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The eigenvalues of circulant matrices compose of the discrete Fourier transform of the first line, on the contrary, the elements of the first line can recovered from the Fourier inversion formula, all circulant matrices have the same eigenvector that with the same order.

循环矩阵的特征值由其第一行元素的离散傅里叶变换组成，并且第一行元素是特征值的傅里叶变换的逆，而且所有同阶循环矩阵的特征向量相同。

I have friends and jokingly said: I and Obama in the same year, his daughter and his daughter are also the same age.

我有朋友开玩笑地说：我和奥巴马在同一年，他的女儿和他的女儿也在同样的年龄。

Grand 碁 predicts the income of the 2nd quarter grows 10% compared to the same period, jotter predicts to will grow 35 ％～ compared to the same period 40%.

宏碁预计第二季度的收入同比增长10%，笔记本预计将同比增长35％～40%。

There are some people that we love,and at the same time ,we have some reasons ,it is the same with those who love JUJU!

世界上总有一些人让我们爱着，有很多原因，喜欢海宁的人同样，可是我知道喜欢海宁的人会给我们同一个答案--单反与坚强！

The jump function provides the same utility as the Undo-Redo function pair with a single command—a 50% reduction in excise for the same functionality.

跳转功能用一个命令提供了类似一对撤销和恢复的功能，而减少了50%的附加工作。

At the same time, considering the jumpiness or incline caused inaccuracy and pretermission when the capsule moving ahead, two couples of infrared ray and electron transducer were designed to detect the light signal of the corresponding parts of the capsule. After the addition operation compensation and differential coefficient, turning the little different simulation signals of the body and cap of the capsule into digital signals for detection. It is more accurate for detection and stable to the disturbance. Step electromotor was used for the capsules direction turning which solved this problem efficiently. The capsules were ranged in order according to their colors with the cap at the same direction.

同时考虑到胶囊行进过程中跳动、倾斜及随机干扰造成的误判、漏判，设计了两对红外光电传感器用以同时检测胶囊上下两个边缘部位的光信号，两个检测信号经加法运算补偿、微分运算处理，将体现胶囊的帽、体微小几何尺寸差别特征的弱模拟信号直接转变成数字量检测，提高了检测的准确率及抗干扰能力，并由步进电机控制胶囊掉头，有效地解决了胶囊体、帽的位置调整，分色调头排列，达到帽、体一致。

And we were the same, just the same, you and i

我们是同样的，刚好同样，你和我

All evil customs connected with forests and warrens, foresters and warreners, sheriffs and their officers, river banks and their wardens, shall immediately by inquired into in each county by twelve sworn knights of the same county chosen by the honest men of the same county, and shall, within forty days of the said inquest, be utterly abolished, so as never to be restored, provided always that we previously have intimation thereof, or our justiciar, if we should not be in England.

关于森林区和围场、林务官和围场吏、郡长及其僚属、河岸区及其区长，各郡应立即由本郡诚实良善之士选举本郡骑士十二名，各发誓言后，对上述诸项展开调查。调查完成后四十日内，各项弊政应彻底革除、永不得再犯。不过，上述事宜应事先通知我们，如我们不在英格兰，则通知司法官。注：本条见于1215年最初的版本，后来版本无。

Blame it on SimX and DoriftoKids, they're painful to judge, simply because both of these two teams have done great in some aspects, but made some mistakes at other aspects of their run, after concluding their scores, I keep getting the same score between them, no if you watch the replay, you'll notice their runs aren't similar, but they both made a fair share of mistakes in order to share that same score over and over again , I have been reviewing my scores of all teams for 3 times, and reviewed the scores between SimX and DoriftoKids for 5 times, trying desperately to find the little details in which I can deduct the points on, but failed I was, so I thought to myself... why not just let the two teams in....

只能怪SimX和DoriftoKids，这两支车队太难分出优劣了，因为他们在比赛中都在一些环节发挥出色，也在一些环节犯了错误，每次为两队评分后，我总是得到相同的分数，但是如果你看了录像，你会发现他们的跑法是不同的，但是他们犯了差不多的错误以致于每次的评分都相同，所有车队的成绩我都检查了三遍，并且这两支队的成绩检查了五遍，尽全力寻找可以扣分的细节，但是失败了，所以我对自己说，两支队为什么不能都进决赛呢。。。

There was no clear explanation because the component was exactly the same as last year and the kerb is exactly the same too.

没有清楚的解释因为组分确切地是相同作为去年和井栏确切地是同样也是。

Chimborazo and Cotopaxi, took me by the hand.

越过琴博腊索山和科托帕克西山。

This car is in a good condition.

这辆车的状况很好。