二次函数

It is proved that the least squareestimators of linear estimable functions of regression coefficients areadmissible under matrix loss and minimax. The necessary and sufficientexistence conditions are derived for the uniformly minimum riskequivariant estimators of linear estimable functions ofregression coefficients under an affine group and a transitive group oftransformations respectively. It is also proved that there are no UMREestimators ofthe covariance matrix and variance under an affine groupof transformations and quadratic loss functions.

本文证明了回归系数的线性可估函数的最小二乘估计是极小极大的且在矩阵损失函数下是可容许的；还分别在仿射变换群和平移群下导出了存在回归系数的线性可估函数的一致最小风险同变估计的充要条件，并证明了在仿射变换和二次损失下不存在协方差阵和方差的 UMRE 估计。

By use of ANN model trained under normal circumstance, inner and outer bus fault can be distinguished clearly. For the research on bus protection theory based on function approximation ability of ANN, it is crucial to establish the functional relation between the input and the output of bus protection object.

在研究基于ANN函数逼近能力的母线保护原理的过程中，首先就母线保护物理对象的输入输出之间的函数关系进行了研究，将物理对象的输入定为母线上各回路电流互感器传变后的同一时刻二次检测电流，输出定为母线上各回路的一次侧同一时刻流过的电流之和。

To obtain current-mode biquadratic filter with high accuracy, a voltage-mode second order universal filter based on two VFA's was transformed into a current-mode biquadratic filter-based on two AOA's by means of the concept of adjoint network.

为获得高精度电流模式双二次滤波器，以双VFA电压模式二阶通用滤波器为原型，用伴随网络的概念设计出AOA电流模式双二次滤波函数的新电路。

The paper focuses on the multivariate Laplacian distribution. Based on MLD, we have obtained the variance of the quadric form, the covariance of two quadric forms and the covariance of the linear function and the quadric form.

对于多元拉普拉斯分布，我们推导出了多元拉普拉斯分布的二次型的方差，两个二次型的协方差，线性函数与二次型的协方差。

On the basis of analyzing detailedly the correlative conclusions of the extreme value problem of two variable Function , this paper extends the essential condition and sufficient condition to multi-variable function by using the Taylor Formula 、Quadratic Form 、Hesse Matrix and so on,and gives a method to judge the extreme value of point whose vice-derivative doesn't exist by utilizing Lagranges theorem ,so that compensates for the blank above ,which turns idea that solve the extreme value of multi-variable function problem one by one into realities.

摘要本文在对二元函数极值问题的相关结论进行分析的基础上，用泰勒公式、二次型、海赛矩阵作为工具，将二元函数极值的必要条件和充分条件推广到多元函数的情形，而且还利用拉格朗日中值定理找到了一个判别不可导点处极值的方法，从而弥补了多元函数不可导点处极值无法判断的空缺。因而，使得用穷举判断的方法来解决多元函数的极值问题这一思路成为现实。

Secondly, a rule of the choice of step-length is presented for a non-quadratic objective function of n variables, according to the rule we prove that the Gradient Method has local n-step quadratic convergence rate for a non-quadratic function under certain conditions.

其次，对于n个变量的非二次目标函数也提出了一个步长选取的准则，并在此准则下证明了当目标函数满足一定的条件时，梯度法具有局部n-步二阶收敛速度。

This paper discusses the defect of quadratic loss function and studies the models of inverted Normal and inverted Gamma loss function.

本文讨论了二次损失函数模型的局限，在此基础上研究了逆正态、逆伽玛损失函数模型；探讨了质量损失函数与信噪比的关系，提出了基于信噪比的多元质量损失函数模型，克服了单质量属性不能反映实际中多维质量属性的质量损失的弊端，实例证明该方法是可行的。

The objective function of the QP problem is a quadratic function which is an approximation of the Lagrangian function of the constrained problem and the constraints of the QP problem are linear approximation of the constraints of the constrained problem.

这些二次规划子问题的目标函数是原约束最优化问题的Lagrange函数的某种二次近似，其约束条件是原约束条件的线性逼近。

The non-sensitive loss function is replaced by quadratic loss function and the inequality constraints are replaced by equality constraints. Consequently, quadratic programming problem is simplified as the problem of solving linear equation groups.

用二次损失函数取代支持向量机中的不敏感损失函数，将不等式约束条件变为等式约束，从而将二次规划问题转变为线性方程组的求解。

Four thin-layer drying models were investigated for the description of FIR-assisted freeze-drying characteristics. The models were exponential model, Page model, diffusion model, and approximation of the diffusion model. Tests were conducted using a three-level, three-factor (drying temperature, distance between sample and FIR heater, and sample thickness) design, and quadratic polynomial analyses were performed to relate the drying parameters of thin-layer drying model. The performance of these thin-layer drying models was evaluated by comparing the coefficient of correlation (R2), the sum of squares, and the RMSE amongst four models. Drying parameter K of the Page model gave the best results in describing freeze-drying with FIR of Tylose and sweet potato.

运用四种薄层乾燥模型（指数、Page、渗透模型及近似渗透模型）研究远红外线冷冻乾燥之乾燥特性，实验采用三阶层、三因子（远红外线加热器设定温度、远红外线加热器至样品表面之距离及样品之厚度）的实验设计，对於薄层乾燥模型的乾燥参数以二次多项式函数表示之，乾燥参数之二次多项式函数的最适性判断主要是藉由决定系数、模式缺乏适合性及均方根误差等值的比较而加以评估，以Tylose及甘薯样品而言，其中四种薄层乾燥模型的乾燥参数以Page模型之K值的结果为最佳。

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。