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Diffstat (limited to 'source')
| -rw-r--r-- | source/dn001.07/paper.tex | 2 | ||||
| -rw-r--r-- | source/wg04/paper.tex | 9 |
2 files changed, 7 insertions, 4 deletions
diff --git a/source/dn001.07/paper.tex b/source/dn001.07/paper.tex index 896566e..a359469 100644 --- a/source/dn001.07/paper.tex +++ b/source/dn001.07/paper.tex @@ -52,7 +52,7 @@ Where $u, u_{0} > 0$ for $S : u \to \mathbb{R}$. \begin{proof} We assert that: \begin{equation} - \lim_{n \to +\infty} I(u) \coloneqq B_{n} \to I_{n}, \quad + \lim_{n \to +\infty} I_{n}(u) \coloneqq B_{n} \to I_{n}, \quad \end{equation} If and only if: $B_{0} > 0, \quad B_{n} \in \mathbb{R}$. \end{proof} diff --git a/source/wg04/paper.tex b/source/wg04/paper.tex index aa0cc59..e780a6a 100644 --- a/source/wg04/paper.tex +++ b/source/wg04/paper.tex @@ -23,7 +23,9 @@ \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} @@ -32,7 +34,7 @@ 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) d \cdot x + I_{1} \coloneqq \sum_{n}^{t} \int_{a}^{b} S(x) dx \end{equation} \subsection{DEFINITION OF THE A-FUNCTION:} \begin{equation} @@ -40,14 +42,15 @@ We assume $x, y, z \in \mathbb{R}, \quad n \in \mathbb{N}, \quad \cos(\pi) < a < \end{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} + I_{2} \coloneqq \int_{a}^{b} (E_{1})dx, \quad E_{1} = Z(x) := \frac{(S(x) \cdot y)}{\Delta t \cdot z} \end{equation} -Where $\Delta t \in \mathbb{R}$ such that $0 < \Delta t$. +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} \end{equation} Where $K_{n} > 0$ such that $S_{n}(u_{n})$ is the A-Function at index $n$ of $u$. +\section{INTRODUCTION} \end{document} |