二次函数

This paper introduces the definition of common quadratic Lyapunov functions and proves that the set which consists of all the common quadratic Lyapunov functions is a convex cone .

给出了共同二次Lyapunov函数的定义，并证明了全体共同二次Lyapunov函数所组成的集合是凸锥

A simple method for quadratic objective function with convex constaints and with linear constaints is given.

文章对目标函数是二次的且约束是一般凸集和二次目标函数且约束是线性的情形，给出了更简单的算法。

Bring forward a kind of learning algorithm fitting on the base of spline function, because the spline function has good flexibility and quadratic smoothing property, the search problem of network weight functions training can be converted into the resoluting extreme value problem of the plurality function through using spline function to represent network input and link weight functions, thus the PNN can be trained with the help of the existing neural network learning algorithms;④build a kind of learning algorithm base on the alternate of Walsh function, the complexity of network computing can be decreased through using the complete orthogonality of Walsh function corollary.

应用结果表明该算法收敛速度快，稳定性好；③提出了一种基于样条函数拟和的学习算法，由于样条函数具有很好的柔韧性和二次光滑性，将网络输入函数和连接权函数用样条函数的形式表示，可把网络权函数训练的函数寻优问题转换为多元函数求极值的问题，从而可借助于现有的神经网络学习算法训练过程神经元网络；④建立了一种基于Walsh函数变换的学习算法，利用Walsh函数系的完备正交性，可大大降低网络计算的复杂度。

The third aspect: we consider comparison of Minimum Norm Quadratic Unbiased Estimator and ordinary least squares estimator of in the multivariate normal linear model Y ~ N{XB, V, where the design matrix A' need not have full rank and the dispersion matrix V can be singular.

使用的损失函数有二次损失函数、嫡损失函数和对称损失函数。论文基于以下三个准则：二次损失风险准则、嫡损失风险准则和对称损失风险准则，将MINQUE和LSE进行比较。

In the model, the non-sensitive loss function was replaced by quadratic loss function and the inequality constraints were replaced by equality constraints.

在该模型中，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换为线性方程组的求解，并提出对核函数的盯参数进行动态选取。

In this paper,we give a sufficient and necessary condition for the level surface s with respect to non-degenerate quadratic functions by the usage of the Hessian metric and of a transversal vector field.

本文利用Hessian度量和横截向量场，给出了非退化二次函数的水平曲面的一个充要条件。

Thunbergii trees were established, and the sun survivorship curves were drawn with field data. The results showed that in the three plots, the height and basal diameter growth of regenerated young P. thunbergii trees had exponential, linear, and quadratic functional relations with age and the age structure was of spindle, discrete, and pyramid types, respectively. Most of the regenerated young trees were distrbuted at 0.3-1.2 m from their nearest standing trees, and the individuals of the young trees decreased near to or far from the nearest standing trees. Inplots Ⅰ and Ⅲ, the expected average life of regenerated young P. thunbergii trees had a decreasing trend with their increasing age, and the survival number of the population also decreased with increasing population age. The survivorship craves of regenerated young P. thunbergii trees in the two plots approximated to the type of Deevey Ⅱ, indicating that the young P. thunbergii populations in the plots were at stable development stage. The population structure of regenerated young P. thunbergii trees in plot Ⅱ was lesser integral, suggesting that the population was of declining types being related to human disturbance, slope and other environmental factors.

结果表明：(1) 3个样地中幼龄植株高生长、基径生长与年龄均分别呈指数函数、直线和二次函数关系；(2) 3个样地黑松幼龄植株年龄结构存在着明显差异，分别表现为纺锤形、残缺型和金字塔型；(3)幼龄植株主要集中分布在距最近立木0.3~1.2m，离立木越近或越远幼龄植株均逐渐减少；(4)对样地Ⅰ和样地Ⅲ黑松幼龄植株生命表和存活曲线的分析表明，随年龄的增加，黑松幼龄植株生命期望值基本上呈递减趋势，黑松幼龄植株种群存活数也随着年龄的增加而降低；样地Ⅰ和样地Ⅲ黑松幼龄植株种群存活曲线近似于Deevey Ⅱ型，表明2个样地黑松幼龄植株种群处于稳定发展阶段；(5)样地Ⅱ幼龄植株种群结构很不完整，表明该种群属于衰退型，与人为干扰及坡度等有关。

Firstly, the sectional data from 27 companies in communications and transportation industry, which are listed before 1999, are linearly regressed. We find their capital structure and firm performance are irrelated significantly. Then the section data are quadricly regressed, but the result is also disillusionary, which indicates that the capital structure of listed companies has not the best range only with the sectional data from 1999 to 2003. Finally, in allusion to the problems in the securities market and illogicality of the capital structure, we put forward some methods to optimize the capital structure for listed companies from four facts.

文章首先对交通运输仓储行业1999年以前上市的27家公司的截面数据进行线性回归，发现在分析时段1999年至2003年，样本公司的净资产收益率和单位经济增加值与资产负债率之间线性不相关；然后文章又对该行业上市公司的截面数据进行二次函数回归，同样也没有得到令人满意的结果，这说明仅就1999年至2003年五年的截面数据而言，上市公司资本结构不存在最优区间；最后，文章对我国证券市场存在的问题以及该行业上市公司资本结构的不合理性提出了改进的设想，并从四个方面提出了优化我国上市公司资本结构的建议。

Analysis indicates that the adjacent channel power is a quadratic function of predistorter efficients. A new optimization method is given which uses the predicted ACP surface to obtain fast convergence and simulation results show that a 20dB reduction in the third IMD and a 10dB reduction in the quatic IMD are achievable.

得出结论为：分析表明功放输出的邻信道功率是预失真器系数的二次函数；利用了新的自适应算法即使用预测的ACP曲面以提供更快的收敛速度；仿真结果表明，3阶产物可获得20dB以上的改善，5阶产物可获得10dB以上的改善。

In order to simulated the characteristics of dynamic regression of saturated sandy soil under cyclic loading, the relation between the real hysteresis loop and the one indicated by the Masing rule is discussed based on a series of laboratory test, the modified proportion coefficient of hysteresis loop simulated by the Masing rule indicating by the stress history is determined, and then, it is modified by a quadratic function.

为了描述周期荷载作用下饱和砂土的动力衰减特性，试验研究了周期荷载条件下不同剪应变幅值时的实际滞回圈与由曼辛法则确定的滞回圈之间的关系，给出了由应变历史表示的用曼辛法则描述的滞回圈的比例修正系数，进而用二次函数进行了修正。

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。