diff --git a/lepaper/arrayscat.lyx b/lepaper/arrayscat.lyx
index bcf4666..0bfa8d9 100644
--- a/lepaper/arrayscat.lyx
+++ b/lepaper/arrayscat.lyx
@@ -597,11 +597,11 @@ Category: Methods and Algorithms for Scientific Computing?
 \end_layout
 
 \begin_layout Abstract
-The (somewhat underrated) T-matrix multiple scattering method (TMMSM) can
- be used to solve the electromagnetic response of systems consisting of
- many compact scatterers, retaining a good level of accuracy while using
- relatively few of degrees of freedom, largely surpassing other methods
- in the number of scatterers it can deal with.
+The T-matrix multiple scattering method (TMMSM) can be used to solve the
+ electromagnetic response of systems consisting of many compact scatterers,
+ retaining a good level of accuracy while using relatively few degrees of
+ freedom, largely surpassing other methods in the number of scatterers it
+ can deal with.
 \end_layout
 
 \begin_layout Abstract
diff --git a/lepaper/finite.lyx b/lepaper/finite.lyx
index f2e7433..a24084f 100644
--- a/lepaper/finite.lyx
+++ b/lepaper/finite.lyx
@@ -488,7 +488,7 @@ noprefix "false"
 
  around the origin (typically due to presence of a scatterer), one has to
  add the outgoing VSWFs 
-\begin_inset Formula $\vswfrtlm{\tau}lm\left(\kappa\vect r\right)$
+\begin_inset Formula $\vswfouttlm{\tau}lm\left(\kappa\vect r\right)$
 \end_inset
 
  to have a complete basis of the solutions in the volume 
@@ -608,7 +608,7 @@ transition matrix,
 \begin_inset Formula $T$
 \end_inset
 
--matrix we can solve the single-patricle scatering prroblem simply by substituti
+-matrix we can solve the single-particle scattering problem simply by substituti
 ng appropriate expansion coefficients 
 \begin_inset Formula $\rcoefftlm{\tau'}{l'}{m'}$
 \end_inset
@@ -680,12 +680,12 @@ literal "false"
 
 , but in general one can find them numerically by simulating scattering
  of a regular spherical wave 
-\begin_inset Formula $\vswfouttlm{\tau}lm$
+\begin_inset Formula $\vswfrtlm{\tau}lm$
 \end_inset
 
  and projecting the scattered fields (or induced currents, depending on
  the method) onto the outgoing VSWFs 
-\begin_inset Formula $\vswfrtlm{\tau}{'l'}{m'}$
+\begin_inset Formula $\vswfouttlm{\tau'}{l'}{m'}$
 \end_inset
 
 .
@@ -974,15 +974,67 @@ noprefix "false"
 \begin_inset Formula $\mezikuli{R^{<}}{R^{>}}{\vect 0}$
 \end_inset
 
- via by electromagnetic radiation is
+ by electromagnetic radiation is
 \begin_inset Formula 
 \begin{equation}
-P=\frac{1}{2\kappa^{2}\eta_{0}\eta}\left(\Re\left(\rcoeffp{}^{\dagger}\outcoeffp{}\right)+\left\Vert \outcoeffp{}\right\Vert ^{2}\right)=\frac{1}{2\kappa^{2}\eta_{0}\eta}\rcoeffp{}^{\dagger}\left(\Tp{}^{\dagger}\Tp{}+\frac{\Tp{}^{\dagger}+\Tp{}}{2}\right)\rcoeffp{}.\label{eq:Power transport}
+P=\frac{1}{2\kappa^{2}\eta_{0}\eta}\left(\Re\left(\rcoeffp{}^{\dagger}\outcoeffp{}\right)+\left\Vert \outcoeffp{}\right\Vert ^{2}\right)=\frac{1}{2\kappa^{2}\eta_{0}\eta}\rcoeffp{}^{\dagger}\left(\Tp{}^{\dagger}\Tp{}+\frac{\Tp{}^{\dagger}+\Tp{}}{2}\right)\rcoeffp{},\label{eq:Power transport}
 \end{equation}
 
