From f3d5743283d10f2adbf02f90342051c2ebb5d352 Mon Sep 17 00:00:00 2001
From: Amlal El Mahrouss <amlal@nekernel.org>
Date: Tue, 17 Feb 2026 10:05:41 +0100
Subject: chore: update papers.

Signed-off-by: Amlal El Mahrouss <amlal@nekernel.org>
---
 source/dn001.07/paper.tex | 2 +-
 source/wg04/paper.tex     | 9 ++++++---
 2 files changed, 7 insertions(+), 4 deletions(-)

(limited to 'source')

diff --git a/source/dn001.07/paper.tex b/source/dn001.07/paper.tex
index 896566e..a359469 100644
--- a/source/dn001.07/paper.tex
+++ b/source/dn001.07/paper.tex
@@ -52,7 +52,7 @@ Where $u, u_{0} > 0$ for $S : u \to \mathbb{R}$.
 \begin{proof}
 We assert that:
 \begin{equation}
-    \lim_{n \to +\infty} I(u) \coloneqq B_{n} \to I_{n}, \quad
+    \lim_{n \to +\infty} I_{n}(u) \coloneqq B_{n} \to I_{n}, \quad
 \end{equation}
 If and only if: $B_{0} > 0, \quad B_{n} \in \mathbb{R}$.
 \end{proof}
diff --git a/source/wg04/paper.tex b/source/wg04/paper.tex
index aa0cc59..e780a6a 100644
--- a/source/wg04/paper.tex
+++ b/source/wg04/paper.tex
@@ -23,7 +23,9 @@
 \end{center}
 
 \begin{abstract}
+\begin{center}
     The paper covers several definitions that are made to be used in analysis; their purpose has been kept abstract for flexibility reasons.
+\end{center}
 \end{abstract}
 
 \section{DEFINITIONS}
@@ -32,7 +34,7 @@ This section will cover the definitions and properties of the formulas we will u
 We assume $x, y, z \in \mathbb{R}, \quad n \in \mathbb{N}, \quad \cos(\pi) < a < b, \quad t = a$
 \subsection{DEFINITION OF THE A-INTEGRAL:}
 \begin{equation}
-    I_{1} \coloneqq \sum_{n}^{t} \int_{a}^{b} S(x) d \cdot x
+    I_{1} \coloneqq \sum_{n}^{t} \int_{a}^{b} S(x) dx
 \end{equation}
 \subsection{DEFINITION OF THE A-FUNCTION:}
 \begin{equation}
@@ -40,14 +42,15 @@ We assume $x, y, z \in \mathbb{R}, \quad n \in \mathbb{N}, \quad \cos(\pi) < a <
 \end{equation}
 \subsection{DEFINITION OF THE A-EQUATION:}
 \begin{equation}
-	I_{2} \coloneqq \int_{a}^{b} E_{1}d \cdot x, \quad E_{1} = Z(x) := \frac{(S(x) \cdot y)}{\Delta t \cdot z}
+	I_{2} \coloneqq \int_{a}^{b} (E_{1})dx, \quad E_{1} = Z(x) := \frac{(S(x) \cdot y)}{\Delta t \cdot z}
 \end{equation}
-Where $\Delta t \in \mathbb{R}$ such that $0 < \Delta t$.
+Where $\Delta t \in \mathbb{R}$ if and only if $0 < \Delta t$.
 \subsection{DEFINITION OF THE K-EQUATION:}
 \begin{equation}
 	K_{n} \coloneqq \int_{a}^{b} S_{n}(u_{n}) \quad d \cdot u_{n}, \quad \forall u_{n} \in \mathbb{R}
 \end{equation}
 Where $K_{n} > 0$ such that $S_{n}(u_{n})$ is the A-Function at index $n$ of $u$.
 
+\section{INTRODUCTION}
 
 \end{document}
-- 
cgit v1.2.3