## Sekai π πΊ

Sekai is the kanji for δΈη, meaning “the world”. That’s a great word because of the scale it designates.

Background Updated $\LaTeX$ version From this $\TeX$-SE question about tlmgr, we see some advantages of installing $\TeX$Live directly from the official site:
avoid errors due to outdated version of $\TeX$Live supplied by the OS’s package manager easier to manage packages with tlmgr. enjoy the newer version of $\TeX$Live not yet available in your current GNU/Linux version. The installation took about 30 minutes and 5G in the disk. I’ve chosen a local installation as this didn’t require sudo privileges.
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## Package Versioning for Julia Projects

### Resolved GLM installation error

Update: Thanks to JuliaRegistries/General#647, the version cap of the package Distributions has now been removed, so that one can directly install the package GLM along with Distributions v0.19.2.
Background I’m reading the book Statistics with Julia, which makes use of GLM.
Problem I encountered the following error, which I posted in the issue GLM.jl#311.
(v1.1) pkg> add GLM Resolving package versions... ERROR: Unsatisfiable requirements detected for package GLM [38e38edf]: GLM [38e38edf] log: ββpossible versions are: [0.
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## Insensitive Laptop Touchpad

### Log of my Ubuntu Tweak config

Problem The touchpad on my new Ubuntu 18.04 LTS laptop was frozen. Toogling π± with <Fn>-<F4> didn’t worked.
Attempt Logout: didn’t work at all Reboot: worked most of the time Partial solution After changing the Mouse Click Emulation in Keyboard & Mouse in Ubuntu Tweak from the default “Fingers” (2 fingers for right click; 3 fingers for middle click) to “Area” (Right/middle click determined by clicked area), one might have to wait for next reboot.
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## Juno Installation 2019

### Log of system-wide config

Goal To install Juno for convenient development in Julia.
Problem After Juno installation, I received the following error.
Analysis From the error message, the system had tried to find an executable file julia, which would then be executed by the shell /bin/sh. Nonetheless, it’s absent from the system’s environment $PATH, so Juno couldn’t find it.
I’ve only changed my $PATH in ZSHRC, which is user-specific.
Solution This Stack Overflow question about $PATH setting on *nix has provided various solution.
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## Conditional Batch File Editing

### Adopted Mmark for Math Posts

Problem During the adoption of Mmark for math posts on this blog, I had to insert markup: mmark at the last line of front matter of the source file of each math post.
Seek help I separated this into two SO questions
Sed conditional match and execute command with offset, and A question about AWK multiple line recognition. Solution From #1., I learnt the use of variables in AWK scripts.
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## My Intended Trigo Answer

The Math.SE question *$2\cos(2x) - 2\sin(x) = 0$* has attracted several
answers from high-rep users.

I am expanding @rhombic’s comment into an answer.

$$ \begin{aligned} 2\cos(2x)-2\sin(x)&=0 \\ 2 - 4\sin^2(x)-2\sin(x)&=0 \\ 2\sin^2(x)+\sin(x) - 1&=0 \\ (2 \sin(x) - 1)(\sin(x) +1) &= 0 \\ \sin(x) = \frac12 \text{ or } \sin(x) &= -1 \\ x = \frac{\pi}{6}, \frac{5\pi}{6} \text{ (rejected) or } & \frac{3\pi}{2} \text{ (rejected)} \end{aligned} $$

## Improved Integration of Hugo and $\KaTeX$

Problem There’s no custom $\KaTeX$ macro in local preview since I’ve merged some recent commits from the upstream of this blog’s theme, in particular, Beautiful Hugo’s pull requests #246 and #255, which allowed self-hosting the theme’s static JS, CSS and font files. This self-hosted option is particularly useful in case of slow response from Cloudflare’s CDN.
Even they do appear on the public GitLab site, the final rendered Markdown + $\TeX$ code would be succumb to syntax errors due to their absence in the preview process.
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## JavaScript Copy Button

Goal To create a copy button for my Math.SE comment template in order to save the trouble of copying and pasting.
My first attempt I put the boilerplate inside a Markdown codeblock to prevent them from getting interpreted by Hugo’s Markdown parser. Under each codeblock, I placed the copy button.
Comment boilerplate goes here ... π
Another comment boilerplate goes here ... π
…
My page’s original layout
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## My Dual Answer

Update: The question has been reopened.
I intended to answer κΉμ’
ν’s problem on Math.SE. However, the programs in the question body aren’t typeset in MathJax. As a result, I downvoted and closed this question because found it unclear. From the proposed dual, it seems that I shouldn’t interpret the primal as a linear program. Anyways, without further clarifications from OP, I found no reason to look at this further.
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## Finite Population Sampling without Replacement

### Personal note of finite population sampling

First moment Population: $ \Omega = \{ x_1, \dots, x_N \} $
Collection of $n$-samples: $\mathcal{S} = \{ s \in \Omega^n \mid \forall i,j \in s, i \ne j \} $
Collection of $n$-samples containing $x$: $ \mathcal{S}_x = \{ s \in \mathcal{S} \mid x \in s \} $
Observe that $ |\mathcal{S}_x| = \binom{N-1}{n-1} $.
Let population mean be zero. $\mu = 0$, i.e. $ \sum_{i = 1}^N x_i = 0 $
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