 \end_inset
 
-In realistic scattering setups, power is transferred by radiation into 
+where 
+\begin_inset Formula $\eta_{0}=\sqrt{\mu_{0}/\varepsilon_{0}}$
+\end_inset
+
+ and 
+\begin_inset Formula $\eta=\sqrt{\mu/\varepsilon}$
+\end_inset
+
+ are wave impedance of vacuum and relative wave impedance of the medium
+ in 
+\begin_inset Formula $\mezikuli{R^{<}}{R^{>}}{\vect 0}$
+\end_inset
+
+, respectively.
+ 
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\nospellcheck off
+\bar no
+\strikeout off
+\xout off
+\uuline off
+\uwave off
+\noun off
+\color none
+
+\begin_inset Formula $P$
+\end_inset
+
+ is well-defined only when 
+\begin_inset Formula $\eta$
+\end_inset
+
+ is real.
+
+\family default
+\series default
+\shape default
+\size default
+\emph default
+\nospellcheck default
+\bar default
+\strikeout default
+\xout default
+\uuline default
+\uwave default
+\noun default
+\color inherit
+ In realistic scattering setups, power is transferred by radiation into
+ 
 \begin_inset Formula $\openball{R^{<}}{\vect 0}$
 \end_inset
 
@@ -1319,7 +1371,7 @@ where
 \begin_inset Formula $T$
 \end_inset
 
-is a block-diagonal matrix containing all the individual 
+ is a block-diagonal matrix containing all the individual 
 \begin_inset Formula $T$
 \end_inset
 
@@ -1357,9 +1409,12 @@ In practice, the multiple-scattering problem is solved in its truncated
 \begin_inset Formula $\tau lm$
 \end_inset
 
--multiindices left.
+-multi-indices left.
  The truncation degree can vary for different scatterers (e.g.
- due to different physical sizes), so the truncated block 
+\begin_inset space \space{}
+\end_inset
+
+due to different physical sizes), so the truncated block 
 \begin_inset Formula $\left[\tropsp pq\right]_{l_{q}\le L_{q};l_{p}\le L_{q}}$
 \end_inset
 
@@ -1394,7 +1449,7 @@ If no other type of truncation is done, there remain
 \begin_inset Formula $\tau lm$
 \end_inset
 
--multiindices for 
+-multi-indices for the 
 \begin_inset Formula $p$
 \end_inset
 
diff --git a/lepaper/intro.lyx b/lepaper/intro.lyx
index 757ec3a..997c552 100644
--- a/lepaper/intro.lyx
+++ b/lepaper/intro.lyx
@@ -117,7 +117,7 @@ Some refs here?
 
 \end_inset
 
- The most commonly used general approaches used in computational electrodynamics
+ The most common general approaches used in computational electrodynamics
  are often unsuitable for simulating systems with larger number of scatterers
  due to their computational complexity: differential methods such as the
  finite difference time domain (FDTD) method or the finite element method
@@ -159,8 +159,8 @@ literal "false"
 
 \begin_layout Standard
 The natural way to overcome both limitations of CDA mentioned above is to
- include higher multipoles into account.
- Instead of polarisability tensor, the scattering properties of an individual
+ take higher multipoles into account.
+ Instead of a polarisability tensor, the scattering properties of an individual
  particle are then described with more general 
 \begin_inset Formula $T$
 \end_inset
@@ -280,20 +280,10 @@ TODO refs to the code repositories once it is published.
  The features include computations of electromagnetic response to external
  driving, the related cross sections, and finding resonances of finite structure
 s.
- Moreover, it includes the improvements covered in this paper, enabling
+ Moreover, it includes the improvements covered in this article, enabling
  to simulate even larger systems and also infinite structures with periodicity
- in one, two or three dimensions, which can be used e.g.
- for quickly evaluating dispersions of such structures
-\begin_inset Marginal
-status open
-
-\begin_layout Plain Layout
-And also their topological invariants (TODO)?
-\end_layout
-
-\end_inset
-
-.
+ in one or two or three dimensions, which can be used e.g.
+ for quickly evaluating dispersions of such structures.
  The QPMS suite contains a core C library, Python bindings and several utilities
  for routine computations.
 \begin_inset Marginal