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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。

Let F be a bijection from set A to set B. Denote M={a Aa F}. If in a theory that ME B is legitimate, then the question m E M?

令F是从集合A到集合B的双射，记M＝aAaF，如果在某个理论中M B是合法的则问题m M？

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。

After addition of surface active agent into sprinkling solution, for particle of 1 μm size, the filtration rate has increased from 40% to 70% approximately under the condition of head wind velocity of 1.5 m/s and spr4nkling density of 2.36 kg/(m^2s), and the filtration rate has increased from 30% to 60% approximately under the condition of head wind velocity of 2.8 m/s and sprinkling density of 2.36 kg/(m^2s).

在喷淋溶液中添加表面活性剂后，对于粒径为1 μm的尘粒，在迎面风速为1.5 m/s、淋水密度为2.36 kg/的条件下，过滤效率由40%左右上升至70%左右。在迎面风速为2.8 m/s、淋水密度为2.36 kg/条件下，过滤效率由30%左右上升至60%左右。

Bone strength, determined using quantitative ultrasound measurement of bone speed of sound at the middle left tibial shaft, decreased significantly in the control group from 2,892 30 m/sec at baseline to 2,799 26 m/sec at four weeks. However, bone SOS of the exercise group remained stable (2,825 32 m/sec at baseline and 2,827 26 m/sec at four weeks). Despite improvement in bone SOS with exercise, there were no accompanying changes in markers of bone formation and resorption.

研究使用超音波测量骨骼声波速度来数量化评估骨骼强度，测量的位置是婴儿的中间左侧胫骨干，研究显示，对照组的婴儿显著减少了骨骼强度，从基线2，892 ± 30 m/sec降到四周时的2，799 ± 26 m/sec，但是锻炼组的骨骼SOS维持稳定(基线：2，825 ± 32 m/sec，四周：2，827 ± 26 m/sec)，虽然锻炼可以改善骨骼SOS，但是骨骼形成和再吸收指标并没有跟著改变。

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。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失