Lorenz Equations

#### Lorenz Equations
\begin{align}
\dot{x} & = \sigma(y-x) \\
\dot{y} & = \rho x - y - xz \\
\dot{z} & = -\beta z + xy
\end{align}


#### Cauchy-Schwarz Inequality
\begin{equation*}
\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)
\end{equation*}



```python
!wget https://github.com/jupyter/notebook/blob/master/docs/source/examples/Notebook/Typesetting%20Equations.ipynb
```

    --2017-08-07 16:43:42--  https://github.com/jupyter/notebook/blob/master/docs/source/examples/Notebook/Typesetting%20Equations.ipynb
    Resolving github.com (github.com)... 192.30.253.112, 192.30.253.113
    Connecting to github.com (github.com)|192.30.253.112|:443... connected.
    HTTP request sent, awaiting response... 200 OK
    Length: unspecified [text/html]
    Saving to: 'Typesetting Equations.ipynb'
    
        [ <=>                                   ] 50,756      --.-K/s   in 0.002s  
    
    2017-08-07 16:43:42 (24.1 MB/s) - 'Typesetting Equations.ipynb' saved [50756]
    



```python

```

98aef697d5ebe2561e300ccd96b5896e4564b9d4
ipynb
Jupyter Notebook
Example 2 Equations in Notebooks.ipynb
davidelbert/mede_example_notebooks_public
89aa118bcd19c378dc47db321c0179e537c38afe
Apache-2.0
Example 2 Equations in Notebooks.ipynb
davidelbert/mede_example_notebooks_public
89aa118bcd19c378dc47db321c0179e537c38afe
Apache-2.0
Example 2 Equations in Notebooks.ipynb
davidelbert/mede_example_notebooks_public
89aa118bcd19c378dc47db321c0179e537c38afe
Apache-2.0
Qwen/Qwen-72B
1. YES
2. YES