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diff --git a/source/wg04/paper.tex b/source/wg04/paper.tex index d205919..aa0cc59 100644 --- a/source/wg04/paper.tex +++ b/source/wg04/paper.tex @@ -22,23 +22,28 @@ \rule[0.01cm]{17cm}{0.01cm} \end{center} -\section{Definitions} +\begin{abstract} + The paper covers several definitions that are made to be used in analysis; their purpose has been kept abstract for flexibility reasons. +\end{abstract} +\section{DEFINITIONS} + +This section will cover the definitions and properties of the formulas we will use in this paper. We assume $x, y, z \in \mathbb{R}, \quad n \in \mathbb{N}, \quad \cos(\pi) < a < b, \quad t = a$ -\subsection{The A-Integral:} +\subsection{DEFINITION OF THE A-INTEGRAL:} \begin{equation} I_{1} \coloneqq \sum_{n}^{t} \int_{a}^{b} S(x) d \cdot x \end{equation} -\subsection{The A-Function:} +\subsection{DEFINITION OF THE A-FUNCTION:} \begin{equation} S(x) : (x, y) \to \mathbb{R} \end{equation} -\subsection{The A-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} \end{equation} Where $\Delta t \in \mathbb{R}$ such that $0 < \Delta t$. -\subsection{The K-Equation:} +\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} |