二次函数

The Beta and quadratic functions were used to describe daily thermal and photoperiod effectiveness, respectively.

分别选用非线性的Beta函数和二次曲线函数来定量描述每日热效应和光周期效应。

Then, with the assumption that the consumption of an investor is the continuous or piecewise continuous function of time, the corresponding optimal investment decision and the effective frontier are derived by using the stochastic linear-quadratic control.

假设投资者的消费是时间的连续函数或者分段连续函数，应用线性二次随机控制的方法得到了这两种情形下的最优投资决策和有效前沿。

The contour is second-order continuous piecewise cubic but not a linear function, and a storage structure of contour information was also studied.

研究结果表明：内插结果是具有整体二阶连续的分段三次函数而不是线性函数；该内插方法与常规方法相比，存贮结构节省60%~70%的存贮空间，并且更适用于基于等高线的各种地学分析。

Coefficient function I1 ,I2 ,I3 of quadratic carve is the invariant under the right - angled coordinate transform.

二次曲线的系数的函数I1，I2，I3是直角坐标变换下的不变量，而系数函数k只是转轴变换下的不变量。

Based on the mechanism of secondary flow formation and development in a turbine cascade, SINE function and polynomial function were applied to develop a non-axisymmetric endwall profiling method.

根据叶栅内部二次流形成和发展的机理，应用正弦函数和多项式函数建立了一种叶栅非轴对称端壁成型方法。

Since the lengths of the line segments and the angles between line segments are treated as representation parameters, it is convenient to construct energy function and to deal with displacement and length constraints. Based on this advantage, a parametrical model for human body is proposed, which can easily produce human body models with different feature sizes. The above method is just suitable for polylines. Therefore, a generic deformation method for both discrete curves and surfaces is presented. The energy function is constructed by analyzing the relationship of the points before and after deformation. Together with the displacement constraints, the deformation problem is converted to a convex quadratic programming. A necessary condition for constraint points and a sufficient condition for the uniqueness of solution are given. The proposed method can be combined with skeleton-driven animation to control the deformation.

将线段长度与线段之间的角度作为表示参数，既有利于能量函数的构造，又便于处理位移约束和长度内蕴约束条件，利用这一优势，将其应用于三维人体的参数化建模，可以方便地产生具有不同特征尺寸参数的人体模型，由于这种方法只适用于折线变形，具有较大局限性，因此，本文进一步提出一种较通用的离散曲线曲面变形方法，通过分析变形前后的位置关系来构造能量函数，再加上位移约束条件，将变形问题转化为一个凸二次规划问题，并且给出了约束点应满足的必要条件及模型解唯一的充分条件，这种方法还可以与骨架驱动变形的思想相结合，能更好的控制变形。

We use least squre method to form conicoid mathematic model and fit the point cloud which has been grouped by octree subdivision method.

应用最小二乘法建立二次曲面的数学模型，对于已用八叉树分组的点云数据实现隐函数拟合。

The surface of image can be looked as a curved surface, and we can simulate a conicoid function in local area. Based on this function we can estimate the gradient and the curvature of the curved surface points, and set proper thresholds of gradient and curvature, we can detect the centre lines of roads with correlative process including removing small areas, area growth, thinning, etc. Lastly through seting proper thresholds of the gradient and the curvature again, the original road junctions can be detected and then verified by the road lines detected formerly.

基于微分几何的道路交叉口识别方法：把影像的灰度表面看作是一个曲面，在局部区域内拟合一个二次曲面函数，通过该函数来估算梯度和曲率并设定合适的梯度和曲率阈值来检测道路中心线，并进行相关处理，例如去除小区域、区域增长、细化等，然后再设定合适的梯度和曲率阈值，检测出初始道路交叉口，并用检测出来的道路来进行确认。

MethodsBy means of orthogonally rotational combination design, microwave extraction mathematical simulation model was concluded by the linear regression analysis.

响应面法是采用多元二次回归方程来拟合因素与响应值之间的函数关系，通过对函数响应面和等高线的分析，能够精确地研究各因子与响应值之间的关系，寻求最优工艺参数，解决多变量问题的一种统计方法［3］。

Meanwhile, comparative analysis indicates that the same weighting function will be produced between the proposed methods for motion error measurement and the ordinary frequency domain three-point method for straightness error measurement, and the homology and unitarily in nature will be confirmed.

权函数的对比分析表明：先行分离出运动误差的单信道或多信道二次相移数据重组法与先行分离出形状误差的普通频域三点法具有相同的权函数，它们在本质上具有同源性和统一性。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。