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\rule[0.01cm]{17cm}{0.01cm}
\end{center}
-\section{Definitions}
+\begin{abstract}
+ The paper covers several definitions that are made to be used for sum analysis; their purpose has been kept abstract for flexibility reasons.
+\end{abstract}
+
+\section{DEFINITIONS}
We assume $x \in \mathbb{R}, \quad a, b \in \mathbb{N}, \quad 0 < a < b < \cos(0)$ for:
-\subsection{The S-Integral:}
+\subsection{DEFINITION OF THE S-INTEGRAL:}
\begin{equation}
I_{1} \coloneqq \int_{a}^{b} S(x)dx
\end{equation}
-\subsection{The S-Function:}
+\subsection{DEFINITION OF THE S-FUNCTION:}
\begin{equation}
S(x) = \sum_{k=1}^{t} (\frac{dx}{du}) \cdot x, \quad x > 0, \quad t > k
\end{equation}