2016-12-06

Super CapsLock On Ubuntu 16.10

On ubuntu 16.10, make CapsLock act as Esc when it is hit, and as Ctrl when it is held. To make it work, modify /etc/default/keyboard, change 1XKBOPTIONS="" to 1XKBOPTIONS="caps:ctrl_mod

Coding

2016-10-07

beautify i3wm

MotivationI enjoy using i3wm, big time. You can switch to different windows/apps conveniently with it. The only problem to me is that it’s not beautiful enough, and it’s ridiculously small in my high-

Math

2016-10-06

The empty set is the subset of any set

The empty set is the subset of any set. This is true. Some people take it as a convention, but in fact, it can be explained. According to the definition of $\subset$, $\varnothing\subset A\Leftrighta

Math

2016-10-01

Understand poisson distribution

IntroductionPoisson distribution can be derived from Binomial distribution when $\lim\limits_{n\to\infty}np = \lambda(\lambda\in\mathbb R)$, in which $n$ is the number of trials, $p$ is the probabilit

Math

2016-10-01

Proof of $$\lim_{x\rightarrow \infty} f(x)^{g(x)} = c^d$$

Theorem: $$c,\ d\in {\bf R},\ \lim_{x\rightarrow \infty} f(x)=c>0,\ \lim_{x\rightarrow \infty} g(x) =d>0$$ then $$\lim_{x\rightarrow \infty} f(x)^{g(x)} = c^d$$ Proof: Because $y(x)=ln(x)$ i

Coding

2016-10-01

Let hexo support mathjax

UpdateThe original answer fails on some mathjax expressions. So don’t use it. Currently changing marked.js works for me. Just use the method below. It works for me. First introduce mathjax into our bl

Math

2016-10-01

Proof of the limit's composition law when x approaches infinity

Theorem: If $f(x)$ is continous at $b$ and $\lim\limits_{x \to\infty}g(x) = b$, then $$\lim\limits_{x \to \infty}f(g(x)) = f(b) = f(\lim\limits_{x\to \infty}g(x))\tag1$$ Proof: Because $f(x)$ is con

Math

2016-09-30

Calculate $$\lim\limits_{n\to\infty}(1-\frac{\lambda_n}n)^n$$

I came upon the calculation of $\lim\limits_{n\to\infty}(1-\frac{\lambda_n}n)^n$ when I was reviewing Poisson distribution. Notice that $\lambda_n = np_n(n\in\mathbb{Z}{\geq 0}, 0\leq p \leq 1)$ and $

Coding

2016-07-17

Hexo Source Code Demystified

PrefaceHexo is an excellent static blog generator, I read its source code recently, and I think it’s worth sharing the inner mechanism of its source code. GeneratorWhen you run the command hexo genera

Journal

2016-07-04

The fee paid to freelancer is not refundable

About two days ago, I got a message from my phone that I was charged for ￥110.72. The money was taken directly from my debit card. At first, I thought the money was stolen using some high-end technolo

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