diff --git a/lepaper/arrayscat.lyx b/lepaper/arrayscat.lyx
index 36a9fbf..01b2c2e 100644
--- a/lepaper/arrayscat.lyx
+++ b/lepaper/arrayscat.lyx
@@ -5,18 +5,21 @@
 \save_transient_properties true
 \origin unavailable
 \textclass article
+\begin_preamble
+\DeclareUnicodeCharacter{0428}{Ш }
+\end_preamble
 \use_default_options true
 \maintain_unincluded_children false
 \language english
 \language_package default
-\inputencoding auto-legacy
+\inputencoding utf8
 \fontencoding auto
 \font_roman "default" "TeX Gyre Pagella"
 \font_sans "default" "default"
 \font_typewriter "default" "default"
 \font_math "auto" "auto"
 \font_default_family default
-\use_non_tex_fonts true
+\use_non_tex_fonts false
 \font_sc false
 \font_roman_osf true
 \font_sans_osf false
@@ -26,10 +29,12 @@
 \use_microtype false
 \use_dash_ligatures true
 \graphics default
-\default_output_format pdf4
+\default_output_format default
 \output_sync 0
 \bibtex_command default
 \index_command default
+\float_placement class
+\float_alignment class
 \paperfontsize default
 \spacing single
 \use_hyperref true
@@ -270,12 +275,12 @@
 
 
 \begin_inset FormulaMacro
-\newcommand{\rcoeffptlm}[4]{\rcoeffp{#1}_{#2#3#4}}
+\newcommand{\rcoeffptlm}[4]{\rcoeffp{#1,#2#3#4}}
 \end_inset
 
 
 \begin_inset FormulaMacro
-\newcommand{\rcoeffincptlm}[4]{\rcoeffincp{#1}_{#2#3#4}}
+\newcommand{\rcoeffincptlm}[4]{\rcoeffincp{#1,#2#3#4}}
 \end_inset
 
 
@@ -290,7 +295,7 @@
 
 
 \begin_inset FormulaMacro
-\newcommand{\outcoeffptlm}[4]{\outcoeffp{#1}_{#2#3#4}}
+\newcommand{\outcoeffptlm}[4]{\outcoeffp{#1,#2#3#4}}
 \end_inset
 
 
@@ -397,6 +402,11 @@ These are compatibility macros for the (...)-old files:
 \end_inset
 
 
+\begin_inset FormulaMacro
+\newcommand{\Kp}{K}
+\end_inset
+
+
 \end_layout
 
 \begin_layout Title
@@ -675,6 +685,17 @@ literal "true"
 \end_inset
 
 
+\end_layout
+
+\begin_layout Standard
+\begin_inset CommandInset include
+LatexCommand include
+filename "infinite-old.lyx"
+literal "true"
+
+\end_inset
+
+
 \end_layout
 
