查询词典 over again

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。

In this wonderful time, we all have to start all over again.

在这美好的时光里，我们的一切都将重新开始。

So if I have to do it all over again,then I will.

所以如果要我再做一次的话，我愿意

It'll be Iraq all over again....

这将是伊拉克的所有超过再次。。。。

He was spare, frugal, hardboiled, but he did over and over again what only the best writers can ever do at all.

这种风格不是属于哈梅特一个人的，也不是属于任何一个人的，这是美国语言（而且也不再是纯粹的美国语言了），我认为这种风格能够表达他本来不知道怎么表达或感到有必要表达的话。

In all thattime, he's vanquished monsters and megalomaniacs, but he's alsoshattered our preconceptions over and over again.

一直以来，他都战胜怪兽且狂妄自大，但是他同样一次又一次粉碎了我们诸多传统想法。

The African violet on your windowsill converts sunlight into a high-energy fuel over and over again in a process so complicated that scientists have yet to come close to duplicating it.

非洲紫罗兰在您的窗台上的阳光转换成为一个高能量的燃料超过和一次又一次的在一个过程复杂，科学家们还在后头接近架床叠屋。

Over and over again we see that demonstrated in the history of God's chosen people, Israel.

在以色列，神所拣选的民族身上，我们一再地看到了这点。

When I was traveling in Europe, I would draw some buildings over and over again. I drew Chartres ten different times.

在欧洲旅行时，我会一遍又一遍地画某个特定的建筑，仅沙特尔大教堂我就重复画过10次，且次次不同。

And he conned the grub of the cache and the grub of the Hudson Bay Company post over and over again.

他反反复复地念想着地窖里和海德森海湾公司码头上的食物。

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