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Then, based on the mean curvature, Gaussian curvature and the function of principal curvature, the minimal loci of the principal normal surfaces of curves, the curves with constant Gaussian curvature and the two curves of which the ratio of their functions is constant can all be obtained, as well as the properties of geodesic curve and lumbar curve.

再根据平均曲率、高斯曲率及主曲率函数，能得到曲线的主法线曲面的极小轨迹、常高斯曲率曲线及两个主曲率函数之比为常数的曲线。还给出曲面上测地线和腰曲线的性质。

It is shown that two-component Wadati-Konno-Ichikawa equation, i.e. a generalization of the wellknown WKI equation is obtained from the motion of space curves in Euclidean geometry, and it is exactly a system for the graph of the curves when the curve motion is governed by the two-component modified Korteweg-de Vries flow. At the same time, a n-component generalization to the WKI equation is obtained. Also, starting from the motion of curves, mKdV and its symmetry recursion operator is exhibited explicitly; two- and n-component mKdV systems are obtained. It is shown that WKI systems are gauge equivalent to mKdV systems. The two-component WKI equation admits an infinity number of conservation laws and a recursion formula for the conserved densities is given by considering an eigenvalue problem together with introducing an appropriate transformation.

在二维和三维欧氏空间上，我们从空间曲线运动出发，推导出了mKdV方程以及它的用以生成高阶对称的递归算子；推导出了多元mKdV方程以及二元和多元WKI方程，并证明了WKI系统和mKdV系统的规范等价性；尔后，通过考虑特征值问题，并引入一个恰当变换，给出了二元WKI方程的用以计算无穷多守恒密度的递归公式，从而证明了二元WKI方程的守恒可积性；系统地分析了两种mKdV方程的Painleve性质，并分别给出了两种不同形式的二元和n元mKdV方程的共振点出现的规律。

Calculating results show that variation of the propellant inlet pressure makes little impact on engine performance parameters, and the engine will transit to a new stable state. The parameter transition curves are smooth. When the engine thrust is adjusted in a small range within a short period, the parameter transition curves are also reposeful. But when the adjusting range becomes large, the parameter transition curves will fluctuate acutely. Thus, when large range adjusting is required, the time of adjusting should be lengthened or the adjusting should be divided into adequate steps.

计算结果表明，当发动机在某一个稳定工况工作时，发动机入口推进剂压强的变化对发动机性能参数的影响不大，发动机的参数都能比较平稳的过渡到一个新的稳定工况；当发动机在短时间内进行小范围的推力调节时，发动机参数的过渡过程的曲线也比较平稳，但是当在短时间内进行大范围推力调节时，参数的过渡过程的曲线振动比较剧烈，因此应当在进行大范围推力调节时，应当对调节时间进行适当延长，或者分级进行推力调节。

And the thermal drift curves were measured in different ranges of grid voltages in order to work out compensatory temperature-voltage curves which eliminated the thermal drift. The means of the using of thermal resister network for circuit's thermal compensation was adopted, which was based on compensatory temperature-voltage curves.

按照试验结果作出了在以上四个栅极电压范围内的温度漂移曲线，并在温度漂移曲线的基础上作出了理想的消除了漂移的温度-电压曲线。

The given method takes the Hermite interpolation curvcs and the cubic non-uniform B-spline curves as the special cases and unifies the representation of the curves interpolating the control polygon and the cubic non-uniform B-spline curves approximating the control polygon.

所给方法以Hermite型插值曲线和非均匀三次B样条曲线为特殊情形，将插值于控制点的曲线和逼近于控制多边形的非均匀B样条曲线统一起来。

ABSTRACT This paper summarizes our researches on two key techniques in curve and surface modeling-the geometric approximation techniques and the geometric interpolation techniques. The former includes three types of geometric approximation techniques: Hybrid polynomial approximation to rational curves and surfaces, offset curves and surfaces approximation, interval Bézier curves and surfaces approximation. The latter includes a series of algorithms for shape blending modeling: the MSI algorithm for shape blending between space polylines or trees, the MSI algorithm for shape blending between triangular meshes, and skeleton-based shape blending algorithms using triangular decomposition and star-shape decomposition.

