曲率

In addition, we made account for the selection of inverted bending curvature of pipe axis and the length of equal curvature region, and pointed out that we can only equalize the curvature in the equal region and carrying out straightening really is in the region of unequal curvature. This is the development and perfect of bending straightening theory and this method can spread to bar straightening machine.

此外，还对反弯曲线曲率和等曲率区长度的选取作了说明，指出在等曲率弯曲区只能使曲率均匀化，而真正实现矫正是在后部的非等曲率弯曲区，这是对矫正理论的深入和完善，并且这一研究方法也可推广到棒材矫正机。

Consider the circle that is tangent to the curve at and has the same curvature there. Its center will lie on the concave side of the curve. This circle is called the circle of curvature. Its radius is the radius of curvature, and

在点处的曲线的法线上，在凹的一侧取一点，使得，以为圆心，半径为的圆叫做曲线在点处的曲率圆，曲率圆的圆心叫做曲线在点处的曲率中心，曲率圆的半径叫做曲线在点处的曲率半径。

The equations of the curvature, curvature radius, main curvature and main curvature radius on hypocycloid抯 and epicycloid抯 theoretical tooth shape and practical tooth profile are deduced respectively.

根据微分几何知识，分别推导出内、外摆线理论齿形和实际齿廓的曲率、曲率半径、主曲率及主曲率半径的方程式，并绘制了内、外摆线理论齿形和实际齿廓曲线及理论齿形的曲率半径变化曲线。

Based on this property, by solving a series ODEs we construct a two-parametric family of helicoidal surfaces under cubic screw motion with prescribed mean curvature or Gauss curvature and solve an open problem left by Beneki.

基于这一点，当螺旋面的平均曲率或Gauss曲率为给定光滑函数时，本文选取伪正交标架，使得两类螺旋面的平均曲率和Gauss曲率的表达式相对简化，通过求解一系列的非线性常微分方程，即可确定一族生成曲线，从而最终确定平均血率或Gauss曲率为给定光滑函数的双参数族螺旋面，并在这一过程中解决了Beneki等人留下的一个公开问题。

Some properties of inversions are proved, It indicates that the inversion is conformal, the image of line of curvature is still the line of curvature of the inversion S of the hypersurface S, the principal curvature, the total curvature, and mean curvature of S are the functions...

在n-1维超曲面的反图变换中，示明反图变换为保角表示法，曲率线系的反影仍为反超曲面的曲率线系，反超曲面的主曲率，全曲率与平均曲率为原超曲面的主曲率的函数等。 3。最后导出公式(1)在四维空间与通常空间之特殊形式

Type IB: Isocline is convergent towards inner arc at a right angle to the fold.

根据等斜线的收敛层度，再细分为三个亚型：IA型：等弧线向内弧强烈收敛，各线长短判别极大，内弧曲率远大于外弧曲率，为典型的顶薄褶皱；IB型：等倾斜线向内弧收敛，并与褶皱面垂直，各线长短大致相等，褶皱层真厚度不变，内弧曲率仍大于外弧曲率，为典型的平行褶皱；IC型：等斜线相内弧轻微收敛，转折端等倾斜线比两翼附近的要略长一些，反应两翼厚度有变薄的趋势，内弧曲率略大于外弧曲率。

In this paper, we will study the definination of lines of curvature and the correlative conception, for example, normal curvature, principal direction and principal curvature and so on, the connection of lines of curvature and correlative conception, especially probe into the solution with the equation of lines of curvature and the equivalence with its determinant theorem.

本课题主要研究曲率线的定义及其相关概念如法曲率、主方向、主曲率等，曲率线与相关概念的关系，重点探讨了曲率线方程的求解及曲率线判定的等价定理。

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。

Theory; the spatial meshing theory includes comparative motion, comparative differential and conjugative curved surface; and the application of meshing theory includes gear drive and worm drive. The spatial meshing theory is the main part of the course.

课程的重点讲解内容有曲线的参数方程、切线、法面、弧长、曲率、空间曲线的基本公式、挠率及平面曲线的基本公式等；曲面第一和第二基本公式，法曲率、主方向和主曲率、欧拉公式、短程挠率、欧拉公式和贝特朗公式推广、相对法曲率和相对短程挠率等；刚体的绝对和相对运动速度、相对微分和绝对微分、相对速度和相对微分、轨迹曲面的法曲率和短程挠率等；空间共轭曲面的啮合条件、诱导法曲率、两类界限点、等距共轭曲面、空间啮合的二次接触原理等；蜗杆传动的数学模型建立及啮合特性分析方法等。

Its implementation processes include:①to perform wavelet transform and frequency decomposition and reconstruction to gain the seismic data with high quality;②to adopt least square method to approach and fit the local secondary curved face, and compute the fit coefficients of the secondary curved face, then use these coefficients to gridding mapping bed plane to compute the average curvature and Gauss curvature, then, obtain other curvatures through the various linear combinations of the two curvatures above;③to generalize the curvature of the bed layer to compute and reconstruct the curvature volume.

其实现过程为：①对地震资料进行小波变换、分频重构，获得高质量的地震资料；②采用最小二乘法一次逼近，对局部二次曲面进行拟合，求取二次曲面拟合系数，并利用这些系数对网格化成图层面计算平均曲率和高斯曲率，再从两个曲率的不同线性组合，获取其他曲率；③将层面曲率推广，计算和重构曲率数据体。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。