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Nature cannot pee while sneezing?
夏力钢 2021-11-12 17:36
At around 5pm, while going to release myself, I sneezed and the pee stopped immediately. This reminds me of momentum conservation. You know both sneeze and pee will make you lose some momentum in the same direction because our nose and urinary system work in the same direction. Th ...
个人分类: 物理妙趣|1672 次阅读|没有评论
Why do I keep writing single-author papers(为什么我坚持写唯一作者文章)?
热度 1 夏力钢 2021-7-19 17:10
Because thousands of authors would appaer on a research paper in our field. For example, the famous paper from ATLAS reporting the observation of the Higgs boson has around 3000 authors. This is not unique. Because every paper from the ATLAS collaboration would have around 3000 authors. ...
个人分类: Life|2554 次阅读|2 个评论 热度 1
Can Higgs explain Leption Universality Violation in B->Kll ?
夏力钢 2021-3-25 10:11
A few days ago, the LHCb collaboration reported an evidence for Lepton Universality Violation (LUV) in the beauty-quark decays B - K l + l - where l represents muon or electron. They measured the ratio of muon to electron to be (more details see their paper ) This ratio i ...
个人分类: 物理妙趣|1770 次阅读|没有评论
A problem about the AM-GM inequality (一道关于均值不等式的题目)
夏力钢 2021-2-1 11:29
Recently, Kai-Liang brought to my attention an extension form of the classic inequality of the arithmetic and geometric means. It is easy to see C2=1. It is not easy to calculate C3. I spent a couple of days on this problem and found the solution. My method is very sta ...
个人分类: FUN MATH|3664 次阅读|没有评论
My experience of using Fourier transformation (我使用傅利叶变换的经历)
夏力钢 2021-1-19 10:42
I was shocked the first time when I knew Fourier transformtion. It is amazing that nearly any function could be expanded as a sum of simple sine and cosine functions. It is very different from another famous expansion, Taylor expansion. Taylor expansion focuses on one point while Fourier ...
个人分类: 数据分析|2004 次阅读|没有评论
素数基本定理证明中有趣的3-4-1引理
热度 1 夏力钢 2020-10-16 17:57
素数基本定理 是描述素数分布的一个非常重要的定理。它表明素数的密度大约是1/log(x),即 不大于x内的素数个数大约为x/log(x) 。 Jacques Solomon Hadamard和Charles-Jean de la Vallée Poussin于1896年按照B. Riemann的思想首次证明。 简单地说,素数基本定理等价于 黎曼zeta函数zeta(s)在实部为1的 ...
个人分类: FUN MATH|3138 次阅读|1 个评论 热度 1
A representations of Euler\'s constant (欧拉常数)
夏力钢 2020-9-10 13:40
欧拉常数通常用 表示,其值约为0.5772。它有N多表示方式,可以看一下它的 百度百科 。我最近在看analytic number theory,知道其中的三种。有一种积分表示特别不好理解,这里给出一个不怎么好看的证明(也许其他地方有更简单的证明方法)。 Anybody wants a try ?
个人分类: FUN MATH|3701 次阅读|1 个评论
A primary-school (Fibonacci-type) problem
夏力钢 2020-9-4 17:34
I knew this problem in a WeChat group chat. It is said to be a problem for primary-school students. Here is the problem. How many integers with all digits being just 1,2 or 3 and the sum of all digits being 10? For example, 12331 and 22222. We could ask a more general qu ...
个人分类: FUN MATH|2098 次阅读|没有评论
金星,御夫座,双子座,猎户座,白羊座和金牛座
夏力钢 2020-8-15 10:41
昨天晚上设了闹钟,凌晨02:30,因为这个时候金星才从东方升起。 凌晨2点半,闹钟准时响起,脑袋还有点不清醒。拿起眼镜和手机,迅速跑上天台。唿,凉爽!瞬间清醒。 金星如约而至,比我想象中小,就在月亮下方。周围有御夫座,双子座,猎户座,白羊座和金牛座。下面的图片都是我用手机拍出来的,也有Star Wa ...
个人分类: 物理妙趣|4487 次阅读|没有评论
陆志勤在《记交大数学二三事》中的一道数学题
夏力钢 2020-8-13 17:23
今天在一个数学公众号(好玩的数学)上看到一篇陆志勤教授以前写的文章,《记交大数学二三事》。里面讲的是他在交大求学的经历。里面提到他大一的时候做的一道习题,截图如下。 我也尝试做了一下,发现不难。可以利用归纳法。n=2时显然成立,设n=k时成立,然后考虑n=k+1的情况。下面给出证明。 1. 不妨 ...
个人分类: FUN MATH|2068 次阅读|没有评论

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