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Diffstat (limited to 'source/wg04/paper.tex')
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1 files changed, 19 insertions, 10 deletions
diff --git a/source/wg04/paper.tex b/source/wg04/paper.tex index 9480ba1..9169d08 100644 --- a/source/wg04/paper.tex +++ b/source/wg04/paper.tex @@ -18,31 +18,31 @@ \maketitle -\begin{center} - \rule[0.01cm]{17cm}{0.01cm} -\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} +\begin{center} + \rule[0.01cm]{17cm}{0.01cm} +\end{center} -The section covers definitions, and properties of the formulas we will use in this paper. +\section{DEFINITION} + +We define the following formulas to establish our proofs: \subsection{DEFINITION OF THE A-INTEGRAL:} \begin{equation} I_{1}(t, a, b, n) \coloneqq \sum_{k=t}^{n} \int_{a}^{b} Z(u) du \end{equation} \subsection{DEFINITION OF THE A-FUNCTION:} -Let a function be: +Let a function which returns a value in $\mathbb{R}$ be: \begin{equation} Z(x) : (0, x) \to \mathbb{R} \end{equation} -Named $Z(x) \in \mathbb{R}$. -\subsection{DEFINITION OF THE A-EQUATION:} +Named $Z(x) \in \mathbb{R}$. Such that $Z(x)$ is a compute-function of argument $x$. +\subsection{DEFINITION OF THE A-EQUATION AND I-INTEGRAL:} \begin{equation} I_{2}(y, z, t, a, b) \coloneqq \int_{a}^{b} E_{1}(x, y, z, t) dx, \quad E_{1}(x, y, z, t) := Z(x \cdot t, y \cdot z) \end{equation} @@ -55,6 +55,15 @@ Where $K_{n} > 0$ and $Z_{n}(u_{n})$ is an A-Function of index $n$ at $u$. \section{INTRODUCTION} -We will in this paper introduce several equations and their usages in analysis. +\section{LEMMAS} + +\subsection{LEMMA ONE: THE A-LEMMA:} + +\subsection{LEMMA TWO: THE K-LEMMA:} + +\section{CONCLUSION} + +\section{REFERENCES} + \end{document} |