diff options
| -rw-r--r-- | source/wg04/paper.2.tex | 20 | ||||
| -rw-r--r-- | source/wg04/paper.tex | 29 |
2 files changed, 31 insertions, 18 deletions
diff --git a/source/wg04/paper.2.tex b/source/wg04/paper.2.tex index 8bb22e8..c6adff4 100644 --- a/source/wg04/paper.2.tex +++ b/source/wg04/paper.2.tex @@ -18,30 +18,34 @@ \maketitle -\begin{center} - \rule[0.01cm]{17cm}{0.01cm} -\end{center} - \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} +\begin{center} + \rule[0.01cm]{17cm}{0.01cm} +\end{center} + \section{DEFINITIONS} We assume $x \in \mathbb{R}, \quad a, b \in \mathbb{N}, \quad b > a > 0$ for: \subsection{DEFINITION OF THE S-INTEGRAL:} \begin{equation} - I_{1}(a, b, u, n) \coloneqq \int_{a}^{b} S(t, u, n)dt + I_{1}(a, b, u, n) \coloneqq \int_{a}^{b} \Phi(t, u, n)dt \end{equation} -\subsection{DEFINITION OF THE S-FUNCTION:} +\subsection{DEFINITION OF THE $\Phi$-FUNCTION:} \begin{equation} - S(t, u, n) = \sum_{k=1}^{n} (\frac{dt}{du}\cdot u), \quad t > 0, \quad n > k + \Phi(t, u, n) = \sum_{k=1}^{n} (\frac{dt}{du}\cdot u), \quad t > 0, \quad n > k \end{equation} \section{INTRODUCTION} -We will develop our conditions before going to the second part of the paper. +\section{LEMMAS} + +\section{CONCLUSION} + +\section{REFERENCES} \end{document} 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} |