查询词典 quadratic sum

In this note, we prove a congruence relation on real quadratic fields which relates class number and certain character sum.

本文证明了关于实二次域的类数和某类特征和的同余式，同时给出某类实二次域的类数可除性的一个判别法则。

Then we study that quadratic Lie colour algebra also can be decomposed to direct sum of ideas who contains no nontrivial non-degenerate idea of L . And the decomposition is unique except the order of the ideas .

然后给出了二次李color代数也可以分解为不包含非平凡的非退化的color理想的直和，而且分解除理想次序外是唯一的。

This article takes calibration data of assorted pressure gauge and jack of Qingfeng Bridge in Ningbo for example. According to that the quadratic sum of deviation in actual value and trend value has the minimum and extremal condition of the function,that is least square method.

本文以宁波市庆丰桥配套的千斤顶和压力表的标定数据为例，以实际值与趋势值的偏差的平方和最小为依据，根据函数存在的极值条件，求出线性方程，此为最小二乘法。

This dissertation investigates the construction of pseudo-random sequences (pseudo-random numbers) from elliptic curves and mainly analyzes their cryptographic properties by using exponential sums over rational points along elliptic curves. The main results are as follows:(1) The uniform distribution of the elliptic curve linear congruential generator is discussed and the lower bound of its nonlinear complexity is given.(2) Two large families of binary sequences are constructed from elliptic curves. The well distribution measure and the correlation measure of order k of the resulting sequences are studied. The results indicate that they are "good" binary sequences which give a positive answer to a conjecture proposed by Goubin et al.(3) A kind of binary sequences from an elliptic curve and its twisted curves over a prime field F_p. The length of the sequences is 4p. The "1" and "0" occur almost the same times. The linear complexity is at least one-fourth the period.(4) The exponential sums over rational points along elliptic curves over ring Z_ are estimated and are used to estimate the well distribution measure and the correlation measure of order k of a family of binary sequences from elliptic curves over ring Z_.(5) The correlation of the elliptic curve power number generator is given. It is proved that the sequences produced by the elliptic curve quadratic generator are asymptotically uniformly distributed.(6) The uniform distribution of the elliptic curve subset sum generator is considered.(7) We apply the linear feedback shift register over elliptic curves to produce sequences with long periods. The distribution and the linear complexity of the resulting sequences are also considered.

本文研究利用椭圆曲线构造的伪随机序列，主要利用有限域上椭圆曲线有理点群的指数和估计讨论椭圆曲线序列的密码性质——分布、相关性、线性复杂度等，得到如下主要结果：(1)系统讨论椭圆曲线-线性同余序列的一致分布性质，即该类序列是渐近一致分布的，并给出了它的非线性复杂度下界；(2)讨论两类由椭圆曲线构造的二元序列的"良性"分布与高阶相关性(correlation of order κ)，这两类序列具有"优"的密码性质，也正面回答了Goubin等提出的公开问题；(3)利用椭圆曲线及其挠曲线构造一类二元序列，其周期为4p(其中椭圆曲线定义在有限域F_p上)，0-1分布基本平衡，线性复杂度至少为周期的四分之一；(4)讨论了剩余类环Z_上的椭圆曲线的有理点的分布估计，并用于分析一类由剩余类环Z_上椭圆曲线构造的二元序列的伪随机性；(5)讨论椭圆曲线-幂生成器序列的相关性及椭圆曲线-二次生成器序列的一致分布；(6)讨论椭圆曲线-子集和序列的一致分布；(7)讨论椭圆曲线上的线性反馈移位寄存器序列的分布，线性复杂度等性质。

It is antinomy to analysis factor effects according to first and second order term index of quadratic polynomial,so this paper put forward a new method to explain and evaluate factor effect by F test based on partial regression sum of squares.

传统的二次多项式回归方程在依系数正负、大小解释各因子效应时，常出现一次项与二次项结果相互矛盾的情形，而一般的SVR模型又不具解释性；本文从偏回归分析定义出发，建立了基于SVR以F测验解释、评价各因子相对重要性的方法。

If A is a symmetric positive definite matrix, then the quadratic form x~ TAx can be written as a sum of squares. Equivalently, A is a sum of rank one matrices VV~T.

若A是对称正定矩阵，则二次型x~ TAx 能写成平方项的和，即A是秩为1的矩阵VV~T的和。

Independent variables are diameter class, relative diameter, number of stems per hectare, basal area per hectare, quadratic mean diameter, degree of closenessand sum of squared diameter of larger trees than th...

自变量有径阶、相对直径、每公顷株数、每公顷断面积、平方平均直径、郁闭度和大于所估径阶的林木直径平方和。

It is concluded that the order number determines the precision of temperature extrapolation method, and it can be controlled when the quadratic sum of residual error between the opposite solving and the original measuring is minimum. For the specific surface temperature curve, it is derived with the temperature on the site 0.0129cm.

分析结果表明，阶数决定著外推测试的结果以及结果的精度，阶数选取不当甚至会出现错误的外推测试结果，但采用反面求解求得的拟合曲线与实测得的原值具有最小的剩余误差平方和，可以有效地抑制其影响。

Based on the order number 10, the quadratic sum of residual error is 533%, the extrapolating result is wrong. But with the order number 9, the quadratic sum of residual error is 0.673%, the result is right

对於表面特定温度为θ(0， t)的曲线，测得其0.0129cm处的温度变化规律反推，选取阶数为10时，剩余误差平方和为533%，外推结果错误，选取阶数为9时，剩余误差平方和为0.673%，外推结果正确。

This paper mainly aims at analysis of gastrointestinal mucosa gene expression profiles of paired samples about spleen deficiency of chronic superficial gastritis and normal people group, and spleen deficiency of chronic superficial gastritis and piwei damp-heat group. 9 and 12 different genes are selected by using Wilcoxon signed rank test, the ratio of quadratic sum between groups and within groups and distance-related analysis in the process of feature selection.

通过对慢性浅表性胃炎脾虚证与正常人、慢性浅表性胃炎脾虚证与脾胃湿热证两组胃肠粘膜配对样本的基因表达谱进行分析，在特征提取阶段分别利用Wilcoxon符号秩检验、组间和组内平方和比率、基于相关距离的冗余分析方法，分别得到9个和12个差异基因。

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。