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../This is a test article

In this test article, we test if Markdown elements are rendered properly. 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.

A problem of the current theme is the legibility of monospace font family for long text. To resolve this issue, we have added a trigger to change the font to serif. The trigger is the date below the title. Just click it.

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

Section

Section

Section

Section

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.

The following is a code block in Python.

# 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
where
    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)

We can also make numbered code block.

1
2
3
4
5
#!/usr/bin/python
# Python codes
import matplotlib.pyplot as plt

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

Test deep section

Ordered list:

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

Unordered list:

  • Elemement 1
  • Element 2

The quote block is simple

*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.

The folowing are admonition blocks. Again, the style is made simple but visible.

Warning

This is a warning message.

Note

This is a note message.

Similarly, you could also use this admonition block to define, for example, theorem and lemma. The quote block could also do the job but it would not boldify the title.

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, if you are using a mobile device and that the equation is too long, then it will mess up the entire screen. This is a MathJax problem, and it should not fixed from the user level. Anyway, to properly adjust long equation in narrow-width devices, wrap the entire admonition with <div class="mathjax-long-eq"> in the Markdown source file. This should fix the problem, temporarily, however, it has a side effect. Try remove the div and see the effect.

I imagine that table should look like a receipt from a typewriter (in combination with monospace fonts). Here it goes.

Syntax Description
Header Title
Paragraph Text

In scientific articles, we often need to cite papers. I don't know how to make a carbon-copy of the citation in LaTeX, so here I used footnote instead for citation 1.

Here are some math equations. Inline math $f(x) = \sin(x) + \mathbb{E} + \mathbf{A} + \mathcal{F}$, $\R^{N\times 2}, \Q, \N, \T$ and displayed math 2. The following equation is long on narrow devices as well. You can wrap it with the <div class="mathjax-long-eq" markdown="1"> environment. But again, use this trick only when necessary, as it has side effects.

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

Some math examples using custom macros.

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

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

I have defined some math-macros in mathjax.html. Please adapt them to your website.

最後,測試漢語排版. 正常字體. 粗體斜體

莊子曰:昔者老子之作也,變化所由,道德爲母。效經列首,天地爲象。上經配天,下經配地。陰道八,陽道九。以陰行陽,故七十有二首;以陽行陰,故分爲上下。以五行八,故上經四十而更始; 以四行八,故下經三十有二而終矣。陽道奇,陰道偶,故上經先而下經後。陽道大,陰道小,故上經衆而下經寡。陽道左,陰道右,故上經覆來,下經反往。反覆相過,淪爲一形,冥冥混沌,道爲中主。重符列驗,以見端緒。 下經爲門,上經爲户。智者見其經效,則通乎天地之數、陰陽之紀、夫婦之配、父子之親、君臣之儀,萬物敷矣。

Conclusion

Some conclusions.

References


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

  2. Another reference. 

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