report: simplify subscripts in math mode

doc/report/applications.tex

@@ -16,9 +16,9 @@ and where other data sources are required. Where possible, we evaluate
 proof of concept implementations.
 
 \begin{itemize}
-    \item \textbf{$\mathcal{Q}_{1}$ ``Find theorems with non-elementary
+    \item \textbf{$\mathcal{Q}_1$ ``Find theorems with non-elementary
     proofs.''}  Elementary proofs are those that are considered easy and
-    obvious. In consequence,~$\mathcal{Q}_{1}$ asks for all proofs
+    obvious. In consequence,~$\mathcal{Q}_1$ asks for all proofs
     which are more difficult and not trivial. Of course, just like the
     distinction between ``theorem'' and ``corollary'' is arbitrary, so
     is any judgment about whether a proof is elementary or not.
@@ -41,7 +41,7 @@ proof of concept implementations.
     could count the number of words, references and so on to rate the
     narrative complexity of a proof. This shows that combining
     symbolic knowledge, narrative knowledge and organizational
-    knowledge could allow us to service~$\mathcal{Q}_{1}$ in a
+    knowledge could allow us to service~$\mathcal{Q}_1$ in a
     heuristic fashion.
 
     \textbf{Implementation} Implementing a naive version of the
@@ -77,7 +77,7 @@ proof of concept implementations.
     see that as long as it is based on basic arithmetic, it will be
     possible to formulate in a SPARQL query.
 
-    \item \textbf{$\mathcal{Q}_{2}$ ``Find algorithms that solve
+    \item \textbf{$\mathcal{Q}_2$ ``Find algorithms that solve
     $NP$-complete graph problems.''} Here we want the tetrapodal search
     system to return a listing of algorithms that solve (graph)
     problems with a given property (runtime complexity). We need
@@ -106,7 +106,7 @@ proof of concept implementations.
     (b)~algorithms that compute a given problem. If ULO had such a
     concept, we could then introduce new data predicates that tell us
     something about the properties of problems and
-    algorithms. Organized in such a schema, query~$\mathcal{Q}_{2}$
+    algorithms. Organized in such a schema, query~$\mathcal{Q}_2$
     would be easy to service.
 
     Of course the question here is whether adding another first level
@@ -143,7 +143,7 @@ proof of concept implementations.
     properties of the generating function) or whether such information
     can be deduced from symbolic knowledge.
 
-    \item \textbf{$\mathcal{Q}_{4}$ ``CAS implementation of Gröbner bases that
+    \item \textbf{$\mathcal{Q}_4$ ``CAS implementation of Gröbner bases that
     conform to a definition in AFP.''} Gröbner Bases are a field of
     study in mathematics particular attractive for use in computer
     algebra systems (CAS)~\cite{groebner}. This query is asking for
@@ -151,7 +151,7 @@ proof of concept implementations.
     in the Archive of Formal Proofs (AFP).
 
     We do have ULO/RDF exports for the AFP~\cite{uloisabelle}. Stated
-    like this, we can probably assume that $\mathcal{Q}_{4}$ is a query
+    like this, we can probably assume that $\mathcal{Q}_4$ is a query
     for a very specific definition, identified by an ULO {URI}. No smart
     queries necessary. What is missing is the set of implementations,
     that is symbolic knowledge about actual implementations, and a way
@@ -159,7 +159,7 @@ proof of concept implementations.
     {AFP}. While surely an interesting problem, it is not a task for
     organizational knowledge.
 
-    \item \textbf{$\mathcal{Q}_{5}$ ``All areas of math that {Nicolas G.\
+    \item \textbf{$\mathcal{Q}_5$ ``All areas of math that {Nicolas G.\
     de Bruijn} has worked in and his main contributions.''}  This query
     is asking by works of a given author~$A$.  It also ask for their
     main contributions, e.g.\ what paragraphs or code~$A$ has authored.
@@ -174,7 +174,7 @@ proof of concept implementations.
     first working version, the exports managed by \emph{ulo-storage}
     are enough to service this query.
 
-    As~$\mathcal{Q}_{5}$ is also asking for the main contributions
+    As~$\mathcal{Q}_5$ is also asking for the main contributions
     of~$A$, that is those works that~$A$ authored that are the most
     important. Importance is a quality measure, simply sorting the
     result by number of references might be a good start. Again, this
@@ -210,7 +210,7 @@ proof of concept implementations.
     GROUP BY ?work
     ORDER BY DESC(?refcount)
    \end{lstlisting}
-   We see that we can formulate the idea behind~$\mathcal{Q}_{5}$ with
+   We see that we can formulate the idea behind~$\mathcal{Q}_5$ with
    one not very complicated SPARQL query. Because here everything is
    handled by the database access should be quick.
 \end{itemize}