多元的

First, we introduce and discuss the various methods of multivariate polynomial interpolation in the literature. Based on this study, we state multivariate Lagrange interpolation over again from algebraic geometry viewpoint:Given different interpolation nodes A1,A2 .....,An in the affine n-dimensional space Kn, and accordingly function values fi(i = 1,..., m), the question is how to find a polynomial p K[x1, x2,...,xn] satisfying the interpolation conditions:where X=(x1,X2,....,xn). Similarly with univariate problem, we have provedTheorem If the monomial ordering is given, a minimal ordering polynomial satisfying conditions (1) is uniquely exsisted.Such a polynomial can be computed by the Lagrange-Hermite interpolation algorithm introduced in chapter 2. Another statement for Lagrange interpolation problem is:Given monomials 1 ,2 ,.....,m from low degree to high one with respect to the ordering, some arbitrary values fi(i= 1,..., m), find a polynomial p, such thatIf there uniquely exists such an interpolation polynomial p{X, the interpolation problem is called properly posed.

文中首先对现有的多元多项式插值方法作了一个介绍和评述，在此基础上我们从代数几何观点重新讨论了多元Lagrange插值问题：给定n维仿射空间K~n中两两互异的点A_1，A_2，…，A_m，在结点A_i处给定函数值f_i(i=1，…，m)，构造多项式p∈K[X_1，X_2，…，X_n]，满足Lagrange插值条件：p=f_i，i=1，…，m (1)其中X=(X_1，X_2，…，X_n)，与一元情形相似地，本文证明了定理满足插值条件(1)的多项式存在，并且按"序"最低的多项式是唯一的，上述多项式可利用第二章介绍的Lagrange-Hermite插值算法求出，Lagrange插值另一种描述是：按序从低到高给定单项式ω_1，ω_2，…，ω_m，对任意给定的f_1，f_2，…，f_m，构造多项式p，满足插值条件：p=sum from i=1 to m=Ai=f_i，i=1，…，m (2)如果插值多项式p存在且唯一，则称插值问题适定。

The key technology of "fattyacid-oil process" in production of alkyd resin is the alcoholysis of oils. The alcoholysis of fattyacid-oil is the result of esterification of fatty acid and alloholysis of oils, of which the medium effect of esterified product of fatty acid and polyols will promote the alcoholysis of oils with polyols.

制造醇酸树脂的"脂肪酸－油法"的技术关键依然是油脂的醇解，整个脂肪酸－油脂体系的醇解是脂肪酸酯化与油脂醇解并行反应的结果，其中，脂肪酸与多元醇的酯化产物的介质效应有力地促进了油脂与多元醇的醇解反应。

NMath Stats contains a data table class with functions for computing descriptive statistics, such as mean, variance, standard deviation, percentile, median, quartiles, geometric mean, harmonic mean, RMS, kurtosis, skewness, and many more; PDF, CDF, inverse CDF, and random variable moments for a variety of probability distributions, including normal, Poisson, chi-square, gamma, beta, Student's t, F, binomial, and negative binomial; Combinatorial functions, such as factorial, log factorial, binomial coefficient, and log binomial; Multiple linear regression; Basic hypothesis tests, such as z-test, t-test, and F-test, with calculation of p-values, critical values, and confidence intervals; One-way and two-way analysis of variance and analysis of variance with repeated measures; Multivariate statistical analyses, including principal component analysis and hierarchical cluster analysis.

nmath统计包含一个数据表的阶层与职能计算描述性统计，如平均，方差，标准差，百分位，中位数， 25 ％，几何平均数，调和的意思是，有效值，峭度，偏度，还有更多的； PDF格式，民防部队，逆民防部队，并随机变量矩的各种概率分布，包括正常，泊松，卡方检定，伽玛，测试版，学生的吨，男，二项式，并负二项分布；组合的功能，例如阶乘，日志阶乘，二项式系数，并登入二项式；多元线性回归；基本假设测试，如的Z测试， t检验， F检验，计算p值，临界值，和置信区间；之一，双向和双方法方差分析和方差分析与反复的措施；多元统计分析，包括主成分分析和聚类分析。

A method for the preparation of microcellular elastomeric polyurethane foams from a reaction mixture comprising a polyisocyanate component containing at least 85% by weight of 4,4'-diphenylmethane diisocyanate or a variant thereof, a polyol composition comprising at least one polyoxyalkylene polyol having an average nominal hydroxyl functionality of from 2 to 6, an average hydroxyl equivalent weight of at least 1300 and an average oxyethylene content of between 50 and 85% by weight, water, a chain extender having an average hydroxyl equivalent weight of from 15 to 250 and optionally a crosslinking agent, the hardblock-content being more than 45% by weight.

