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A relatively direct method is expounded in this paper to prove the termwise differentiation of power series, and a simple method is expressed to calculate the Fourier coefficient.

用比较直接的法明幂级的和在收敛域内可以逐微分的公式;并得到了计算傅立叶系的一种简便法.

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By using the method of coordination transformation and expandedness Fourier series, an analytic solution is obtained from studying the Newtonian fluids laminar flow in eccentric anulus.

采用坐标变换和展开成傅立叶级的法,推导出了牛顿流体偏心环空轴向流动速度场的严格学解析解.

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By proving properties of demicontinuous function and series with function terms, use methods of finite coveting theorem and its application in proving problems are introduced.

通过半连续及级等有关性质的明,介绍了有限覆盖定理的使用法,说明了它在明问题中的作用。

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With growth rate photograph of slow road carrying capacity is compared, the growth of the car shows growth of progressional in successive years.

和增长速度缓慢的道路承载能力相比,汽车的增长呈级的连年增长。

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当月 CNN 10 学生英语 2021年5月合集

Its wind speeds were greater than 200 miles per hour making it an EF-5 tornado, the strongest classification on the Enhanced Fujita Scale.

龙卷风风速时超200英里,为EF-5型龙卷风,是改良藤田的最高强度。

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当月 CNN 10 学生英语 2021年3月合集

Fujita is the namesake of the enhanced Fujita Scale which characterizes the intensity of tornadoes.

改进版藤田是以藤田命名的,该描述了龙卷风的强度。

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CNN 精选 2015年5月合集

Anything above 200 miles per hour is considered an EF-5 tornado.

只要超时200英里的速度都会被认为是藤田5的龙卷风。

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生物学基础入门

So to summarise, trophic levels are the number of steps in an organisms is within a food chain.

总而言之,营养是一个生物体在食物链中的层。

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CNN 精选 2015年5月合集

So, now, the EF scale, Enhanced Fujita Scale, starts at 0 and goes only to 5.

现在, EF, 增强的藤田,从0开始, 只到5。

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高等学之美

And, in this case, it's an infinite polynomial so  I should really be calling it a power series.

而且,在这种情况下,它是一个无穷多项式的,所以我应该称之为幂。

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高等学之美

Dividing by R2, this gives us an infinite sum which should converge to pi.

除以R2,这给出了一个应该收敛到π的无穷。

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HISTORY This Week

They came up with something called the F-scale, which we still use today.

他们提出了一个叫做藤田的系统,我们至今仍在使用。

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99%不为人知的故事

Whereas most of these developments were driven by a company's need to develop their own system to count their proceeds or a mathematical progression that necessitated a new tool–a more powerful tool–in this case, TI had invented the microchip.

虽然这些发展大部分是由公司需要开发自己的系统来计算其收益或需要新工具(一种更强大的工具)的学推动的,但在这种情况下,TI 发明了微芯片。

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科技 Crash Course

If the level is not 1, the code inside the ELSE block will be executed instead, and the number of bugs that Grace has to battle is set to 3 times the level number.

如果等不是1,ELSE块中的代码将会被执行, Grace需要战斗的虫子量将被设置为等的3倍。

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Veritasium真理元素

If you put in minus a quarter for X in this series, you'll get a very rapidly converging series expansion that will quickly give you square root of three to high accuracy.

如果你在这个系列中为X减去四分之一,您将得到一个非常快速收敛的展开式,它将快速为您提供高精度的三的平方根。

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TED-Ed(视频版)2024年6月合集

If we add all the possible probabilities of a human win, the total is the sum of a geometric series.

如果我们把人类获胜的所有可能概率相加,总就是几何的和。

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Veritasium真理元素

So that just alternating series with plus and minus signs as the coefficient.

因此这只是以正负号交替的作为系。

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高等学之美

To be more precise about it, the Taylor series expansion of tan(theta) shows that this approximation will only have a cubic error term.

更精确地说,tan(θ)的泰勒展开表明,这个近似只会有一个三次误差项。

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Veritasium真理元素

Does Newton's infinite series actually give you the value of one over one plus X?

牛顿的无穷实际上给出的是一除以一加上 X 的值吗?

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高等学之美

More generally, this is the core idea  that underlies Fourier transforms, and Fourier series, and the infinite  swell of topics that follow from those.

更一般地说, 这是傅里叶变换和傅里叶的核心思想,以及随之而来的无穷无尽的主题。

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高等学之美

A number one bigger than this was in the series expansion of a fundamental function in a totally different part of math, relevant to these things called modular forms and elliptic functions.

一个比这大一号的出现在了一个基本函的展开中, 这个基本函属于学中完全不同的一个部分,与所谓的模形式和椭圆函有关。

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高等学之美

Another example that several astute commenters on the " Inventing Math" video pointed out, is the connection between the divergent sum of all powers of 2 and the way that the number -1 is represented in computers with bits.

另一个例子是, 几个精明的评论者在观看“发明学” 视频时指出的,2的所有幂次的发散与计算机中用比特表示-1的方式之间的联系。

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