曲线

Wear degree decreases, and the wear particle distribution curves become protrusive and precipitous gradually in the initial stage.

通过分析铜合金销与碳钢盘在干摩擦条件下相互对磨所产生的磨粒群和销试样磨损量，发现磨粒的累积分布和微分分布特性随磨损时间的变化而变化：在磨损开始阶段，磨损程度逐渐减小，磨粒群分布曲线由平缓变得逐渐凸、陡；达到磨损平衡状态后，磨损率达到最小，磨粒群微分布曲线的幅值达到最大，横向宽度达到最小；随着销与盘间互适性变弱，磨损程度增大，磨粒分布曲线变得越来越平缓，横向宽度逐渐增大；磨粒分布曲线随磨损时间的变化规律与磨损率随磨损时间的变化规律有明显的对应关系，可为科学诊断和预测摩擦学系统状态提供有用信息。

The concept of exponential transformations of rectangular Cartesiancoordinates is introduced, showing that a plane curve is more frequently expressed by a unionof four or fewer quadrantal equations defined uniquely in the respective quadrants whichthe curve covers and are therefore quadrant invariant, then the Fermat curve s with someof their geometric properties are formulated.

引入直角笛卡儿坐标幂变换的概念，说明一平面曲线是较经常地用4个或更少的象限方程的并集来表示的；这些象限方程是在曲线所在的各个象限中惟一定义的，因而是象限不变的。然后列出费马曲线的方程，并简述了费马曲线的一些几何性质

Furthermore,it can represent the elliptic curves,parabola and other quadratic curves without using rational form.

给出了一种基于三角函数的类三次参数曲线，该曲线不仅具有类似于三次Bézier曲线的诸多性质，而且无需有理形式即可精确地表示椭圆、抛物线等二次曲线。

Constructing C 2 interpolation curve by quartic Bézier curve offers additional freedom degrees those can be used to adjust the shape of the curve.

用四次B？zier曲线构造C2 连续的插值曲线可提供额外的自由度，用于控制曲线的形状。新方法构造辅助曲线用于描述B？

In order to overcome these weaknesses, we use quartic B-spline structure the yield curve, which indicates the less node cubic B-spline model is better under the situation that do not use the forward rate curve, if need to make use of forward rate curve to carry on the economy analysis, the suggestion use quartic B-spline method.

为克服这些缺点，我们用四次B-样条构造收益率曲线，实证表明能克服三次B-样条曲线上述缺点。因此，在不使用远期利率曲线情况下较少节点的三次样条模型是较好选择，当需要利用远期利率曲线进行经济分析时，建议使用四次B-样条法。

The results indicate that the reconstructed quintic spline curve can ensure the cutter transit well for corner contour, and that the cutting performance is superior to that of the quadratic one.

同时也重构了一条四次样条曲线与五次样条曲线作对比分析，结果表明，五次曲线能使裁刀获得良好的且较四次曲线优越的轮廓拐角加工性能。

Rational planar curve; rational space curve; rational ruled surface; moving curve/surface;μ-bases; singularity; self-intersection curve; moving curve/moving surface ideal; ideal-theoretic/set-theoretic generators

基础科学，数学，几何、拓扑平面有理曲线；空间有理曲线；有理直纹面；动曲线/曲面；μ基；奇点；自交线；动曲线/动曲面理想；集论/理想论生成元

Through the new research methods, this thesis has made the following contributions in this field: 1. For the first time the curvature radii and relative angles of a planar continuous curve at discrete points are chosen as local parameters to represent the curve, which reflect clearly the local geometrical characteristics of the curve and are easy to be dealt with.

借助于新的研究方法，本文在这一领域作出如下贡献：（1）首次提出用曲线上离散点处曲率半径和相对转角作为局部参数表示平面连续曲线，直观地反映曲线各个局部的几何特征，且便于曲线的修改和变换，并通过机构运动分析，快速求出机构轨迹的这两个局部参数。

Three types of interfacial tension curves were observed. The first curve comprised two curves that were located on either side of 1:1 molar ratio, and the interfacial tension decreased with the increase of excessed surfactant component. The second one was a saddle-shaped curve that strode over the 1:1 molar ratio. The third type was a saddle-shaped curve that was located beside the 1:1 molar ratio.

观察到三种界面张力曲线类型，第一类为摩尔比1：1的两边的两条曲线，界面张力随过剩表面活性剂组分的比例增加而降低；第二类为一条跨过摩尔比1：1的马鞍型曲线；第三类为位于摩尔比1：1的一边的一条马鞍型曲线。

The Stained pulp curve in different head are described as: elliptical dished head: H=178. 78+0.5926R-0.0141R〓 semispherical head: H=146. 76+0.0093R-0.0071R〓 conical dished head (α=27°): H=118. 2+0.0248R-0.0061R〓 conical dished head (α=23°): H=151. 7-0.1024R-0.0065R〓 If only for the quality and the efficiency of bleach of up-flow reactor, the conical dished head is the best option with the good engineering feasibility.

对实验数据处理回归后得到流经椭圆形封头时纸浆分布曲线方程；流经球形封头时纸浆分布曲线方程；流经锥形封头（半锥角27°）时纸浆分布曲线方程；流经锥形封头（半锥角23°）时纸浆分布曲线方程。

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。