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Existence, uniqueness and continuous dependence of C〓 solutions for an iterative functional equation related to invariant curves of functional differential equations with piecewise constant arguments are given under weaker conditions than that known results of C〓 solutions.

本章首先讨论了与逐段常时滞泛函微分方程不变曲线有关的一类迭代函数方程的连续解的存在唯一性和连续依赖性，不但弱化了已有结果的C〓光滑性的条件，还讨论了连续解的对称性，并根据对称性将一些结果推进到高维。

Similarly, numerical experiments are performed to demonstrate the efficiency and efficacy of the geodesic distance based MFS for piecewise smooth domain. In addition, the effect of the number of collocation points and the stability with respect to the anisotropy are discussed.In Appendix A.

在后面同样给出了数值例子以说明方法的优越性，不同的是这里考察了分片光滑的几何区域，并加上了配置点数目对数值结果的影响以及该方法对各向异性的稳定性分析。

We decompose curvature signal with wavelet at first and then extract itslow frequency coefficients as new smooth curvature signal, which is used to constructa G~2 continuous piecewise rational cubic Bezier curve with GHI method subsequently.

本文首先对估算得到的离散曲率进行小波分解，提取其低频部分作为新的曲率，然后利用几何Hermite插值方法，重建出光顺的截面线。

We decompose curvature signal with wavelet at first and then use its low frequency coefficients as new smooth curvature signal, which is used to construct a G^2 continuous piecewise rational cubic Bezier curve with (Geometric Hermite Interpolation, GHI) GHI method subsequently.

针对在逆向工程的实践中常见的轮廓线的光顺问题，给出了一种先对曲率图进行小波分解，提取其低频部分作为新的曲率图，并利用几何Hermite插值方法，生成G^2连续的分段三次有理Bézier曲线，从而重建出光顺的产品轮廓曲线的新方法。

A method to analyze the dynamics of piecewise continuous system is presented, based on it, the chaotic oscillation of a harmonically forced spring-mass system with friction is studied. The impact of friction and other parameters on the chaotic oscillation of this system is analyzed.

分析了系统参数和摩擦模型对系统混沌行为的影响；发现了摩擦模型的选取对系统动力学行为分析的重要性；揭示出在一定条件下，系统参数、环境条件或润滑条件的改变都有可能使系统进入无序的混沌运动状态。

During the procession of EMD, piecewise Cubic Hermite Interpolating Polynomial is employed. Furthermore, in order to alleviate edge effects the method of adding extremes is used.

在经验模态分解过程中，采用了分段三次Hermite插值，并通过添加极值的方法减轻边缘效应的影响，使谐波分析能够更准确。

Due to the limited number of measurements on the response data, both Kalman Estimator technique and Singular Value Decomposition incopoerated with piecewise cubic Hermite Polynomial curve fitting method are used to reconstruct the unmeasured reponses and establish the full response measurement.

由於有限的量测资料，本文介绍卡氏重建器与结合分段式立方Hermite型插值多项式之奇异值分解重建法，以重建未量测点之反应历时，以利进行部分量测系统之外力识别。

To avoid these shortcomings, this paper uses particle swarm optimization approach, instead of Gauss-Newtonian algorithm, to optimize projecting direction, and applies Hermite polynomial, instead of piecewise linear regression, to fit ridge function.

但一般投影寻踪回归算法构造技术较为复杂，采用多次局部光滑回归，计算量较大，外推较为繁杂，容易陷于局部解。

A efficient encoding for piecewise linear approximation vertices based on hexagonal neighborhood system approach is proposed.

在后继帧的编码中，以初始时空分割为基础，采用前向运动补偿、非线性内插等算法，跟踪均匀时空区域的时域变化，维持帧间时空分割的一致性。

In the third chapter,we study mainly iterative roots of piecewise homeomorphic maps of an Y-star.

在第三章，我们主要研究了Y星上逐片同胚映射的迭代根的问题。

The network space is the typical form of abstract space when it comes to the digital stage.

网络空间是抽象空间数字化阶段的典型形式。

The Notarial System,as the system of judicial certification in our country,is both the constructor and the defender of social credit system,It has its special value and function in the social honesty.

公证制度作为我国司法证明制度，既是社会信用体系的建设者，同时也是社会信用的捍卫者，在诚信中有其特殊的价值和功能。