## surfshark vpn

surfshark-vpn doesn’t seem to work for Linux somehow for several months. At least I thought it was just because I was overseas. Surfshark itself seems to be working. Just the script itself doesn’t seem to be able to connect to any server anymore. Manual configuration with OpenVPN works. But DNS Leak test from SurfShark failed…

## URLs in bibliography: LaTeX not breaking line as expected

“I am trying to include long URLs in a bibliography, but those often overflow into the margin of the document.” The following works like a charm. \usepackage{url} % breakurl \def\UrlBreaks{\do\/\do-} \usepackage{breakurl} \usepackage[breaklinks]{hyperref}

## 16×9 Beamer setting

To use 16×9 aspect ratio for Beamer, we can simply change \documentclass{beamer} to \documentclass[aspectratio=169]{beamer} However, Bakoma won’t display correctly afterward. Go to Option -> Document Properties -> Paper. Just change paper width and paper height to 454bp and 255bp should make things work.

## Skew-symmetric matrix representation of cross product

We can define Note that we have and Triple product expansion We will show the above with the triple product expansion: Proof: (1)   Similarly for the and components. Proof of Note that for any     thus Proof of For any (2)   Thus,

## Rodrigues’ rotation formula

The rotation matrix for rotating an object along normal direction with angle is given by where such that We can easily validate that the equation is correct, note that as desired. And for any vector perpendicular to as desired as well. Compute and from  Note that  Thus, . Moreover, since , we can compute as…

## ARIMA

It is ARMA after applying lap-1 and lap-M difference to data.

Lie algebra is a vector space $latex g$ with a map $latex [\cdot, \cdot]:g\times g \rightarrow g$ such that $latex [\cdot,\cdot]$ is bilinear $latex [x,x]=0$ Jacobi inequality: $latex [x,[y,z]]+[y,[z,x]]+[z,[x,y]]=0,\forall x,y,z$. Note that 2) $latex \Rightarrow [x,y]=-[y,x]$ since $latex 0=[x+y,x+y]=[x,x]+[y,y]+[x,y]+[y,x]$. Note that the converse is true most of time as well since that implies \$latex…