曲率圆

Curve C at the spot P(x0, y0) curvature is the maximal circle of the curve C tangency at the spot P(x0, y0). Contrail curve G of the center D of curvature circle entitles evolute of curve C.

曲线C在点Px0，y0）曲率圆是与该曲线C相切于点P(x0，y0的最大圆，曲率圆的圆心D的轨迹曲线G称为曲线C的渐屈线。

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。

First, a special normal transversal at the initial point is constructed and a second-order Taylor's algorithm is used to trace the projections along the aforementioned normal transversal. A curvature based method for controlling iteration step is further proposed by projecting the given point onto the curvature circle of the normal transversal at the initial point. Finally gradient based method for correcting iteration errors is put forward.

首先构造初始点处的一条特殊的法截线，并给出沿着该法截线追踪投影点的二阶泰勒迭代方法；然后将给定点向初始点处的法截线的曲率圆作投影，提出基于曲率的步长控制策略，在此基础上给出了基于梯度的迭代误差矫正方法。

Thus, evaluation of the minimum zone circle could be solved effectively.Three methods of assessment of roundness error were proposed in this dissertation. Based on the criteria of the minimum zone circle, minimum circumscribed circle and maximum inscribed circle and convex hull, a unified approach was proposed to evaluate roundness error of the minimum zone circle, minimum circumscribed circle and maximum inscribed circle. Evaluation of the minimum zone circle, minimum circumscribed circle and maximum inscribed circle was fulfilled with rotation based the contact pattern. The minimum circumscribed circle and maximum inscribed circle were evaluated with curvature and the curvature circle.

本文提出了三种圆度误差评定的方法：根据最小区域圆、最小外接圆、最大内接圆在极坐标系下的判别准则，利用计算几何中的凸壳理论，提出了一种统一的评定方法，实现了对最小区域圆、最小外接圆、最大内接圆的误差评定；基于接触斑点的检验原理，利用旋转法，实现了最小区域圆、最小外接圆和最大内接圆的误差评定；利用曲率和曲率圆，实现了对最小外接圆和最大内接圆的误差评定。

Secondly, in this part, we will introduce the notation of average geodesic curvature for curves in the hyperbolic plane, and investigate the relationship between the embeddedness of the curve and its average geodesic curvature. Finally, we will employ the Minkowskis support function to construct a new kind of non-circular smooth constant breadth curves in order to attack some open problems on the constant width curves for example, whether there is a non-circular polynomial curve of constant width, etc.

其次，对双曲平面上的曲线引入平均测地曲率的概念，并讨论双曲平面上凸曲线的嵌入性与它的平均测地曲率之间的关系，其目的是为了将双曲平面上曲线的性质与欧氏平面中曲线的性质作一些对比；最后，我们利用Minkowski支撑函数构造了一类新的非圆的光滑常宽曲线，其目的是想回答有关常宽曲线的一些未解决问题如是否存在非圆的多项式常宽曲线？

Here, we will give an independent proof of the existence for inequality (2.1.3), and by the way, give an estimate on the width of the bi-enclosing annulus of closed convex curves in the plane. Secondly, in this part, we will introduce the notation of average geodesic curvature for curves in the hyperbolic plane, and investigate the relationship between the embeddedness of the curve and its average geodesic curvature.

其次，对双曲平面上的曲线引入平均测地曲率的概念，并讨论双曲平面上凸曲线的嵌入性与它的平均测地曲率之间的关系，其目的是为了将双曲平(来源：ABC论84文网www.abclunwen.com)面上曲线的性质与欧氏平面中曲线的性质作一些对比；最后，我们利用Minkowski支撑函数构造了一类新的非圆的光滑常宽曲线，其目的是想回答有关常宽曲线的一些未解决问题如是否存在非圆的多项式常宽曲线？

The minimum curvature circles of parabola, ellipse and hyperbola all are their inscribed circle, their equations are^2+y^2=p^2、 and respectively.

