chore: update papers, reworking them.

Signed-off-by: Amlal El Mahrouss <amlal@nekernel.org>

1 files changed, 9 insertions, 10 deletions

diff --git a/source/wg04/paper.tex b/source/wg04/paper.tex
index 13b4faf..2aa892d 100644
--- a/source/wg04/paper.tex
+++ b/source/wg04/paper.tex
@@ -22,21 +22,20 @@
 	\rule[0.01cm]{17cm}{0.01cm}
 \end{center}
 
-\section{Formulas definitions}
+\section{Definitions}
 
-Let us define four formulas using the definitons below:
-We assume $x \in \mathbb{R}, \quad n \in \mathbb{N}, \quad 0 < k < a < b < 1$
-\subsection{Sum Integral:}
+We assume $x, y, z \in \mathbb{R}, \quad n \in \mathbb{N}, \quad \cos(\pi) < a < b < \cos(0), \quad t = a$
+\subsection{The A-Integral:}
 \begin{equation}
-    I_{1} \coloneqq n \int_{a}^{b} S(x) dx
+    I_{1} \coloneqq \sum_{n}^{t} \int_{a}^{b} S(x) dx
 \end{equation}
-\subsection{Sum Formula:}
+\subsection{The A-Function:}
 \begin{equation}
-	S(x) \coloneqq \cos(x)\times\sin(x)
+	S(x) : (x, y) \to \mathbb{R}
 \end{equation}
-\subsection{Sum Equation:}
+\subsection{The A-Equation:}
 \begin{equation}
-	I_{2} \coloneqq \int_{k}^{a} Z(x)dx, \quad  Z(x) := (S(x) \times x)
+	T_{2} \coloneqq \int_{a}^{b} E_{1}dx, \quad E_{1} = Z(x) := \frac{(S(x) \cdot y)}{\Delta t \cdot z}
 \end{equation}
-\end{document}
 
+\end{document}