二次函数

At the same time, we prove that the best linear unbiased prediction of a linear predictable variable Qy and the best linear unbiased prediction βn=(X"sV-1Xs)-1 X"sVs-1ys of regression coefficients of the finite populations βn=(X"V-1X)-1X"V-1y are admissible under matrix loss function and in the class of the linear predictions and the class that contains all predictions, and under quadratic loss function in the class of the linear predictions.

在线性预测类和一切预测类中是可容许预测，而在二次损失函数下其在线性预测类中是可容许预测。

The paper is devoted to the quartic invariant algebraic curves in quadratic system.

本文在给定参数满足一定的条件下，研究了一类二次系统的四次不变代数曲线系统平衡点的稳定性态，并运用Dulac函数法给出了该系统不存在极限环的充分条件，这一研究在同类问题中具有一定的拓展性。

Application of this new frequency warping method in ALID

将这种新的频率弯折方法应用于自动语言辨识研究中，对比实验表明，二次弯折函数的效果

This method can guarantee continuity and one-order smoothness of the estimated failure rate curve.

基本思路是：对那些寿终时刻，分别用单位时间内的失效频率做为失效率的估计，然后用二次样条函数来拟合出失效率曲线，这种处理可保证失效率曲线的连续性与一次光滑。

A method of time delay estimation by two times spectral analysis, where the time delay is the time interval between peaks of spectrum of the cross power spectral density, is proposed in the paper. It can be used to estimate time delay of not only single target but also multi-target without unwrap.

本文提出了两次谱分析时延估计方法，即将互功率谱函数再次进行谱估计，二次谱峰值位置间距即为时延估计，这种方法既能够估计单目标时延，又能够估计多目标时延，并且不用相位解绕。

Firstly, the author establish the functions of stability on the basis of the spline function method ,according to the theory of geometrical nonlinear and the theory of stability, educe the stability equation of structure based on variational principle, then carry through the flexuosity analysis of CFST arch.The big distortion geometrical nonlinear was considered by the stability equation,the author simplified the problem of geometrical nonlinear through ignored quadratic term and reserve the simple term, at last boiled down to solve the linear stability equation of eigenvalue .

利用样条函数方法、根据几何非线性变形理论和结构稳定性理论，先建立起结构稳定的泛函，再由变分原理导出结构的稳定方程，进行钢管混凝土拱屈曲分析；本文所建立的稳定方程考虑了几何非线性的大变形效应，通过忽略几何非线性的二次项，保留一次项，将几何非线性问题简化，最后归结为求解线性稳定问题的特征值稳定方程，建立了结构非线性静力稳定性问题的新算法及失稳类型判别准则。

The first part discusses about the effects of the five factors:temperature,relative air moisture,rate of frass sifting,density of larvae,fodder water percentage to growth speed and survival rate of older mealworm (Tenebrio molitor L.) larvae through rotational composite design of quadratic regression. Two models were established to describe the effects of the five factors. The models showed that percentage of fodder water is the major factor that has effect on the growing speed of T. molitor larvae,and fodder water is the major factor on death rate. The models also show that temperature on growth speed,temperature and fodder have important effects on death rate,and the significant test showed they have significant difference on 1% or 5% level. From the two models,by frequency analysis,we can get the optimizing rearing condition,in which the mealworm larvae overweight 10% per day,temperature is 25-26 ,frass sifting rate is once 2-4 days,density of larvae is 0.61-0.79 g/cm2,fodder water is 33.27%-39.71%. And the rearing condition,in which total death rate of T.

第一部分：采用五因素二次正交旋转组合设计，以黄粉虫幼虫饲养过程中饲养温度(X_1)相对湿度(X_2)、虫粪筛除频率(X_3)、饲养密度(X_4)以及饲料含水量(X_5)五因素为参试因素，考查它们对黄粉虫高龄幼虫的生长及存活的影响，建立了以黄粉虫幼虫增重率及死亡率为目标函数的回归模型，并进行了简化： Y_增=127.5079+18.6559x_5+2.7894x_3x_4-2.3854x_3x_5-3.0594x_1~2+1.8241x_3~2-3.8559x_5~2 Y_死=1.7459+0.4108x_1+0.0975x_2+0.9025x_4+0.3442x_5+0.0834x_1~2+0.3060x_4~2-0.2623x_5~2 分析结果表明：影响黄粉虫幼虫生长后期增重及死亡的主要因素分别为饲料含水量和饲养密度；饲料含水量和温度对黄粉虫增重有着重要的影响，饲养密度、温度、饲料含水量对黄粉虫的死亡有着重要的影响，其影响均达1％或5％显著水平；黄粉虫幼虫后期日增重率大于10％的饲养条件为：温度26～27℃、筛粪频率2～4天／次、饲养密度0.61～0.79g／cm~2、饲料含水量33.27～39.71％。

Through Hilbert transform, a signal's plane trace can be get. There are two frequencies in the tested signal, so the signal's plane trace may be looked as the track of the out pole's end when two poles rotate around parallel axles. Using the knowledge of motion synthesis in theory mechanics, a formula to describing the change of plane trace's step length and angle for two-frequency be get. So we may prolongate the tested signal's plane trace from the echo's initial arriving moment, and get a certain length of the signal's prolongation.

通过Hilbert变换可得到测试信号的平面迹线，测试信号中只含有两个频率成分，视为双频信号，双频信号的平面迹线相当于两连杆绕平行轴转动时外杆杆端迹线，利用理论力学中运动合成和瞬心知识，推导出双频信号平面迹线步长平方满足余弦线性复合函数，而迹线转角可视为线性变化，据此可对回波到来之前的测试信号平面迹线作延长，得到一定长度的信号延展段，信号延展段与实测段作差可得到一次、二次回波的第一个波峰值。

In order to design optimum nozzle for air-air missile solid rocket motor, the mass model of solid rocket motor, the nozzle specifice impulse model of solid rocket motor and the objective function are established. Five different type of nozzles are choosen lor calculation: Conical, parabolidal,two different arcs,quadiatic polynominal and cubic polynominal.

以两种空-空导弹固体火箭发动机喷管作为算例，为此，建立固体火箭发动机的质量模型，喷管的质量比冲模型和目标函数模型，选择五种喷管扩散段内型面：锥形喷管，抛物线喷管，双圆弧喷管，二次多项式喷管和三次多项式喷管，进行优化设计，利用优化理论，成功地完成了五个设计变量的优化问题。

Vertical NAD distributions could be well-fitted by β function and the two-dimennsional NAD distribution by the trend surface equation of relative crown height and relative crown radius.

NAD的水平和垂直分布均可用β分布函数表达，而相对冠高和冠径的二次趋势面表达式可很好地描述NAD二维空间分布。

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。