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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。

By the use of the component sandstone electric conductivity model, the effect of the pore structure characteristic parameter to cementation exponent m and saturation exponent n in the Archie formula were studied. It can be found the cementation exponent m mainly reflects the pore space size and its sizes distribution. The m is bigger, the pore space is bigger, the throat is simpler, and the reservoir is better.

通过致密砂岩电导模型分析研究致密砂岩孔隙结构特征参数对Archie公式中的胶结指数m和饱和度指数n的影响,发现岩石胶结指数m主要是岩石孔隙空间大小及其大小分布的表征,m值越大的岩石其孔隙储集空间越大,孔喉越简单,储集性能越好;反之,m值越小,岩石储集性能越差。

Suppose C is a Graph with k loops andf: G 梸- G is a continuous map with at least a peri- odic point. We prove the following three conditions are equivalent:(1) f is equicontinuous;(2) One of the following End + 2k + 1 conditions holds: in FJm.~0(E~+2L!= flJ1,m = l,2,挃,End J=1 + 2k; 1 0 = flf is a ioop on Gandf I~:0?- 0 is conjugate j=1 to a rational rotation;(3) One of the following End + 2k + 1 conditions holds: k m Lfl.m/~oE~(G+2i!~ is uniformly convergent, m = 1,2,,End+2k; n There is a poistive integer number n,~~~ is uniformly convergent.

假设G是含有k个圈的图,f是G到自身上的连续映射,并且至少有一个周期点,我们证明了下列三条陈述是等价的:(1)f是等度连续的;(2)下列End+2k+1个条件之一成立: m)F l)O=是G的一个圈,且fl_o:O→O共轭于一个有理旋转;(3)下列End+2k+1个条件之一成立: m)是一致收敛的,m=1,2,…,End+2k; l)存在某个正整数n,是一致收敛的。

Four types of arrays of single carbon nanotubes, with field emitter diameters of 1μm, 0.6μm, 0.4μm and 0.2μm, were fabricated, respectively, by combining conventional ultraviolet lithography and the recently-developed technique of "aperture reduction via varying glancing angle".

通过普通的紫外光刻工艺,结合"变倾角缩口"新技术,研制了不同发射单元尺寸的碳纳米管阵列阴极。扫瞄电镜分析表明,随着缩口尺寸的依次减小(从0.6μm到0.4μm,最后到0.2μm),发射单元内CNTs的根数也不断减少。

The concentrations of zinc nitrate hexahydrate are 0.01 M, 0.025 M, 0.05 M, 0.1 M, 0.2 M, and 0.4 M, respectively.

硝酸锌六水合物的体积浓度分别为0.01M,0.025M,0.05M,0.1M,0.2M 和0.4 M。

An MHP based thermal vacuum sensor was designed in the supporting beams of 65 μm long and 21 μm wide, and the gas gap below micro hotplate of 0.5 μm. The micro sensor was fabricated successfully with surface micromachining technology.

设计了一种边长为93μm、四臂支撑的方形微热板结构的电阻真空传感器,支撑桥长65μm、宽21μm,微热板与衬底之间的气隙高度为0.5μm;采用表面微机械加工技术成功实现了该传感器的加工。

Both the infimum Vm of the Volume Vof M and the necessary and sufficient conditions of "V=Vm" are obtained under 2 cases of minimal M and pseudoumbilical M.

研究了复射影空间CP4中共形平坦的正曲率全实子流形M,分别在M极小与M 伪脐2种情况下,得到M的体积V的下确界Vm和达到下确界的充要条件。

Through a comparative study of ~(99)Tc~m-DTPA and ~(99)Tc~m-OCT SPECT orbital imaging,evaluated the clinic significance of two imaging in estimating activity of TAO.The aim of this study was to develop a new method:simple,rapid and costefficient method for staging patients with TAO.

本研究采用~(99)Tc~m-二亚乙基三胺五乙酸~(99Tc~m-diethylene tri-aminepentaacetic acid,~(99)Tc~m-DTPA进行眼眶显像并与~(99)Tc~m-奥曲肽~(99Tc~m-octreotide,~(99)Tc~m-OCT眼眶显像进行比较,研究其在反映TAO患者眶周炎性程度的价值,旨在探索一种新眼眶显像方法:既经济又迅速,显像效果稳定又可靠。

Based on Pierre Becker's viewpoint of optimum m(active SiO2)/m=0.53, and combined with the production of 28% P2O5 phosphoric acid with Yunnan and Anning phosphate rock in the plant, the conclusion that the range of optimum m(active SiO2)/m covers 0.53~0.63 is drawn .

分析磷矿中不溶性SiO2和可溶性SiO2(即活性SiO2)对磷酸,磷铵生产的影响,根据皮埃尔贝凯提出磷矿中m(活性SiO2)/m=0.53较为合适的观点,结合该厂使用云南矿,安宁矿生产28% P2O5稀磷酸时,SiO2的分配情况,计算出m(活性SiO2)/m的范围是0.53~0.63。

Optimum conditions are as follows: DMF is used as solvent, compound quaternary ammonium salt as catalyst, n(p-nitrochloro benzene):n=1: 1.2, m:m(p-nitrochloro benzene)=4%, m:m(p-nitrochloro benzene)1:1, and reacted under 155~160℃ for 18 h; reduction reaction is carried out in methanol with Raney nickel, which is used as catalyst; the raw product is added an antioxidant, and distilled simply under reduced pressure to obtain 4-fluoroaniline with excellence quality, purity is over 99.5%, total yield is 89.3%.

实验结果表明,氟化反应的最佳条件为:二甲基甲酰胺为溶剂、复合季铵盐为催化剂,n:n=1:1.2,m(催化剂:m=4%,m:m=1:1,于155~160℃下反应18h;还原反应在甲醇中进行,以阮内镍为催化剂;粗产品加入抗氧剂,减压条件下简单蒸馏得高品位的对氟苯胺。

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And I'm Telling You I'm Not Going
Say It Loud - I'm Black And I'm Proud
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Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气,收缩臀部肌肉;拱起身体,尽量抬起头来,右腿伸直朝向天花板(膝微屈,以避免肌肉紧张)。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化,但却比去年同期高8%。

However, to get a true quote, you will need to provide detailed personal and financial information.

然而,要让一个真正的引用,你需要提供详细的个人和财务信息。