 \begin_layout Standard
diff --git a/lepaper/comparison.lyx b/lepaper/comparison.lyx
index 41e96c1..6257c19 100644
--- a/lepaper/comparison.lyx
+++ b/lepaper/comparison.lyx
@@ -1,29 +1,37 @@
-#LyX 2.1 created this file. For more info see http://www.lyx.org/
-\lyxformat 474
+#LyX 2.4 created this file. For more info see https://www.lyx.org/
+\lyxformat 583
 \begin_document
 \begin_header
+\save_transient_properties true
+\origin unavailable
 \textclass article
 \use_default_options true
 \maintain_unincluded_children false
-\language finnish
+\language english
 \language_package default
-\inputencoding auto
-\fontencoding global
-\font_roman TeX Gyre Pagella
-\font_sans default
-\font_typewriter default
-\font_math auto
+\inputencoding utf8
+\fontencoding auto
+\font_roman "default" "TeX Gyre Pagella"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
 \font_default_family default
-\use_non_tex_fonts true
+\use_non_tex_fonts false
 \font_sc false
-\font_osf true
-\font_sf_scale 100
-\font_tt_scale 100
+\font_roman_osf true
+\font_sans_osf false
+\font_typewriter_osf false
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures true
 \graphics default
-\default_output_format pdf4
+\default_output_format default
 \output_sync 0
 \bibtex_command default
 \index_command default
+\float_placement class
+\float_alignment class
 \paperfontsize default
 \spacing single
 \use_hyperref true
@@ -59,6 +67,8 @@
 \suppress_date false
 \justification true
 \use_refstyle 1
+\use_minted 0
+\use_lineno 0
 \index Index
 \shortcut idx
 \color #008000
@@ -67,10 +77,14 @@
 \tocdepth 3
 \paragraph_separation indent
 \paragraph_indentation default
-\quotes_language swedish
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style english
+\dynamic_quotes 0
 \papercolumns 1
 \papersides 1
 \paperpagestyle default
+\tablestyle default
 \tracking_changes false
 \output_changes false
 \html_math_output 0
diff --git a/lepaper/examples.lyx b/lepaper/examples.lyx
index 40ab743..dee469a 100644
--- a/lepaper/examples.lyx
+++ b/lepaper/examples.lyx
@@ -1,5 +1,5 @@
-#LyX 2.3 created this file. For more info see http://www.lyx.org/
-\lyxformat 544
+#LyX 2.4 created this file. For more info see https://www.lyx.org/
+\lyxformat 583
 \begin_document
 \begin_header
 \save_transient_properties true
@@ -7,27 +7,31 @@
 \textclass article
 \use_default_options true
 \maintain_unincluded_children false
-\language finnish
+\language english
 \language_package default
-\inputencoding auto
-\fontencoding global
+\inputencoding utf8
+\fontencoding auto
 \font_roman "default" "TeX Gyre Pagella"
 \font_sans "default" "default"
 \font_typewriter "default" "default"
 \font_math "auto" "auto"
 \font_default_family default
-\use_non_tex_fonts true
+\use_non_tex_fonts false
 \font_sc false
-\font_osf true
+\font_roman_osf true
+\font_sans_osf false
+\font_typewriter_osf false
 \font_sf_scale 100 100
 \font_tt_scale 100 100
 \use_microtype false
 \use_dash_ligatures true
 \graphics default
-\default_output_format pdf4
+\default_output_format default
 \output_sync 0
 \bibtex_command default
 \index_command default
+\float_placement class
+\float_alignment class
 \paperfontsize default
 \spacing single
 \use_hyperref true
@@ -63,6 +67,7 @@
 \justification true
 \use_refstyle 1
 \use_minted 0
+\use_lineno 0
 \index Index
 \shortcut idx
 \color #008000
@@ -73,11 +78,12 @@
 \paragraph_indentation default
 \is_math_indent 0
 \math_numbering_side default
-\quotes_style swedish
+\quotes_style english
 \dynamic_quotes 0
 \papercolumns 1
 \papersides 1
 \paperpagestyle default
+\tablestyle default
 \tracking_changes false
 \output_changes false
 \html_math_output 0
diff --git a/lepaper/finite-cs.lyx b/lepaper/finite-cs.lyx
index 28072a4..a6bfc45 100644
--- a/lepaper/finite-cs.lyx
+++ b/lepaper/finite-cs.lyx
@@ -7,16 +7,16 @@
 \textclass article
 \use_default_options true
 \maintain_unincluded_children false
-\language finnish
+\language english
 \language_package default
-\inputencoding auto-legacy
+\inputencoding utf8
 \fontencoding auto
 \font_roman "default" "TeX Gyre Pagella"
 \font_sans "default" "default"
 \font_typewriter "default" "default"
 \font_math "auto" "auto"
 \font_default_family default
-\use_non_tex_fonts true
+\use_non_tex_fonts false
 \font_sc false
 \font_roman_osf true
 \font_sans_osf false
@@ -26,10 +26,12 @@
 \use_microtype false
 \use_dash_ligatures false
 \graphics default
-\default_output_format pdf4
+\default_output_format default
 \output_sync 0
 \bibtex_command default
 \index_command default
+\float_placement class
+\float_alignment class
 \paperfontsize default
 \spacing single
 \use_hyperref true
@@ -77,7 +79,7 @@
 \paragraph_indentation default
 \is_math_indent 0
 \math_numbering_side default
-\quotes_style swedish
+\quotes_style english
 \dynamic_quotes 0
 \papercolumns 1
 \papersides 1
diff --git a/lepaper/finite-old.lyx b/lepaper/finite-old.lyx
index 84eb30e..c6721bb 100644
--- a/lepaper/finite-old.lyx
+++ b/lepaper/finite-old.lyx
@@ -1,29 +1,37 @@
-#LyX 2.1 created this file. For more info see http://www.lyx.org/
-\lyxformat 474
+#LyX 2.4 created this file. For more info see https://www.lyx.org/
+\lyxformat 583
 \begin_document
 \begin_header
+\save_transient_properties true
+\origin unavailable
 \textclass article
 \use_default_options true
 \maintain_unincluded_children false
-\language finnish
+\language english
 \language_package default
-\inputencoding auto
-\fontencoding global
-\font_roman TeX Gyre Pagella
-\font_sans default
-\font_typewriter default
-\font_math auto
+\inputencoding utf8
+\fontencoding auto
+\font_roman "default" "TeX Gyre Pagella"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
 \font_default_family default
-\use_non_tex_fonts true
+\use_non_tex_fonts false
 \font_sc false
-\font_osf true
-\font_sf_scale 100
-\font_tt_scale 100
+\font_roman_osf true
+\font_sans_osf false
+\font_typewriter_osf false
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures false
 \graphics default
-\default_output_format pdf4
+\default_output_format default
 \output_sync 0
 \bibtex_command default
 \index_command default
+\float_placement class
+\float_alignment class
 \paperfontsize default
 \spacing single
 \use_hyperref true
@@ -59,6 +67,8 @@
 \suppress_date false
 \justification true
 \use_refstyle 1
+\use_minted 0
+\use_lineno 0
 \index Index
 \shortcut idx
 \color #008000
@@ -67,10 +77,14 @@
 \tocdepth 3
 \paragraph_separation indent
 \paragraph_indentation default
-\quotes_language swedish
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style english
+\dynamic_quotes 0
 \papercolumns 1
 \papersides 1
 \paperpagestyle default
+\tablestyle default
 \tracking_changes false
 \output_changes false
 \html_math_output 0
@@ -81,12 +95,10 @@
 \begin_body
 
