In this part, we try to show some useful examples and new extensions that are added into this theme.

More examples

Examples for wiki card

Check here to see Norm-coercive mappings in Wikipedia.

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.

Examples for equations

Note that too many equations in a page may lead the loading to be very slow.

This is a plain equation:

$$ x = {-b \pm \sqrt{b^2-4ac} \over 2a}. $$

Note that this equation is in “display style”, which is not the same as “inline style”. An equation with inline style is like this: $x = {-b \pm \sqrt{b^2-4ac} \over 2a}$.

This is a single line equation with number:

\begin{align} \label{dfdf} x = {-b \pm \sqrt{b^2-4ac} \over 2a}. \end{align}

Here we make a reference for this equation, $\eqref{dfdf}$.

This is a single line equation which is very long:

\begin{align} \rho = \frac{ \sum_k \left(x_k - \overline{x}\right) \left(y_k - \overline{y}\right) }{ \sqrt{ \sum_k \left(x_k - \overline{x}\right)^2 \sum_k \left(y_k - \overline{y}\right)^2 } } \cdot \frac{ \sum_k \left(x_k - \overline{x}\right) \left(y_k - \overline{y}\right) }{ \sqrt{ \sum_k \left(x_k - \overline{x}\right)^2 \sum_k \left(y_k - \overline{y}\right)^2 } } \cdot \frac{ \sum_k \left(x_k - \overline{x}\right) \left(y_k - \overline{y}\right) }{ \sqrt{ \sum_k \left(x_k - \overline{x}\right)^2 \sum_k \left(y_k - \overline{y}\right)^2 } }, \end{align}

This is a multi-line equation:

\begin{equation} \begin{aligned} \mathcal{L}(\mathbf{A},~\boldsymbol{\theta}) &= \sum_k ( \mathbf{y}_k - \mathbf{A} \mathbf{x}_k - \boldsymbol{\theta} )^T ( \mathbf{y}_k - \mathbf{A} \mathbf{x}_k - \boldsymbol{\theta} )\\ &= \sum_k \left[ \mathbf{y}_k^T\mathbf{y}_k + \mathbf{x}_k^T \mathbf{A}^T\mathbf{A} \mathbf{x}_k + \boldsymbol{\theta}^T \boldsymbol{\theta} + 2 \boldsymbol{\theta}^T \mathbf{A} \mathbf{x}_k - 2 \mathbf{y}_k^T \mathbf{A} \mathbf{x}_k - 2 \mathbf{y}_k^T \boldsymbol{\theta} \right]. \end{aligned} \end{equation}

Refer a multi-line equation is very trick, you could do this by $(3)$, the short code is:

[$(3)$](#mjx-eqn-3)

where we use 3 to get the equation with number 3.

This is a matrix example:

\begin{equation} \begin{aligned} \mathbf{z} = \begin{bmatrix} \mathbf{z}_E \succ 0\\ \mathbf{z}_S = 0 \end{bmatrix} && \mathrm{and} && \left\{ \begin{matrix} \mathbf{H_E x} = \mathbf{h}_E, \\ \mathbf{H_S x} \succ \mathbf{h}_S. \end{matrix} \right. \end{aligned} \end{equation}

This is another matrix example:

\begin{equation} \begin{aligned} \mathbf{H}_E \mathbf{m} = \begin{bmatrix} 1 & 0 & 0 & 0 & 0 & \cdots & 0 \\ 0 & 1 & 0 & 0 & 0 & \cdots & 0 \\ 0 & 0 & 1 & 0 & 0 & \cdots & 0 \\ \vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \cdots & 1 & \cdots & 0 \end{bmatrix}_{P_E \times N} \mathbf{m} = \begin{bmatrix} m_{E1} \\ m_{E2} \\ m_{E3} \\ \cdots \\ m_{EP_E} \end{bmatrix} = \mathbf{m}_E = \mathbf{0}. \end{aligned} \end{equation}

More extensions

Show pdf

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Plotly

Plotly is a powerful tool for drawing interactive figures. Users could check here to see the documentation of this library. Here we show an example of a 3D surface plot. Note that in a page there should be no more than 12 plots. If exceeding, the extra plots could not be loaded.

Comparison between the interpolated Jaccard index and original one.

Mermaid

Mermaid is an drawing tool for flowchart, gantt chart and sequence diagram. Users could check here to see the documentation of this library. Here we show an example of a flow chart.

graph TB c1-->a2 subgraph one a1-->a2 end subgraph two b1-->b2 end subgraph three c1-->c2 end