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diff --git a/source/wg04/paper.tex b/source/wg04/paper.tex index e780a6a..3c64e6a 100644 --- a/source/wg04/paper.tex +++ b/source/wg04/paper.tex @@ -34,23 +34,25 @@ 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) dx + I_{1}(x, t, a, b, n) \coloneqq \sum_{n}^{t} \int_{a}^{b} S(x) dx \end{equation} \subsection{DEFINITION OF THE A-FUNCTION:} \begin{equation} - S(x) : (x, y) \to \mathbb{R} + S(x, y) : (x, y) \to \mathbb{R} \end{equation} \subsection{DEFINITION OF THE A-EQUATION:} \begin{equation} - I_{2} \coloneqq \int_{a}^{b} (E_{1})dx, \quad E_{1} = Z(x) := \frac{(S(x) \cdot y)}{\Delta t \cdot z} + I_{2}(x, y, z, a, b, \Delta t) \coloneqq \int_{a}^{b} (E_{1}(x, y, z, \Delta t))dx, \quad E_{1}(x, y, z, \Delta t) := \frac{(S(x) \cdot y)}{\Delta t \cdot z} \end{equation} 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} + K_{n}(u_{n}, a, b) \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} +We will in this paper introduce several equations and their usages in analysis. + \end{document} |