From: couchot Date: Wed, 22 Jul 2015 06:47:19 +0000 (+0200) Subject: referencesdéfiniesplusieurs fois X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/hdrcouchot.git/commitdiff_plain/020defdbb2ac938563eba1071c78520973093e4b?ds=inline;hp=23f35c6593b3de7d37b266c9ef6c35da97d98998 referencesdéfiniesplusieurs fois --- diff --git a/12TIPE.tex b/12TIPE.tex index 4cbc26d..85efe78 100644 --- a/12TIPE.tex +++ b/12TIPE.tex @@ -119,7 +119,7 @@ Leur preuve est donnée en annexe~\ref{anx:chaos:unaire}. \end{theorem} \begin{theorem} -\label{Prop: T est dans R} $\mathcal{T} \subset \mathcal{R}$. +\label{Prop: T est dans R:u} $\mathcal{T} \subset \mathcal{R}$. \end{theorem} On peut conclure que $\mathcal{C} = \mathcal{R} \cap \mathcal{T} diff --git a/14Secrypt.tex b/14Secrypt.tex index b7cb0d3..d4f76f4 100644 --- a/14Secrypt.tex +++ b/14Secrypt.tex @@ -83,7 +83,7 @@ bistoc(X):- allpositive(S4). \end{lstlisting} \end{scriptsize} -\caption{Prolog Problem to Find DSSC Matrix when $n=2$}\label{fig:prolog} +\caption{Code PROLOG permettant de trouver toutes les matrices DSSC pour $n=2$}\label{fig:prolog} \end{figure} Enfin, on définit la relation $\mathcal{R}$, qui est établie pourles deux @@ -156,7 +156,8 @@ Cependant, le graphe $\textsc{giu}(f^*)$ (donné à la Figure~\ref{fig:iteration:f*}) est le $3$-cube dans lequel le cycle $000,100,101,001,011,111,110,010,000$ -a été enlevé. +a été enlevé. Dans cette figure, le le graphe $\textsc{giu}(f)$ est +en continu tandis que le cycle est en pointillés. Ce cycle qui visite chaque n{\oe}ud exactement une fois est un \emph{cycle hamiltonien}. La matrice de Markov correspondante est donnée à @@ -173,7 +174,7 @@ On s'intéresse par la suite à la génération de ce genre de cycles. \label{fig:iteration:f*}]{ \begin{minipage}{0.55\linewidth} \centering - \includegraphics[width=\columnwidth]{images/iter_f0c}% + \includegraphics[width=\columnwidth]{images/iter_f0d}% \end{minipage} }% \subfigure[Matrice de Markov associée à $\textsc{giu}(f^*)$ diff --git a/15TSI.tex b/15TSI.tex index 7d1d842..76e0203 100644 --- a/15TSI.tex +++ b/15TSI.tex @@ -26,7 +26,7 @@ $x^0\in\Bool^{\mathsf{N}}$ et une stratégie $S = \left(s_t\right)_{t \in \math \in \mathcal{P}(\{1, \ldots, {\mathsf{N}}\})^{\Nats}$, les configurations $x^t$ sont définies par la récurrence -\begin{equation}\label{eq:asyn} +\begin{equation}\label{eq:asyn:g} x^{t+1}=F_{f_g}(s_t,x^t). \end{equation} Soit alors $G_{f_g}$ une fonction de $\Bool^{\mathsf{N}} \times \mathcal{P}(\{1, \ldots, {\mathsf{N}}\})^{\Nats}$ @@ -93,12 +93,12 @@ annexe~\ref{anx:chaos:generalise}. \end{theorem} \begin{theorem} -\label{Prop: T est dans R} $\mathcal{T} \subset \mathcal{R}$. +\label{Prop: T est dans R:g} $\mathcal{T} \subset \mathcal{R}$. \end{theorem} \begin{theorem}%[Characterization of $\mathcal{C}$] -\label{Th:CaracIC} +\label{Th:CaracIC:g} Soit $f:\Bool^{\mathsf{N}}\to\Bool^{\mathsf{N}}$. La fonction $G_{f_g}$ est chaotique si et seulement si $\textsc{gig}(f)$ est fortement connexe. \end{theorem} diff --git a/caracgeneralise.tex b/caracgeneralise.tex index 0427db8..54d99af 100644 --- a/caracgeneralise.tex +++ b/caracgeneralise.tex @@ -56,7 +56,7 @@ par contraposée, on a la démonstration souhaitée. Prouvons à présent le théorème suivant: \begin{theorem} -\label{Prop: T est dans R} $\mathcal{T} \subset \mathcal{R}$. +\label{Prop: T est dans R:gp} $\mathcal{T} \subset \mathcal{R}$. \end{theorem} @@ -91,7 +91,7 @@ On peut conclure que $\mathcal{C} = \mathcal{R} \cap \mathcal{T} = \mathcal{T}$. On a alors la caractérisation suivante: \begin{theorem}%[Characterization of $\mathcal{C}$] -\label{Th:CaracIC} +\label{Th:CaracIC:gp} Soit $f:\Bool^{\mathsf{N}}\to\Bool^{\mathsf{N}}$. La fonction $G_{f_g}$ est chaotique si et seulement si $\textsc{gig}(f)$ est fortement connexe. \end{theorem} diff --git a/caracunaire.tex b/caracunaire.tex index c74aaf0..1111939 100644 --- a/caracunaire.tex +++ b/caracunaire.tex @@ -94,7 +94,7 @@ On peut conclure que $\mathcal{C} = \mathcal{R} \cap \mathcal{T} = \mathcal{T}$. On a alors la caractérisation suivante: \begin{theorem}%[Characterization of $\mathcal{C}$] -\label{Th:CaracIC} +\label{Th:CaracIC:up} Soit $f:\Bool^{\mathsf{N}}\to\Bool^{\mathsf{N}}$. 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