 \begin_layout Subsection
-
-\lang english
 The multiple-scattering problem
 \begin_inset CommandInset label
 LatexCommand label
-name "sub:The-multiple-scattering-problem"
+name "subsec:The-multiple-scattering-problem"
 
 \end_inset
 
@@ -94,8 +106,6 @@ name "sub:The-multiple-scattering-problem"
 \end_layout
 
 \begin_layout Standard
-
-\lang english
 In the 
 \begin_inset Formula $T$
 \end_inset
@@ -147,6 +157,7 @@ where
 LatexCommand cite
 after "chapter 7"
 key "kristensson_scattering_2016"
+literal "true"
 
 \end_inset
 
@@ -183,8 +194,6 @@ The expansion coefficients
 \end_layout
 
 \begin_layout Standard
-
-\lang english
 At a given frequency, assuming the system is linear, the relation between
  the expansion coefficients in the VSWF bases is given by the so-called
  
@@ -226,6 +235,7 @@ th nanoparticles) its elements drop very quickly to negligible values with
 \begin_inset CommandInset citation
 LatexCommand cite
 key "SCUFF2,reid_efficient_2015"
+literal "true"
 
 \end_inset
 
@@ -233,8 +243,6 @@ key "SCUFF2,reid_efficient_2015"
 \end_layout
 
 \begin_layout Standard
-
-\lang english
 The singular VSWFs originating at 
 \begin_inset Formula $\vect R_{n}$
 \end_inset
@@ -262,6 +270,7 @@ Analytical expressions for the translation operator
 \begin_inset CommandInset citation
 LatexCommand cite
 key "xu_efficient_1998"
+literal "true"
 
