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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。

It's a long long journey till i know where i'm supposed to be it's a long long journey i don't know if i can believe when shadows fall and block my eyes i am lost and know that i must hide it's a long long journey till i find my way home to you many days i've spent drifting on through empty shores wondering what's my purpose wondering how to make me strong i know i will falter i know i will cry i know you'll be standing by my side it's a long long journey and i need to be close to you sometimes it feels no one understands i don't even know why i do the things i do when pride builds me up till i can't see my soul will you break down these walls and pull me through cause it's a long long journey till i feel that i am worth the price you paid for me on calvary beneath those stormy skies when satan mocks and friends turn to foes it feel like everything is out to make me lose control coze it's a long long journey till i find my way home to you..

to you 这是一次长的长的旅途我知道何处我应该是这是一次长的长的旅途我不知道如果我能相信当阴影落和阻拦我的眼睛我失去和知道，我必须掩藏这是一次长的长的旅途我寻找我的道路家庭对您许多天我花费了漂移通过空的岸想知道什么是我的目的想知道怎么使我加强我知道我将蹒跚而行我知道我将哭泣我知道您坚持我的边这是一次长的长的旅途并且我需要是紧挨您有时它感觉没人了解我甚而不知道为什么我做我的事当自豪感修造我我不能看我的灵魂意志您划分这些墙壁和拉扯我通过起因这是一次长的长的旅途我认为我是价值价格您支付了我在受难像在那些风雨如磐的天空之下当恶魔嘲笑并且朋友转向仇敌这摸起来象一切是使我丢失控制聊天这是一次长的长的旅途我寻找我的道路家庭对您。。。

Journey 歌手:张韶涵专辑:over the rainbow 曲:corrinne may 词:corrinne may it's a long long journey till i know where i'm supposed to be it's a long long journey i don't know if i can believe when shadows fall and block my eyes i am lost and know that i must hide it's a long long journey till i find my way home to you many days i've spent drifting on through empty shores wondering what's my purpose wondering how to make me strong i know i will falter i know i will cry i know you'll be standing by my side it's a long long journey and i need to be close to you sometimes it feels no one understands i don't even know why i do the things i do when pride builds me up till i can't see my soul will you break down these walls and pull me through cause it's a long long journey till i feel that i am worth the price you paid for me on calvary beneath those stormy skies when satan mocks and friends turn to foes it feel like everything is out to make me lose control coze it's a long long journey till i find my way home to you..

to you 这是一段很长很长的旅程直到我明白那里是我认为的去处这是一段很长很长的旅程而我不知道是否能相信当阴影落下阻挡了我的视线我失败了并且明白我必须躲藏这是一段很长很长的旅程直到我找到回家的路是走向你我曾用尽了许多日子来回漂流在无人的岸边疑惑著我的目的是什么疑惑著如何使自己更坚强我知道我将会变的脆弱我将会哭泣我知道你将会站在我的身边这是一段很长很长的旅程而我需要更向你靠近有时候这种感觉没有人能了解我不曾知道为何我完成了那件做过的事当骄傲像高墙般将我拱起直到我看不到自己的灵魂你是否会拉著我穿越过这高墙因为这是一段很长很长的旅程直到我觉得那代价是值得的你给了我基督受难像在这暴风雪的影响下当人们魔鬼般的嘲弄一个个变成敌人感觉就像每件事我因来不及而失去控制这是一段很长很长的旅程直到我找到回家的路是走向你走向你

It was a thirty eight, the poor mans machete Held it in my hand, thinking damn man it's heavier then expected, Wedged it behind my belt buckle Knowin that its evil, even thought that I could smell trouble The extra strength felt weak, But over there on the corner saw what I needed and proceeded to cross the Street Put the heat in the mail box to loose it Figured that the post office knows whats best to do with it Mosey down the road thinkin' bout the old I use to roam this zone with two feet of snow Right here, this use to be a record shop I've gotten love, I've gotten drunk, I've gotten beat up in that parking lot I've had my lake street pride for three decades These alleyways, and these streetlights have seen my best days Before I was a germ learnin how to misbehave, All the way to the grave, south side is my resting place Took a right on Lindale I'm getting near But then the road became empty and the people disappear'd The clowds ran away, opened up the sky And one by one I watched every constellation die And there I was frozen, standin in my backyard Face to face, eye to eye, starin at the last star I should've known, walked all the way home To find that she wasn't here, I'm still all alone

It是三十八，贫困者大砍刀 Held它在我的手，想法的人它是更重然后期望， Wedged它在我的皮带扣之后它邪恶，甚而认为的Knowin我可能嗅到麻烦感到的The额外力量微弱， But在角落在那看了什么我需要并且继续横渡 Street Put在疏松它的邮箱的热邮局知道的Figured什么是最佳做与它 Mosey击倒路thinkin回合老 I用途漫游有雪的二英尺的这个区域 Right这里，这个用途是记录商店 I在那停车场得到爱，我得到了喝，我得到了打了 I有我的湖街道自豪感三十年 These巷道和这些街灯看了我的最佳的几天 Before我是毒菌learnin如何行为不端，一直对严重，南侧是我的休息处 Took在我得到近的Lindale的权利另一方面But路成为了空和人disappear'd The clowds跑掉了，开放天空 And我逐个观看每个星座死那里And我在我的后院结冰了，替换者面对面，眼睛注视的，在最后星的starin I应该知道，一直走在家 To发现她没有在这里，我仍然是所有单独的

But how to use those facts in new situations, how to observe the world penetratingly, how to explore and discover independently, how to approach unfamiliar types of problems, how to analyse rigorously and play creatively, how to organize themselves and others to achieve their goals? These things, the heart of high-quality Western education, are still largely slighted by schools in China -- and they are precisely the capacities that will be vital to China's economic and cultural development in 20 or 30 years.

可是，怎样在新的情况下去使用那些知识，怎样深入地观察这个世界，怎样独立地探索和发现，怎样去解决不熟悉的问题，怎样严谨地分析问题继而能够玩出富有创造性的成果，怎样把自己和别人组织起来去实现共同的目标，这些问题是高质量的西方教育的核心，却仍然在很大程度上被中国的学校所忽视———而对于二三十年后中国经济和文化的发展，这些能力恰恰是至关重要的。

I've been busy traveling here and there and doing lots of thinking about my career path as well as how to handle all the issues that's bombarding me recently!

我也花了不少时间思考我的career还有怎么adapt to我身边发生的事情！

I've been busy traveling here and there and doing lots of thinking about my career path as well as how to handle all the issues that's bombarding me recently!

我也花了不少时间思考我的career还有怎麼adapt to我身边发生的事情！

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。

There's no need to worry, for your husband knows how to fob the gang off.

把……打发走 to fob off 不用着急，你丈夫知道怎么样把那帮人打发走。

There's no need to worry, for your husband knows how to fob the gang off.

打发走 to fob off 不用着急，你丈夫知道怎么样把那帮人打发走。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。