Index

$$ $$

This is the index page. The first page shown by MWiki.

Links to Internal Pages ¶

Bookmarks ¶

Special Hyperlinks Examples ¶

Links to Mastodon Open Source communities:

Paper with DOI Hyperlink:

Time Aware Least Recent Used (TLRU) cache management policy in ICN
- https://doi.org/10.1109/ICACT.2014.6779016

See this arxiv paper:

arxiv:1609.06088 - Time Derivative of Rotation Matrices: a tutorial, shiyu zhao, (2016)

See this Arxiv paper:

Time Derivative of Rotation Matrices: a Tutorial, shiyu zhao, (2016)
- https://arxiv.org/abs/1609.06088

Semantic Scholar Article:

Secure Distribution of Protected Content in Information-Centric Networking - S2CID:198967720

Semantic Scholar Article:

Secure Distribution of Protected Content in Information-Centric Networking
- https://api.semanticscholar.org/CorpusID:198967720

RFC Standards:

See RFC 7231 - Hypertext Transfer Protocol (HTTP/1.1): Semantics and Content

RFC Standards:

Hypertext Transfer Protocol (HTTP/1.1): Semantics and Content
- https://datatracker.ietf.org/doc/html/rfc7231

Python PEP (1):

Python WSGI - Webserver Gateway Interface PEP 333

Python PEP (2):

Python WSGI - Webserver Gateway Interface
- https://peps.python.org/pep-333
- Abstract: This document specifies a proposed standard interface between web servers and Python web applications or frameworks, to promote web application portability across a variety of web servers.

Hyperlink to CVE (Common Vulnerability Exposures):

See: <cve:CVE-2024-53104>: CVE-2024-53104
See: <r-cve:CVE-2024-53104>: https://www.cve.org/CVERecord?id=CVE-2024-53104
Brief: media: uvcvideo: Skip parsing frames of type UVC_VS_UNDEFINED in uvc_parse_format

Internal Pages ¶

Hyperlinks to internal pages that still does not exist will be shown in red, while hyperlinks to existing internal pages will be shown as green.

Images ¶

Image of Java Duke Mascot (External Image):

![Java's Duke Mascot](/static/example_java_duke_mascot.svg)

Internal Image:

logo-java-coffee-cup.png

![[logo-java-coffee-cup.png]]

Copying and pasting images.

If the website is served using https (http + TLS), it is possible to paste images from other web pages (web sites) or documents. First click at the image to copied to the clipboard with the right mouse right button and select copy. Then hit Ctrl+v or right click to the open context meny and click at paste on the Wiki page editor. Pasted images are always saved in the folder <path-to-wiki-folder>/pasted

For instance, this Python logo image whose MWiki markdown is

![[pasted-image-1743470376610.png]]

corresponds to the file

./sample-wiki/pasted/pasted-image-1743470376610.png

Figure ¶

Figure of Java Duke Mascot (External Image)

```{figure} /static/example_java_duke_mascot.svg
:width: 200px
:alt: Java duke mascot, one of the symbols of the Java programming language.

Java's Duke mascot
```

Java duke mascot, one of the symbols of the Java programming language.

Figure 1: Java's Duke mascot

Internal Figure

```{figure} ![[logo-java-coffee-cup.png]]
:name: unique-identifier-of-the-image-optional
:height: 200px
:alt: An iconic symbol of the Java programming language. Note the alt text should provide a detailed description of the image for better accessibility.

Java coffee cup symbol. 
```

Figure 2: Java coffee cup symbol.

Math ¶

Definition ¶

DEFINITION: (Inverse Matrix)

The inverse matrix $A^{-1}$ of a matrix $A: n \times n$ is defined as a matrix that when multiplied by the square matrix A yields the identity matrix. Note that not always an inverse matrix of a square matrix Q exists.

\notag A^{-1} A \triangleq A^{-1} \triangleq \mathbf{I}

Theorem ¶

THEOREM 1: (Determinant of Orthogonal Matrix)

The determinant of a orthogonal matrix $Q \in \mathbb{R}^{n \times n}$ of n rows and n columns is always 1.

\notag \det(Q) = 1

Proof

\notag \begin{split} \det (Q Q^T) &= \det(Q) \det(Q^{T}) \\ \det (Q Q^T) &= \det(Q) \det(Q) \\ \det (Q Q^{-1}) &= \det(Q) \det(Q) \\ \det (\mathbf{I}) &= \det(Q)^2 \\ 1 &= \det{Q}^2 \\ \det(Q) &= 1 \end{split}

Solved Exercise ¶

Example: Chain Rule for Derivative Multi-Variate Functions

Let the function f be $$f(x, y) = x^2/A^2 + y^2/B^2 - C$$ . Find the derivative of f with respect to t. And x and y are functions of t, $x = x(t) = A \cos t$ and $y = y(t) = B \sin t$ .

Solution

\notag \begin{split} \frac{df}{dt} &= \frac{\partial f}{\partial x} \frac{dx}{dt} + \frac{\partial f}{\partial y} \frac{dy}{dt} \\ &= \frac{\partial}{\partial x} (x^2/A^2 + y^2/B^2 - C) \frac{d}{dt} ( A \cos t) \\ & + \frac{\partial}{\partial y} (x^2/A^2 + y^2/B^2 - C) \frac{d}{dt} ( A \sin t) \\ &= (2x/A^2) (-A \sin t) + (2y/B^2) (A \cos t) \\ &= -2x \sin(t) / A + 2y \cos(t) / B \\ &= -2(A \cos(t)) \sin(t) / A + 2(B \sin(t)) \cos(t) / B \\ &= -2 \cos t \sin t + 2 \sin t \cos t \\ &= 0 \end{split}

Pseudocode of Algorithms in LaTeX ¶

Code in LaTeX:

```{pseudo}
\begin{algorithm}
\caption{Buble Sort Algorithm}
\begin{algorithmic}
\PROCEDURE{BubbleSort}{$A, n$}
   \STATE $B = $ \CALL{CopyArray}{$A, n$}
   \STATE $\:$ \textit{// i = 0, 1, ..., n - 1}
   \FOR{$i = 0$ \TO  $i < n$}
       \STATE $\:$ \textit{// j = 0, 1, ..., n - 2 }
       \FOR{$j = 0$ \TO $j < n - 1$}
           \IF{$B[j] > B[j+1]$}
               \STATE swap $B[j]$ with $B[j+1]$
           \ENDIF
       \ENDFOR
   \ENDFOR
   \RETURN{$B$}
\ENDPROCEDURE
\end{algorithmic}
\end{algorithm}
```

Rendering:

\begin{algorithm}
\caption{Buble Sort Algorithm}
\begin{algorithmic}
\PROCEDURE{BubbleSort}{$A, n$}
   \STATE $B = $ \CALL{CopyArray}{$A, n$}
   \STATE $\:$ \textit{// i = 0, 1, ..., n - 1}
   \FOR{$i = 0$ \TO  $i < n$}
       \STATE $\:$ \textit{// j = 0, 1, ..., n - 2 }
       \FOR{$j = 0$ \TO $j < n - 1$}
           \IF{$B[j] > B[j+1]$}
               \STATE swap $B[j]$ with $B[j+1]$
           \ENDIF
       \ENDFOR
   \ENDFOR
   \RETURN{$B$}
\ENDPROCEDURE
\end{algorithmic}
\end{algorithm}