profile extraction according to the requirement of the design of compliant mechanism;(4) developing a method to abstract the compliant mechanism into a form of links and joints by using the principle of connectivity on topology;(5) developing a method of shape optimization of planar path-generating compliant mechanisms, by representing the profile of the abstracted compliant mechanism as simple curves such as straight lines and arcs, establishing the models of the size optimization of the parameters of these curves, so that the compliant mechanism has a machinable shape;(6) At last, proving the feasibleness and effectiveness of the design method by making simulation design and validating it in FEA software.

主要工作包括：(1)分析了柔顺机构拓扑优化和形状优化的研究现状，分析了目前柔顺机构的研究重点、主要成果和尚未解决的问题；(2)分析了基于SIMP的柔顺机构概念设计方法及其相关工具和模型；(3)针对柔顺机构轮廓提取的特殊要求，提出了密度等值线法的改进方案，对密度函数插值点密度值进行优化，提出优化模型和选择优化算法；(4)根据轨迹输出平面全柔顺机构自身的形状特点，提出了轨迹输出平面全柔顺机构的抽象方法，即应用拓扑学上的连通性原理将柔顺机构抽象成杆件和结点形式，并对相应的数学原理进行了证明；(5)提出了平面全柔顺机构的形状还原和尺寸优化方法，对抽象的柔顺机构进行还原，将其轮廓还原成简单曲线的连接，从而建立尺寸优化模型，对机构进行尺寸优化设计，在得到可加工的机构轮廓的同时又能对关键部位进行特别处理；(6)进行了柔顺机构的数值仿真设计，并将所得设计结果导入商用有限元软件中进行仿真实验，证明了设计方法的可行性和有效性。

The work including:(1) This paper introduces arithmetic for image pre-processing. First, because of illumination, the image intensity is not uniform. The classic binarization algorithms such as Ostu algorithm and Bersen algorithm can not extract object well, so we use S.D.

本文的主要工作包括：(1)从图像预处理入手，首先针对光照造成的图像灰度不均匀，经典的阈值分割方法如Ostu、Bernsen算法不能很好提取目标的问题，采用了利用梯度点信息插值的S.D。

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。