本发明是有关一种制备微孔弹性聚氨基甲酸酯泡沫体的方法，其反应混合物包括：一种含至少85重量％的4，4′－二苯甲烷二异氰酸酯或其变体的聚异氰酸酯组分，一种多元醇组合物，其包含至少一种平均标称羟基官能度从2至6、平均羟基当量至少1300且平均氧乙烯含量介于50至85重量％之间的聚氧亚烷基多元醇，水，一种平均羟基当量为15至250之增链剂，以及视需要使用的交联剂，该硬性嵌段－含量（hardblock-content）大于45重量％。

Culture is such a complicate polytope so that people understand it differently. Pluralistic culture and discourse are reasonable and also the premium for creativity.

文化是一个复杂的多面体，不同的人对文化有不同的解读，多元文化、多元话语是合理的，这也是创新产生的前提。

The outstanding characteristic of PLS is that it can make the multiple linear regression analysis, the principal components analysis and the canonical correlation analysis combined. In the same arithmetic, it can implement modeling, predigesting the data structure and analyzing of the correlation between two gropes of variables at the same time. It brings huge advantage to the multiple linear regression analysis.

PLS的一个突出特点是将多元线性回归分析、变量的主成分分析和变量间的典型相关分析有机地结合起来，在一个算法下，同时实现了回归建模、数据结构简化和两组变量间的相关分析，给多元数据分析带来极大的便利。

Through improving the geometric parameters of the cemented carbide bit such as the rake angle of main cutting edge,outer fringe cusp and chis...

通过对钻削加工用硬质合金钻头的几何参数进行改进，主要是对主切削刃前角、外缘转点以及横刃进行改进，达到降低钻削功率的目的，同时，利用多元线性回归理论，得出基于实验数据的多元回归钻削功率的数学模型，从理论上证明此次刀具改进的有效性。

Based on the facts and reasons of Chint Group Corporation are: Schneider Electric Low Voltage Co., Ltd. produced and sold 5 items song limit's rocker-shaped mini-circuit breaker products,which violated the High Breaking Miniature Circuit Breaker of Chint Group Corporation's the utility model patents numbered ZL97248479.5. From August 2, 2004 to July 31, 2006, Schneider Electric Low Voltage Co., Ltd. produced and saled infringing products more than 880 million yuan. Through the product margins that it reported to the department of commerce and tax , the Schneider Electric Low Voltage Co., Ltd. Had earned more than 334.8 million yuan.

正泰集团的事实与理由是：施耐德电气低压有限公司生产并销售的5款带曲形限位器的摇臂的小型断路器产品，侵犯了正泰集团一项专利号为 ZL97248479.5&高分断小型断路器&的实用新型专利，2004年8月2日至2006年7月31日，施耐德电气低压有限公司共生产销售侵权产品价值8.8亿多元，通过其上报工商、税务部门的产品利润率计算，施耐德电气低压有限公司获利3.348亿多元。

Under this background, directed by Marxism—Leninism, Mao Tse—Tung thought, Deng Xiaoping"s theory and Chairman Jiang"s important thought,I wrote this article with document analytical method, investigative study method, comparative analysis and so on. I have been insisting on the principle of combining theory with practice, centralising functional analysis of politics and factors that influence the effect of mental and moral education. And I mainly analyse the related factors that restrain the effect of mental and moral education. Furthermore, according to the practice of teaching in school, I gave the measures to strengthen the entire effect of mental and moral education.

在文化多元、价值多元背景下，本文以马克思列宁主义，毛泽东思想，邓小平理论，&三个代表&重要思想和科学发展观为指导，运用文献分析法、理论研究法、经验研究法、调查研究法和比较分析法等研究方法，坚持理论联系实际的原则，以&高中思想政治课的德育功能分析，德育'低音频'效果检视，影响高中思想政治课的德育效果的诸因素分析&为中心，着重分析制约高中思想政治课整体德育效果的相关因素，并在此基础上，联系学校教育教学实际，提出了增强高中思想政治课整体德育效果的对策与路径。

But when a rectangular continuous data set appears to have a longer tailed than normal distribution or it contains some values that are influential on statistical inference with normal distribution, the multivariate t distribution becomes useful for multiple imputations as an alternative to the multivariate normal distribution.

在多重插补法的基础上，当一个矩形连续数据集看起来有一个比正态分布还长的尾巴，或者是它包含了一些对正态分布的统计推断有影响的数据，多元t分布作为多元正态分布的替代分布，对于多重插补来说变的很有用了。

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。