mshj/mshj_blog
1
0
Fork 0
mirror of https://github.com/JimenezJC/mshj_blog.git synced 2025-12-06 10:09:56 -05:00
Code Issues Projects Releases Packages Wiki Activity Actions

Initial Blog Commit

Browse source
This commit is contained in:
Juan 2025-07-04 16:10:22 -04:00
commit 07775036ce
92 changed files with 4980 additions and 0 deletions
Download patch file Download diff file Expand all files Collapse all files

120
public/posts/test-tex/index.html Normal file
View file

@ -0,0 +1,120 @@
<!DOCTYPE html>
<html lang="en-us"><head><script src="/livereload.js?mindelay=10&amp;v=2&amp;port=1313&amp;path=livereload" data-no-instant defer></script>
<meta charset="utf-8" />
<meta http-equiv="X-UA-Compatible" content="IE=edge" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<meta name="description" content="Inline math:
\(\varphi\)
Displayed math:
$$\begin{aligned}
\varphi &amp;\Rightarrow \psi \\
\varnothing &amp;\rightarrow A
\end{aligned}$$
$$
R_{\mu \nu} - {1 \over 2}g_{\mu \nu},R &#43; g_{\mu \nu} \Lambda
= {8 \pi G \over c^4} T_{\mu \nu}
$$
The equation $$(x_i \cdot x_j)^2$$ is called kernel function and is often written as $$k(x_i, x_j)$$.
$$
\arg\max_\alpha \sum_j \alpha_j - \frac{1}{2} \sum_{j,k} \alpha_j, \alpha_k y_j y_k (x_j \cdot x_k)
$$
$$
f(X) = \frac{1}{(2\pi)^{\frac{n}{2} |\Sigma|^{\frac{1}{2}}}} e^{ - \frac{1}{2} (X - \mu)^T \Sigma^{-1} (X - \mu)}
$$">
<title>
Test Tex
</title>
<link rel="shortcut icon" type="image/x-icon" href="/" />
<link rel="stylesheet" href="/css/main.900100e9dbee2d56c58fac8bb717037cae7e26a9c36c29d2ff587bdd65f0cbbe510b41d81a3bb234919cdfdc7550d786b2fab70c8fc507772d732fe097106d12.css" integrity="sha512-kAEA6dvuLVbFj6yLtxcDfK5&#43;JqnDbCnS/1h73WXwy75RC0HYGjuyNJGc39x1UNeGsvq3DI/FB3ctcy/glxBtEg==" />
<script>
MathJax = {
tex: {
inlineMath: [['$', '$'], ['\\(', '\\)']],
displayMath: [['$$','$$'], ['\\[', '\\]']],
processEscapes: true,
processEnvironments: true
},
options: {
skipHtmlTags: ['script', 'noscript', 'style', 'textarea', 'pre']
}
};
window.addEventListener('load', (event) => {
document.querySelectorAll("mjx-container").forEach(function(x){
x.parentElement.classList += 'has-jax'})
});
</script>
<script src="https://cdnjs.cloudflare.com/polyfill/v3/polyfill.min.js?features=es6"></script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
</head>
<body a="auto">
<main class="page-content" aria-label="Content">
<div class="w">
<div class="post-meta">
<a href="/">..</a>
<p>
<time datetime="2022-08-26 22:28:10 &#43;0800 &#43;0800">
2022-08-26
</time>
</p>
</div>
<article>
<h1>Test Tex</h1>
<p>Inline math: <span>
\(\varphi\)
</span>
</p>
<p>Displayed math:
<span>
$$\begin{aligned}
\varphi &amp;\Rightarrow \psi \\
\varnothing &amp;\rightarrow A
\end{aligned}$$
</span>
</p>
<p>$$
R_{\mu \nu} - {1 \over 2}g_{\mu \nu},R + g_{\mu \nu} \Lambda
= {8 \pi G \over c^4} T_{\mu \nu}
$$</p>
<p>The equation $$(x_i \cdot x_j)^2$$ is called kernel function and is often written as $$k(x_i, x_j)$$.</p>
<p>$$
\arg\max_\alpha \sum_j \alpha_j - \frac{1}{2} \sum_{j,k} \alpha_j, \alpha_k y_j y_k (x_j \cdot x_k)
$$</p>
<p>$$
f(X) = \frac{1}{(2\pi)^{\frac{n}{2} |\Sigma|^{\frac{1}{2}}}} e^{ - \frac{1}{2} (X - \mu)^T \Sigma^{-1} (X - \mu)}
$$</p>
<p>$$
\mu_i = \sum_{j=1}^N \frac{p_{ij} x}{n_i} \
\Sigma_i = \sum_{j=1}^N \frac{p_{ij} (x_j - \mu_i) (x_j - \mu_i)^T}{n_i}\
w_i = \frac{n_i}{N}
$$</p>
<p>$$
S_i^{(t)} = \big { x_p : \big | x_p - \mu^{(t)}_i \big |^2 \le \big | x_p - \mu^{(t)}_j \big |^2 \ \forall j, 1 \le j \le k \big}
$$</p>
<p>(The error above is a demo for incorrect formulas.)</p>
</article>
</div>
</main>
</body></html>