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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。

The test was conducted in the following manner; MM-164 liver carcinoma (1 x 10 [6] cells) was injected to left rear footpad of mice and the footpad was cut after 48 hours. Then, normal feed was given to the control group, 20% Maitake powder was given to group and 1 mg/Kg of D-fraction was intraperitoneally given for 70 times to group with normal food. All three groups were bred for another 30 days, and the number of tumor focus metastasized in the liver was counted by microscope.

我们进行了以下实验：MM-164肝癌细胞（1*106）注射到小鼠的左后足，在48小时后，截掉小鼠的左后足，组A：正常饮食作为对照组，组B：每天灌喂20%的灰树花粉，组C：腹腔注射1mg/Kg.bw的灰树花D-组分，三十天后处死，用显微镜检测肝部转移位点，结果见表5。

The test was conducted in the following manner; MM-164 liver carcinoma (1 x 10 [6] cells) was injected to left rear footpad of mice and the footpad was cut after 48 hours. Then, normal feed was given to the control group, 20% Maitake powder was given to group and 1 mg/Kg of D-fraction was intraperitoneally given for 70 times to group with normal food. All three growere bred for another 30 days, and the number of tumor focus metastasized in the liver was counted by microscope.

舞茸能够抑制转移吗，我们进行了以下实验：MM-164肝癌细胞（1*106）注射到小鼠的左后足，在48小时后，截掉小鼠的左后足，组A：正常饮食作为对照组，组B：每天灌喂20%的舞茸粉，组C：腹腔注射 1mg/Kg.bw的舞茸D-组分，三十天后处死，用显微镜检测肝部转移位点，结果见表5。

Given to guide the use of the word The copolymer are epoxy, with the 9M ammonia at 40 ℃ reaction 3H, on into amino resin.

利用given为引导词）该共聚物还有环氧基，与9M氨水在40℃反应3H，就转化为氨基树脂。

Given to guide the use of the word Known residence time distribution and the first order reaction rate constant, non-ideal flow reactor (non-ideal flow reactor) will be able to determine the characteristics of the decision.

利用given为引导词）已知停留时间分布和一级反应的速度常数，则非理想流动反应器（non-ideal flow reactor）的特性就能确定的决定。

Given two bridge-builders, a man and a woman, given a certain bridge to be built, and given as always the unchangeable laws of mechanics in accordance with which this special bridge and all other bridges must be built, it is simply inconceivable that the preliminary instruction given to the two bridge-builders should differ in quantity, quality, or method of presentation because while the bridge is building one will wear knickerbockers and the other a rainy-day skirt.

假定分别有男女两位桥梁建造者，要去建造指定的一座桥，在建造这一独特的桥及其它一般的桥的力学规律总是不变的情况下，简直不可想象，男女建造者所受的基本教育应有所不同；更不可想象，只是因为在施工时，一个穿灯笼裤，另一个穿防雨裙，而必须让他们在质量、数量及教学方法上接受不同的教育。

The main work and innovation1 In general , a image compression method has different effect to different image . Some are fit for image which has much high frequency . Some are fit for image which has much low frequency .This paper analysis the applicability of fractal algorithm . In this dissertation , an improved algorithum is given . The basic algorithum without eight change and the joint use of quantitative coding , The compression ratio and PSNR can be adjusted , and it can get more quickly speed of coding .2 To a group of exact fractal code , the decoding image can be any resolution .With this characteristic ,choose the proper domain block and range block,this paper get an algorithum which can get higher decoding PSNR and speed than the basic fractal algorithum.3 Give a new method to calculate the scale factor . The calculation of basic algorithum is complex and enormous . The factor of scale is an important variable of the basic algorithm. Now there are two methods to calculate the factor of scale .A new method was given to calculate the factor of scale. The calculation load and complexity are reduced by the new method. Compared with the basic algorithm , the method can reduce coding time.4 The basic fractal algorithum is based on the Collage theorem and contraction mapping theorem . A mathematic model based on basic fractal algorithum is given .

本文的主要工作及创新点主要包括以下几点：1一般情况下，一种图像压缩的方法对不同特点的图像，压缩效果会有所不同，本文利用分形压缩编码对不同特点的图像进行编码，分析了分形编码对不同图像的编码适用性，利用去掉8种变换的分形编码算法与简单的均匀量化编码方案相结合，得到了一种可以调节压缩比与解码质量的分形编码方案，该提高编码速度6倍以上。2分形编码的特点之一是分形解码的分辨率无关性，即对于一组分形编码可以将其解码到任意分辨率下，本文利用分形编码的这一特点，结合不同的量化编码方案，选择合适的定义域块与值域块及适当的编解码分辨率，得到了一种提高解码质量，编码速度提高12倍以上的加速算法。3比例因子是基本分形算法中的一个重要变量，目前有两种计算比例因子的方法，文中给出了一种新的求比例因子的方法，该方法简化了求比例因子的计算，从整体上减小了基本分形算法的计算量，简化了算法4分形压缩的数学基础是不动点定理与拼贴定理，本文根据基本的自动分形编码方法，建立数学模型对其进行推导，得到了用普通数学的极限理论解释分形编码的数学表达式，从而对由基本分形编码得到的解码图像中的像素点的值给出了确定的表达式。

Had been doing have/has been doing 一般进行完成过去 was/were given was/were being given had been given 现在 am/is/are given am/is/are being given have/has been given /将来 will/shall be given / will/shall have been given /过去将来 should/would be given / should/would have been given

不定式：不定式：二不定式常考的考点：不定式常考的考点： 1不定式做定语不定式做定语----将要发生将要发生 2不定式做状语----目的不定式做状语目的 3不定式充当名词功能不定式充当名词功能---To see is to believe。

I cannot explain it to you because you were never given that choice; it was never given to you to remember what happened, five hundred years ago, it was never given to you to replace your limiters, it wasn't even given to you to choose to leave the mountain and follow Sanzo. YtmrRDQs

我无法向你解释，因为你从未被给予这样的选择权；从未给过你机会去记住曾发生过什么，五百年前的事情；从未给过你机会戴回你的妖力制御装置；甚至都从未给过你机会去选择离开山上，跟随三藏。

Priority to start will be given to horses with a higher rating at time of Entry.

优先出赛资格 Priority to start 报名时评分较高之马匹将可获优先出赛。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。