fixed curved line in uml meta model diagram.

Added an interpretation of the UML meta model showing how
it is inherently hierarchical.

submission_thesis/CH4_FMMD/copy.tex

@@ -931,6 +931,32 @@ this can be expressed as  $$ \derivec : \mathcal{\FG}  \rightarrow \mathcal{{\DC
 \end{figure}
 
 
+%% Here we need how this meta model translates into the FMMD Hierarchy
+
+\subsection{How the UML Meta Model maps to an FMMD Hierarchy}
+
+The UML meta model above (see figure~\ref{fig:cfg}) describes a hierarchical structure. %% Might be a UML pattern that is well known ..... 05MAY2012
+This is because, as {\dcs} inherit the properties of 
+components, {\dcs} may be used to form {\fgs}.
+%
+Consider the hierarchy from the example in figure~\ref{fig:dc2}.
+The lowest level in this hierarchy are the {\bcs}, the resistors and the op-amp.
+%
+The resistors are collected into a {\fg}, and the ${PD}$ derived component is created above them.
+%
+As this derived component inherits the properties of a component we may use
+it in {\fg} higher in the hierarchy. 
+%
+The $PD$ derived component is now placed into a functional group
+with the op-amp. 
+%
+This {\fg} is now analysed and the a {\dc} created to 
+represent the failure mode behaviour of the $INVAMP$.
+%
+We may now use the  $INVAMP$ {\dc} in even higher level {\fgs}.
+
+
+
 \subsection{Keeping track of the derived components position in the hierarchy}
 \label{sec:alpha}
 The UML meta model in figure \ref{fig:cfg}, shows the relationships