查询词典 conjugate curve of the second order

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

First,The properties of the spherical Bezier Curvesproposed by Ken Shoemake(Spherical Bezier curve of first kind)are listed,such asEndpoint property,Symmetry property,Invariant property under solid motion,Spherical convex hull property,etc.,and the fact that this kind of spherical BezierCurve is devoid of subdivision property is pointed out;Based on subdivision,theconcept of a new kind of spherical Bezier curve(Spherical Bezier curve of secondkind)is proposed.This kind of spherical Bezier curve is continuous differentiable.Furthermore,generalization of Bezier curve on more comprehensive manifolds isdiscussed.2Spherical Chaikin algorithm and general spherical corner-cuttingalgorithm.

首先，文中列举了Ken Shoemake提出的点点生成的球面Bezier曲线(第一类球面Bezier曲线)的性质，如端点性质、对称性质、运动不变性质、球面凸包性质等，并指出这种球面Bezier曲线没有剖分性质；基于细分，文中给出了一种新的球面Bezier曲线(第二类球面Bezier曲线)的构造方法，指出这种曲线是连续可微的；作为这些理论的应用，文中改进了Ken Shoemake提出的球面插值曲线构造方法；进一步，文中探讨了Bezier曲线在更广泛的流形上的推广方法。2球面Chaikin算法和一般的球面割角算法。

In order to obtain more general solution of second order linear differential equation with constant coefficients, which is important in theory and practice, on the basis of knowing a special of the second order linear differential equation with constant coefficients and by using the method of variation of constant, the second order linear differential equation with constant coefficients is transferred to the reduced differential equation and a general formula of the second order linear differential equation with constant coefficients is derived.

为了更多地得到理论上和应用上占有重要地位的二阶常系数线性非齐次微分方程的通解，这里使用常数变易法，在先求得二阶常系数线性齐次微分方程一个特解的情况下，将二阶常系数线性非齐次微分方程转化为可降阶的微分方程，从而给出了一种运算量较小的二阶常系数线性非齐次微分方程通解的一般公式，并且将通解公式进行了推广，实例证明该方法是可行的。

Based on Bezier curve continuance of first－order and second－order derivative, the characteristic vector equation of two Bezier curve is presented in point of intersection. The algorithm is not only of high accuracy with all of the interpolated points being on the curve theoretically, but also of very high speed in the real－time interpolation processes. The interpolation velocity does not change and the segment tolerance of interpolation can be control by selecting the parameter in cerement rationally every time.

为保证两段Bezier曲线在连接点处一阶导数、二阶导数连续，导出了两段Bezier曲线特征向量应满足的关系方程，Bezier插补法不仅在理论上可使所有的插补点落在曲线上，而且实时插曲补速度高，每次插补时可合理地选择参数增量，能使插补速度保证不变，也可控制弓高误差。

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The factors such as conjugate framework withsmall conjugation energy, central asymmetry, long conjugate chain,introduction of electron donors-acceptors, strong electron-donating orelectron-withdrawing abilities, long distance between electron donors andelectron acceptors, good coplanarity and so on lead to high third-order optical nonlinearities.

离域能小的共轭骨架，非中心对称结构，长的共轭链，吸供取代基的引入，取代基强的供电子性或吸电子性，长的吸供电子取代基之间的距离，以及良好的共平面程度等因素有利于获得较大的三阶非线性光学性能。

In order to roll round billets with accurate roughing shapes by a three-high roughing mill and stabilize production, a flexible pass design method was used to optimize the traditional conjugate pass through the distortion design of the bottom, side wall and pressure difference of the pass, realizing the application of the conjugate round pass on the three-roll mill.

为轧制料形尺寸准确的圆料、稳定生产，采用变通孔型设计方法对共轭孔型进行优化设计，通过对共轭孔型槽底、侧壁、压力差的变形设计，实现了共轭圆孔型在三辊粗轧机上的应用，轧槽咬钢顺利，成品圆料容易控制，完全满足后续工序的要求，同时减小了轧线的轧制事故，单套轧辊的轧制量可提高60%以上，取得了良好的经济效益。

On the basic that existing second-order sufficient condition for an isolated minimizer of order 2 for unconstrained multi-objective optimization, using the so called oriented distance from a point to a set, l-stable function and generalized second-order Peano direction derivative, some second-order sufficient conditions for an isolated minimizer of order 2 for constrained multiobjective optimization problems with l-stable functions are obtained.

在已有的无约束l-稳定函数多目标优化问题的二阶充分条件的基础上，借助定向距离函数和l-稳定函数的性质及引入的广义二阶Peano方向导数，进一步刻画了具有抽象约束的l-稳定函数的多目标优化问题的二阶孤立极小点的二阶充分条件。

The interpolation algorithm of introduced error compensation for complex parametric curve in space is proposed for the high precision interpolation of parametric curve on the basis of studying the first, second order taylor expression parametric curve interpolation algorithm and the plane parametric curves interpolation algorithm.

以一、二阶泰勒展开式参数曲线插补算法和平面参数曲线插补算法研究为基础，提出引入误差补偿值的复杂空间参数曲线高精度插补算法以实现空间曲线的高精度插补。

Chaikin algorithm is the simplest discrete curve modeling method.In thepaper planar Chaikin algorithm is generalized into sphere,and the practicability ofthe algorithm as well as the continuous differentiable property of the generatingcurve is proved.It is shown that the curve generated by Chaikin algorithm is apiecewise spherical Bezier curve of second kind of order two.Furthermore,generalspherical corner-cutting algorithms are discussed,and it is pointed out that thecurve generated through corner-cutting has"Spherical Variation DiminishingProperty".3Curve interpolation method restricted on a smooth surface based ontransformation.

Chaikin算法是最简单的离散曲线造型方法，文中将Chaikin算法推广到球面，证明了算法的可行性和生成曲线的连续可微性，指出球面Chaikin算法得到的曲线是分段的二次第二类球面Bezier曲线，并给出了用球面Chaikin算法构造球面插值曲线的算法；进一步，文中讨论了一般的球面割角算法，指出由球面割角算法得到的曲线具有"球面变差缩减性质"。3基于变换的约束在光滑曲面上的曲线插值方法。

You can snipe the second and third union leaders from this position.

您可以鹬第二和第三工会领袖从这一立场出发。

Aiming at the currently shortage of XML streams quality detecting, this paper proposes a new forecasting method of XML streams quality by least squares support vector machines, which is used the method of XML keys' vector matrix as windows, and vector product wavelet transform to multilevel decompose and refactor the XML streams series, that can fulfill real-time checking demand of XML quality, and ensure constraint, consist- ency and integrality. For even more adapting net load, it proposes a control strategy by weight and adaptive adjustment to ensure XML streams quality.

针对当前XML数据流质量检测存在的不足，提出构建XML键的矢量矩阵作为窗口，利用矢量积小波变换多级分解与重构XML数据流，再结合最小二乘支持向量机对XML数据流质量进行预测的一种方法，满足XML数据流质量重构时实时检测的要求，保证XML数据的约束性、一致性与完整性；为了更好的适应网络负载，采取加权与自适应窗口调整等调度策略充分保证XML数据流的质量检测。