本文是作者对曲线曲面造型中两类核心技术几何逼近技术和几何插值技术的研究成果的总结，其中前者包括有理曲线曲面的Hybrid多项式逼近、等距曲线曲面逼近和区间曲线曲面逼近等三类几何逼近方法；后者包括用于形状混合造型的几何插值方法的一系列算法：空间多边形形状混合的MSI插值算法、三角网格形状混合的MSI插值算法、树的形状混合的MSI插值算法以及基于骨架树形状混合的三角剖分算法和星形剖分算法。

With the shape parameters, the trigonometric polynomial curves can approach more to the quadratic Bézier curves or to the given control polygon than the quadratic Bézier curves.

由三个控制顶点生成的曲线具有与二次Bézier曲线类似的性质，但具有比二次Bézier曲线更好的逼近性。

Joint behavior of beam and column is the key of entire structure.This paper uses finite elemnt analyzing software ANSYS to analyze the bearing mechanics of joint under monotonic load and periodic load,and gets load-displacement curves,viscosity curves and frame curves.The paper mainly analyzes how axis-push ratio,gradation of concrete,plate layout and steel type to affect tensibility performance and viscosity feature of joint.The results indicate that concrete-filled squar tube column has good tensibility performance and dissipative ability.

梁柱节点的性能是影响结构整体性能的关键，而目前对方钢管混凝土柱—钢梁节点抗震性能的研究工作尚不完善，本文通过有限元软件ANSYS来分析方钢管混凝土柱—钢梁节点，研究节点区在单调荷载和低周反复荷载作用下的受力机理，得节点区的荷载位移曲线、滞回曲线及骨架线；着重分析方钢管混凝土柱的轴压比、混凝土等级，隔板形式和钢材型号在低周反复荷载作用下对节点延性和耗能等抗震性能指标的影响。

When t=1/2, Path of the C-curves and H-curves ofdegree two and three are lines, but not for the Path of degree four, weneed more about the control polygon. Paths are commonly curves. Butthe reference [38] pointed out that they can closely be approximated bylines. By this method we can get a C-curve passing a given point easily.

一般情况下，C曲线族的Path也是曲线，文献[38]以三次C曲线为例，提出用直线进行近似，应用这一方法，我们可以简洁的求出过一定点的C曲线，只要给定的点在C曲线族的范围内，则可以首先求出过这一点的C曲线族的Path，然后可以确定过这一点的C曲线的形状参数α，以及曲线参数t.H曲线的情况与C曲线类似。

By using hyperbolas to fit axial curves, considering the maximal error of the fitting curves as the objective function, the optimal fitting hyperbola is obtained and the maximal error of fitting curves is minimal after optimization.

通过双曲线来拟合齿向曲线，使拟合曲线的最大误差为目标函数，利用优化的方法，使最大误差最小，得到最优的拟合双曲线，从而加工出所需要的齿形。

Summary In copyright infringement cases,if the alleged infringer uses or even plagiarizes the copyrighted works or parts thereof,which causes no substantially adverse effect on the normal exploitation of the work,nor does it inflict any substantial damages to the right owner,the de minis doctrine should be applied to exempt the liabilities of the defendant and seek the balance of interests between the right owner and the general public embodied by the copyright law.

在侵犯著作权案件中，如果被控侵权行为人虽未经著作权人的同意，使用甚至抄袭了受著作权保护的作品或作品的片段，但若情节轻微，未对该作品的正常使用产生任何实质不利的影响，亦未对权利人的权利造成实质性的损害，则应适用&不计琐细原则&，免除行为人的责任，以寻求在权利人利益与著作权法所体现的社会公共利益之间的平衡。

This new product will become our best seller.

这个新产品会成为我们最畅销的产品。