Example article testing element rendering

In this test article, we test if Markdown elements are rendered correctly. First let us see basic inline elements, such as inline code block lambda x: wrapper(x), URL link, Italic, and bold font. Note that the underscore _ is seen as italic decorator hence, please use \_ in math equation to escape this.

Table of contents appears at the place with marker [TOC].





Lorem ipsum dolor sit amet, consectetur adipiscing elit. Aliquam eget condimentum leo. Proin a orci egestas, tincidunt diam id, efficitur ipsum. Mauris imperdiet suscipit erat, id auctor lorem gravida id. Donec est leo, tempus fermentum ex et, congue auctor nibh. Nullam nec vehicula erat. Nullam semper, nunc id interdum fermentum, ante arcu molestie eros, eget pharetra orci libero in ante. Morbi pharetra laoreet mauris vel ultricies.

Interdum et malesuada fames ac ante ipsum primis in faucibus. Morbi ornare mauris turpis, eu tincidunt nibh mollis in. Suspendisse potenti. Integer viverra eget tortor a dictum. Etiam tempor, erat sed placerat ultricies, lacus quam sodales ex, ac vulputate dolor nibh vel ipsum. Donec risus nisl, rutrum non aliquet nec, lacinia vel turpis. Etiam volutpat ornare tortor ac porttitor. Morbi vitae orci sem. Praesent vitae magna quis mi efficitur auctor. Cras vitae sagittis turpis, sit amet mollis diam.

Fusce blandit imperdiet sapien, et interdum massa aliquet nec. Cras eget augue dolor. Morbi dignissim condimentum sapien, quis faucibus dolor semper et. Praesent eu condimentum purus. Sed euismod, ante ac commodo varius, mauris neque efficitur est, vel elementum elit augue vel dolor. Donec sodales fringilla est, eget pulvinar nunc laoreet quis. Donec arcu massa, posuere a elit sed, placerat viverra ipsum. Proin ac neque ut ex eleifend tempor. Donec sit amet rhoncus magna, eu hendrerit neque. Morbi sit amet velit orci. Suspendisse mollis velit eget interdum euismod. Sed arcu justo, vulputate et laoreet vel, commodo et quam.

Phasellus feugiat felis sed vestibulum pellentesque. Nullam nec aliquam ante. Aliquam non consequat dolor, ac imperdiet sem. Nam laoreet dapibus odio in facilisis. Praesent sem nisi, placerat nec ligula sed, iaculis ullamcorper nisl. Fusce ut diam cursus, porttitor dui vel, eleifend eros. Donec sed urna justo. Nulla facilisis tellus dui, eu feugiat magna volutpat vel. Integer convallis tempus neque ut pretium. Duis at fringilla nisi. Etiam finibus, erat at sodales sollicitudin, elit nunc elementum lacus, nec scelerisque ipsum est quis dolor. Sed varius est libero, nec tincidunt metus fermentum a. Aenean vel nisi purus. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia curae;

Vestibulum tempor leo a arcu feugiat tincidunt. Integer eros tortor, commodo nec sapien vel, condimentum consectetur lorem. Phasellus interdum sodales sem. Ut malesuada nisi urna, sit amet pharetra mi faucibus quis. Nunc eu imperdiet massa, eu rutrum turpis. Nulla porttitor porta pharetra. Phasellus maximus nisi ut nunc viverra lobortis. Maecenas malesuada felis sit amet condimentum iaculis.

# Python scripts
import numpy as np

def func(x):
    return x ** 2

a = np.array([1., 2., 3.])
print(f'Value is: {a:.2f}')

Another Rust code block

// Rust code
fn test<T>(a: T) -> T
    T: Mytype
    let b = b;        // highlight here
    let c = 'hello';  // hightlight here
    b + 1

and another Matlab code block

% Matlab code
a = [1:1:100];
b = a .^ 2;
plot(a, b)

Numbered code block.

# Python codes
import matplotlib.pyplot as plt

plt.plot([1., 2., 3.])

Add a figure (the max-width of image is set to 90% of the article width, and is auto-centred.)

test image

Second section

Ordered list:

  1. Element 1
  2. Element 2
  3. Element 3

Unordered list:

  • Elemement 1
  • Element 2

Quote block,

Aliquam porttitor fringilla urna, ut mollis metus placerat ac. Morbi convallis suscipit suscipit. Ut accumsan neque et elit consequat eleifend. Integer eros nibh, scelerisque at pharetra quis, tincidunt vitae metus. Suspendisse nunc felis, interdum eu euismod non, gravida posuere augue. Duis malesuada orci quis justo porttitor, ac cursus magna gravida. Nam vehicula turpis quis elementum faucibus.

Admonition. Colours are picked from Sphinx website. In principle you could add some icons (e.g., exclamation mark) before these titles, but I do not consider this necessary. If you wish, Google "css ::before icon" for how to so so.


This is a warning message.


This is a note message.

Similarly, you could also use this admonition env to define, for example, theorem and lemma, though using quote block could also do the job.

Lemma 1 (Kolmogorov--Chentsov).

Let $X\colon [0, \infty)\to\mathbb{R}$ be a stochastic process. Suppose that for every $T>0$, there are $\alpha,\beta, C>0$ such that $$ \begin{equation} \mathbb{E}\big[ \abs{X(t) - X(s)}^\alpha \big] \leq C \, \abs{t-s}^{1+\beta}, \end{equation} $$ for all $s,t\in[0,T]$. Then there is a version $\widetilde{X}$ of $X$ that is Hölder-continuous of every order $\gamma \in (0, \beta \, / \, \alpha)$ 3.

Proof. Here shows the proof. However, increasing the top margin of the proof environment (or equivalently increase the bottom margin of the second p child) seems to be non-trivial.

Some table.

Syntax Description
Header Title
Paragraph Text

Here's a sentence with a reference1.

Some math. Inline math $f(x) = \sin(x) + \mathbb{E} + \mathbf{A} + \mathcal{F}$, $\R^{N\times 2}, \Q, \N, \T$ and displayed math 2

$$ \begin{equation} \diff X(t) = A \, X(t) \diff t + B \diff W(t), \tag{5} \label{equ:eq} \end{equation} $$

Some examples

$$ \begin{equation} \begin{split} &\expec{X \cond \FF} \\ &\expecbig{\expp^{\imag X}} \\ &\expecBig{ \big(\expp^{X} - X^2\big)^3 \cond Y}\\ &\cov{X, Y \cond \FF} \\ A\,A^\trans &= A^\trans \, A\\ \norm{A}_2 &\coloneqq \sup_{\norm{u}_2=1} \norm{A \, u}_2\\ &(\jacobian_x\phi)(x)\\ &(\hessian_x\phi)(x)\\ &(A\phi)(x)\\ f_u(v) &= \innerp{u}{v} \\ &\innerpBig{u + z}{\sum^N_{i=1} v_i}\\ \limsup_{N,M\to\infty} X_k &\coloneqq \lim_{N\to\infty} \sup_{M\geq N} X_k \end{split} \end{equation} $$

Now I reference Equation \eqref{equ:eq}.

At last, let me check the support for Chinese. 測試行. 粗體斜體



Some conclusions


  1. This is the footnote/reference. Looks like fine but needs some small adjustments. 

  2. Another reference. 

  3. Achim Klenke. Probability theory. Springer, 2014. 

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