抛物线、椭圆和双曲线的最小曲率圆都是它们的内切圆，其方程分别为^2+y^2=p^2、。

Combining with the National Natural Science Foundation ofChina(No.50478032), following researches were done in this thesis: 1 The variation regularity of the ultimate anti-bending capacity of therectangular-sectioned beam with different corrosion has been obtained through thequalitative analysis of 48 beams (32 corroded beams and 12 comparing beams) withaccelerated corrosion; 2 The conclusion has been obtained that the strain of corroded steel bar andconcrete no longer fit in with the assumption of plane section through the analysis ofthe strain data, the strain relation of steel bar and concrete in the mid-span section ofvariously corroded beams at ultimate has been obtained. Through the building of newgeometric relation, the expression of the height of compressive area in the corrodedbeam with rectangular section has been deduced, and the formula with corrosion rateas the main variable for the anti-bending capacity of the corroded concrete beam hasbeen suggested and verified by experiment.; 3 The influence of steel bar corrosion and the concrete regression to the flexureductility coefficient of the corroded structure component has been analyzed. Based onthe relation of steel bar and concrete at yield and ultimate, the expression for theflexure at yield and ultimate of corroded reinforced concrete beam, and the model forthe calculation of the flexure ductility has been built.

本文结合国家自然科学基金项目(50478032)"既有钢筋混凝土桥梁时变可靠度研究"，主要进行了以下研究工作： 1通过对48根快速锈蚀钢筋混凝土矩形截面梁(32根锈蚀梁和12根对比试验梁)数据的定性分析，得到了不同锈蚀率下，锈蚀钢筋混凝土矩形截面梁极限抗弯承载力的变化规律； 2通过对应变数据的分析，论证了锈蚀构件钢筋和混凝土的应变不再符合平截面假定的结论，并通过回归分析得出了不同锈蚀率的螺纹钢筋梁和光圆钢筋梁在极限弯矩作用下，跨中截面处钢筋应变和钢筋处混凝土应变的关系，通过构造新的几何关系，得出了锈蚀钢筋混凝土矩形截面梁计算受压区高度的表达式，既而得出了以锈蚀率为主要变量的锈蚀钢筋混凝土矩形截面梁的正截面抗弯计算建议公式，并通过试验数据加以验证； 3分析了钢筋锈蚀和混凝土劣化对锈蚀构件曲率延性系数的影响，结合钢筋屈服和极限弯矩两种状态下钢筋和混凝土的应变关系，分别得到了锈蚀钢筋混凝土矩形截面梁屈服曲率和极限曲率的计算表达式；既而推导出曲率延性系数的计算模型。

The annulus model captures the key features of rotating convection in full spherical geometry and has been widely employed to study convection, magnetoconvection and dynamos in planetary systems, usually in connection with the small-gap approximation neglecting the effect of azimuthal curvature of the annulus.

圆环模型被广泛用来研究行星系统的对流，磁对流和发电机。通常在这些研究中用到了小间隙的近似，忽略了圆环的环向曲率效应。我们这一工作用数值模拟方法解完全的非线性对流方程组来研究有限间隙的旋转圆环中的非线性对流。

This paper establishes cubic spline function, analyzes subsection curve function and curve slope and curvature, at last decides to place the curve especial points which can be obtain easement curve length and other line parameters, such as the ZH point (end of line and beginning of transition curve), the HY point (end of transition curve and beginning of circular curve), the QZ point, the YH point (end of circular curve and beginning of transition curve), the HZ point (end of transition curve and beginning of line).

针对公路平面线形的8种组合类型，其线形元素特征则由最基本的直线、圆曲线、缓和曲线组成的特点，解析三次样条函数模型，得分段曲线函数、曲线斜率、曲率，从而确定曲线特征点（直缓ZH点、缓圆HY点、曲中QZ点、圆缓YH点、缓直HZ点）位置，进而得到曲线缓和曲线长度及其他线形参数。

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。