typos and merge problems

doc/src/week48/week48.do.txt

@@ -203,7 +203,7 @@ We can rewrite this (see the solutions below) in terms of a convex optimization
 !bt
 \begin{align*}
     &\mathrm{min}_{\lambda}\hspace{0.2cm} \frac{1}{2}\bm{\lambda}^T\bm{P}\bm{\lambda}+\bm{q}^T\bm{\lambda},\\ \nonumber
-    &\mathrm{subject\hspace{0.1cm}to} \hspace{0.2cm} \bm{G}\bm{\lambda} \preceq \bm{h} \hspace{0.2cm} \wedge \bm{A}\bm{\lambda}=f.
+    &\mathrm{s.t} \hspace{0.2cm} \bm{G}\bm{\lambda} \preceq \bm{h} \hspace{0.2cm} \wedge \bm{A}\bm{\lambda}=f.
 \end{align*}
 !et
 Below we discuss how to solve these equations. Here we note that the matrix $\bm{P}$ has matrix elements $p_{ij}=y_iy_jK(\bm{x}_i,\bm{x}_j)$.
@@ -490,12 +490,13 @@ We remind ourselves about the general problem we want to solve
     &\mathrm{s.t.} \hspace{0.2cm} \bm{G}\bm{x} \preceq \bm{h} \wedge  \bm{A}\bm{x}=f.
 \end{align*}
 !et
-Note: we use _s.t._ for subject to. 
+_Note_: we use _s.t._ for subject to. 
+
 Let us show how to perform the optmization using a simple case. Assume we want to optimize the following problem
 !bt
 \begin{align*}
     &\mathrm{min}_{x}\hspace{0.2cm} \frac{1}{2}x^2+5x+3y \\ \nonumber
-    &\mathrm{subject to} \\ \nonumber
+    &\mathrm{s.t.} \\ \nonumber
     &x, y \geq 0 \\ \nonumber
     &x+3y  \geq 15 \\ \nonumber
     &2x+5y  \leq  100 \\ \nonumber