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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

To make the quartic Bézier curve have the desired shape, the new method constructs an additional curve to describe the shape of the quartic Bézier curve.

新方法的优点是曲线须满足的连续性方程是严格三对角占优势的、曲线的不连续点在给定的数据点处、曲线是局部可调整的。

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。

With the point near the corner and the point on any edge of the corner, a piece of quartic spline curve was constructed to approximately calculate the geometrical parameter of the constructed quintic spline curve, An example of reconstructing a corner was given, and the reconstructed curve was interpolated, after which the feed rate, acceleration and jerk were analyzed respectively.

利用拐角附近点及其一条邻边上的点构建一条四次样条曲线近似计算构建的五次样条曲线几何参数。

If the method is combined with the subdivision method of curve,the rational spline curve with higher-order continuity is presented which is the approximation of offset curve.

该方法与离散算法相结合，可得到等距曲线的高阶连续的有理样条逼近曲线，最后，通过数值实例与已有方法作了比较。

Further, it is found that the limit curve is a uniform rational cubic B-spline curve or the curve's control polygon when its tension parameters tend to zero or infinity respectively.

Barsky[4 ] 将具有张力参数样条的双曲样条曲线引入CAGD ，称之为张力样条参数曲线，并证明了这种曲线是一类泛函问题的极小解。

In the traditional reservoir operation system, in general, we use the rule curve as a method of operation, and the reservoir rule curve is the result of system simulation method. Due to the regular and simple rule curve operation unable to satisfy the actual demand effectively. In order to improve the defect, there are many system planning theories and optimum seeking methods to find the optimum operation strategies. The reservoir operators are uncomfortable with the complicated optimum operation strategies. In this article the fuzzy inference model is used to establish a simple and effective operation rule for the reservoir operator.

在传统的水库操作系统中，一般都使用操作规线为操作方式，水库操作规线是系统模拟法所获得的结果，由於规律、简单的规线操作方式往往无法有效满足实际需求，为了改善传统操作上的缺点，近多有利用系统规划之理论，应用各种优选方法求取最佳操作策略，系统最佳操作策略其模式复杂，水库操作人员不易接受，故本文即以模糊推论系统建立一简单有效之操作规则予水库操作人员，作为水库操作放水之依据。

The results are much better than the other approaches'. Then we give another method for approximating offset curves. The circle is first approximated by regular polygon within some tolerance. The exact offset curve is then approximated by the convolution of the regular polygon with a B-spline curve or a NURBS curve having the same degree.

与此同时作者从基圆的正多边形逼近出发，通过求解包络的技巧给出了等距曲线逼近的另一个算法，可整体估计误差，所得的等距逼近曲线为与基曲线同次数的B样条或NURBS曲线，克服了国际上现有同类算法中逼近曲线次数几倍于基曲线次数的缺陷。

Capital accumulates the motion curve that is market economy, unemployed population is the inevitable result that capital accumulates, the work population motion curve that also is market economy at the same time; Allocate be market economy to allocate the rule by element function, polarization of the rich and the poor is the inevitable result that allocates regular action by element; Inflation is the motion curve of market price case and money.

资本积累是市场经济的运动规律，失业人口是资本积累的必然产物，同时也是市场经济的劳动人口运动规律；按要素功能分配是市场经济的分配规律，贫富两极分化则是按要素分配规律作用的必然产物；通货膨胀是市场价格和货币的运动规律。

Looking to bounce back from defeat against Cesena last weekend, the Calabrian boss will be sticking to his tried and tested 4-3-3, with Lopez and Sedivic joined up front in Giampaolo's absence by either Nanni or Plasmati.

鉴于上周末对切塞纳的比赛中反败为胜，这支南方球队将会更坚持其一贯而有效的4-3-3阵型，洛佩斯和塞德维奇将取代受伤缺席的詹保罗，和纳尼或者帕斯马蒂中的一个搭档锋线。

Meanwhile, their exposure to the more freewheeling ways of the West broadened dramatically.

另外，西方较自由的生活方式对年轻人的影响增大。