2016-12-18

change openwrt source to UTSC

The following steps only apply to Netgear 4300 and openwrt 15.05.1. Modify /etc/opkg.conf to the following lines. 1234567891011dest root /dest ram /tmplists_dir ext /var/opkg-listsoption overlay_root

Coding

2016-12-06

Install fcitx on ubuntu 16.10

Run the following command. 1sudo apt-get install fcitx fcitx-table fcitx-googlepinyin fcitx-module-cloudpinyin Search for language support, and check Keyboard input method system is fcitx Reboot. Go t

Coding

2016-12-06

Auto Adjust Brightness On Ubuntu 16.10 Using Systemd

This works on ubuntu 16.10 Create a file brightness.service in /lib/systemd/system with the following contents(Change 100 to whatever brightness you want, roughly it’s between 0 ~ 1000). 12345678[Unit

Coding

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

Archive: 2016