二次函数

The present paper applies the quadratic splines to the Chemical Engigeering calculations for integration, interpolation and differentiation with good precision.

在样条函数的研究和应用日益广泛的今天，作者将人们所忽视的二次多项式样条函数引用到化工计算中的插值，求积和求导等方面，取得良好的结果。

Under quadratic loss function, the definition of conditional admissible prediction is given and some necessary and sufficient conditions for linear predictions Ly_s of conditional linear predictable variable Qy to be admissible are obtained.

在二次损失函数下，给出了条件可容许预测的定义，在齐次线性预测类和非齐次线性预测类中得到了条件线性可预测变量Qy的线性预测Ly_s是可容许预测的充要条件。

The path is defined as linear combination of a sequence of conjugate directions whichare obtained by applying standard conjugate direction method to approximate quadratic functionof unconstrained optimization.

Bulteau和Vial在[7]中构造了无约束最优化问题的共轭梯度路径，其基本思想是将标准共轭方向法应用于无约束优化目标函数f的局部二次近似函数，得到一组共轭方向序列。

Firstly, we prove that if we select nodes properly, and let the distance between these nodes sufficiently small, cubic polynomial spline can approximate a continuously differentiable function, which with continuous derivatives of second order and discontinuity of the first kind in the derivatives of fourth order, to any desirable accuracy. This result lays a theoretical foundation for representing trajectories by splines and double orthogonal basis.

一是证明了适当选取节点并使节点距充分小时，三次多项式样条可以逼近具有二次连续导数的分段四次连续可微函数到足够的精度，这一结论为用样条和双正交基表示弹道打下了理论基础。

In order to discuss the rationality of various warping displacement modes, second-degree parabola, cubic parabola, fourth-degree parabola and cosine function are selected respectively. It has been demonstrated that these displacement modes have limitation to some extent, and a more reasonable mode needs to be developed.

为了探讨各种剪滞翘曲位移模式的合理性，分别选取二次抛物线、三次抛物线、四次抛物线及余弦函数等翘曲位移模式进行计算；结果表明，这些翘曲位移模式在一定程度上均存在不足，目前还缺乏一种更加合理的位移模式。

Then, a modifiable cubic polynomial curve is presented based on the basis functions, and the relation between the curve and the classical Bézier curves is discussed.

然后，基于该调配函数生成了一类可调控的三次多项式曲线，并讨论了该曲线与二次Bézier曲线及三次Bézier曲线之间的关系。

There is mutual contradiction between direction estimation of user's signal and power allocation among all users in the beamforming algorithm. A twice game beamforming algorithm based on game theory is proposed to deal with it. Beamforming game algorithm mathematics model is constructed. During the first game, direction of signal and power allocation are mapped the game theory as "player", which are modeled as the problem of maximin function and obtain direction estimation first. Then during the second game, power allocations of different users are described as a multi-user game. Power updated algorithm is designed. The existence and uniqueness of the Nash equilibrium in the twice game beamforming algorithm based on game theory are proved by mathematics derivation.

摘要针对波束成形算法中，用户的信号方向估计值和用户之间的功率分配存在着相互矛盾，本文提出了一种基于博弈论的二次博弈波束成形算法，构建了波束成形博弈算法数学模型，首先在第一次博弈的时候，将波束成形算法中的信号方向和功率分配映射为博弈论数学模型中的"局中人"，将其建模为函数的极大极小值求解问题，先求解出信号方向；然后在第二次博弈的时候，将不同用户的功率分配过程描述为一个多用户的博弈过程，设计了功率分配更新算法，通过数学推导论证了纳什平衡点的存在性和唯一性。

The algorithm has following properties: Although the merit function has the form of least squares of a system of overdetermined equations, in the Newton equation of our algorithm, only the coefficient matrix of the system of overdetermined equations is used instead of its product as in Guass-Newton method for solving the least squares problems. That is, our Newton method is more like that for the system of nonlinear equations rather than that for LSPs. The global convergence is obtained for VLCP with vertical block P_0 + R_0 matrix; The local quadratic convergence rate is proved under the condition that the solution is BD-regular; Although there is only a Newton equation in our algorithm, the finite convergence property can be shown if matrix is vertical block P— matrix (without the hypotheses of strict complementarity).

该算法具有下列特点：所构造的价值函数虽然具有超定方程组的最小二乘问题的形式，但在基此建立的Newton算法中，其Newton方程的形式更象非线性方程组的Newton法中的Newton方程，仅利用了超定方程组的系数矩阵本身的信息，避免了一般最小二乘问题的Guass-Newton法中必须计算系数矩阵的乘积的工作量；对竖块P_0+R_0矩阵的垂直线性互补问题，算法具有全局收敛性；在解是BD-正则条件下，证明了算法的局部二次收敛性；虽然算法只含一个Newton方程，但对竖块P-矩阵垂直线性互补问题，算法具有有限步收敛性。

In this paper, we define quadratic spline as wavelet, do the two dimentional dyadic wavelet transform on near-infrared galactophore image, and get local modulus maxima from wavelet transforms results----rnodulus and angles, so we can find the blood vessel edge image in each scales, at last, we compute a good edge image which synthesize the characters in each scale.

本文中用二次样条小波作为小波基函数，对乳腺近红外图像进行二维二进小波变换，计算小波变换结果的局部模极大值点，得到各个尺度下的乳腺近红外图像血管的边缘，最后得到综合了各个尺度特征的较好的血管图像的边缘。

Third, mensurated the front axles load-time history when truck was running on general tar-paved roads, mountainous roads and the proving ground enhancement roads, second sampled and pretreated to the load-time history with RPCⅢ software of MTS corporation, acquired the relationship of the frequence of the mean and amplitude load, obtained the zero mean equivalent loads using Goodman experiential fatigue equation, acquired the Weibull distributing functions of equivalent loads of respective roads.

第三，测定了汽车前桥在一般沥青公路、山区公路和试验场强化试验路面的载荷时间历程。对载荷时间历程进行了二次采样和数据预处理。采用雨流计数法得到了各路面的载荷均、幅值的频次关系，并根据Goodman经验疲劳公式，得到了零均值的等效载荷及相应的频次。利用数理统计的方法得到了各路面的等效载荷的Weibull分布函数。

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。