diff --git a/lib/ftrsd/ftrsd_paper/ftrsd.lyx b/lib/ftrsd/ftrsd_paper/ftrsd.lyx
index 97d7ec16b..2db64d8f1 100644
--- a/lib/ftrsd/ftrsd_paper/ftrsd.lyx
+++ b/lib/ftrsd/ftrsd_paper/ftrsd.lyx
@@ -246,7 +246,7 @@ The minimum Hamming distance of the JT65 code is
 \end_inset
 
 , which means that any particular codeword differs from all other codewords
- in at least 52 or the 63 symbol positions.
+ in at least 52 of the 63 symbol positions.
  
 \end_layout
 
@@ -849,7 +849,7 @@ The FT algorithm uses quality indices made available by a noncoherent 64-FSK
 \end_inset
 
  of the symbol's fractional power 
-\begin_inset Formula $p_{1,\,j}$
+\begin_inset Formula $p_{1,\, j}$
 \end_inset
 
  in a sorted list of 
@@ -919,7 +919,7 @@ t educated guesses to select symbols for erasure.
 , the soft distance between the received word and the codeword: 
 \begin_inset Formula 
 \begin{equation}
-d_{s}=\sum_{j=1}^{n}\alpha_{j}\,(1+p_{1,\,j}).\label{eq:soft_distance}
+d_{s}=\sum_{j=1}^{n}\alpha_{j}\,(1+p_{1,\, j}).\label{eq:soft_distance}
 \end{equation}
 
 \end_inset
@@ -937,7 +937,7 @@ Here
 \end_inset
 
  if the received symbol and codeword symbol are different, and 
-\begin_inset Formula $p_{1,\,j}$
+\begin_inset Formula $p_{1,\, j}$
 \end_inset
 
  is the fractional power associated with received symbol 
@@ -981,7 +981,7 @@ In practice we find that
 \begin_layout Standard
 \begin_inset Formula 
 \begin{equation}
-u=\frac{1}{n}\sum_{j=1}^{n}S(c_{j},\,j).\label{eq:u-metric}
+u=\frac{1}{n}\sum_{j=1}^{n}S(c_{j},\, j).\label{eq:u-metric}
 \end{equation}
 
 \end_inset
@@ -1014,7 +1014,7 @@ The correct JT65 codeword produces a value for
 
  bins containing noise only.
  Thus, if the spectral array 
-\begin_inset Formula $S(i,\,j)$
+\begin_inset Formula $S(i,\, j)$
 \end_inset
 
  has been normalized so that the average value of the noise-only bins is
@@ -1263,7 +1263,7 @@ For each received symbol, define the erasure probability as 1.3 times the
 a priori
 \emph default
  symbol-error probability determined from soft-symbol information 
-\begin_inset Formula $\{p_{1}\textrm{-rank},\,p_{2}/p_{1}\}$
+\begin_inset Formula $\{p_{1}\textrm{-rank},\, p_{2}/p_{1}\}$
 \end_inset
 
 .
@@ -1595,7 +1595,7 @@ If
 \begin_inset Formula $u$
 \end_inset
 
- is the largest found so far, presevre any previous value of 
+ is the largest found so far, preserve any previous value of 
 \begin_inset Formula $u_{1}$
 \end_inset