 \end_inset
 
@@ -269,8 +278,6 @@ key "xu_efficient_1998"
 \end_layout
 
 \begin_layout Standard
-
-\lang english
 If we write the field incident onto the 
 \begin_inset Formula $n$
 \end_inset
diff --git a/lepaper/finite.lyx b/lepaper/finite.lyx
index 4672110..8dd3de6 100644
--- a/lepaper/finite.lyx
+++ b/lepaper/finite.lyx
@@ -1,5 +1,5 @@
-#LyX 2.3 created this file. For more info see http://www.lyx.org/
-\lyxformat 544
+#LyX 2.4 created this file. For more info see https://www.lyx.org/
+\lyxformat 583
 \begin_document
 \begin_header
 \save_transient_properties true
@@ -7,27 +7,31 @@
 \textclass article
 \use_default_options true
 \maintain_unincluded_children false
-\language finnish
+\language english
 \language_package default
-\inputencoding auto
-\fontencoding global
+\inputencoding utf8
+\fontencoding auto
 \font_roman "default" "TeX Gyre Pagella"
 \font_sans "default" "default"
 \font_typewriter "default" "default"
 \font_math "auto" "auto"
 \font_default_family default
-\use_non_tex_fonts true
+\use_non_tex_fonts false
 \font_sc false
-\font_osf true
+\font_roman_osf true
+\font_sans_osf false
+\font_typewriter_osf false
 \font_sf_scale 100 100
 \font_tt_scale 100 100
 \use_microtype false
 \use_dash_ligatures true
 \graphics default
-\default_output_format pdf4
+\default_output_format default
 \output_sync 0
 \bibtex_command default
 \index_command default
+\float_placement class
+\float_alignment class
 \paperfontsize default
 \spacing single
 \use_hyperref true
@@ -63,6 +67,7 @@
 \justification true
 \use_refstyle 1
 \use_minted 0
+\use_lineno 0
 \index Index
 \shortcut idx
 \color #008000
@@ -73,11 +78,12 @@
 \paragraph_indentation default
 \is_math_indent 0
 \math_numbering_side default
-\quotes_style swedish
+\quotes_style english
 \dynamic_quotes 0
 \papercolumns 1
 \papersides 1
 \paperpagestyle default
+\tablestyle default
 \tracking_changes false
 \output_changes false
 \html_math_output 0
@@ -92,8 +98,6 @@ Finite systems
 \end_layout
 
 \begin_layout Itemize
-
-\lang english
 motivation (classes of problems that this can solve: response to external
  radiation, resonances, ...)
 \begin_inset Separator latexpar
@@ -104,8 +108,6 @@ motivation (classes of problems that this can solve: response to external
 
 \begin_deeper
 \begin_layout Itemize
-
-\lang english
 theory
 \begin_inset Separator latexpar
 \end_inset
@@ -115,8 +117,6 @@ theory
 
 \begin_deeper
 \begin_layout Itemize
-
-\lang english
 T-matrix definition, basics
 \begin_inset Separator latexpar
 \end_inset
@@ -126,23 +126,17 @@ T-matrix definition, basics
 
 \begin_deeper
 \begin_layout Itemize
-
-\lang english
 How to get it?
 \end_layout
 
 \end_deeper
 \begin_layout Itemize
-
-\lang english
 translation operators (TODO think about how explicit this should be, but
  I guess it might be useful to write them to write them explicitly (but
  in the shortest possible form) in the normalisation used in my program)
 \end_layout
 
 \begin_layout Itemize
-
-\lang english
 employing point group symmetries and decomposing the problem to decrease
  the computational complexity (maybe separately)
 \end_layout
@@ -150,8 +144,6 @@ employing point group symmetries and decomposing the problem to decrease
 \end_deeper
 \end_deeper
 \begin_layout Subsection
-
-\lang english
 Motivation
 \end_layout
 
@@ -167,8 +159,6 @@ The basic idea of MSTMM is quite simple: the driving electromagnetic field
 \end_layout
 
 \begin_layout Subsection
-
-\lang english
 Single-particle scattering
 \end_layout
 
@@ -227,8 +217,6 @@ todo define
 \end_layout
 
 \begin_layout Standard
-
-\lang english
 Throughout this text, we will use the same normalisation conventions as
  in 
 \begin_inset CommandInset citation
@@ -242,20 +230,14 @@ literal "true"
 \end_layout
 
 \begin_layout Subsubsection
-
-\lang english
 Spherical waves
 \end_layout
 
 \begin_layout Standard
-
-\lang english
 \begin_inset Note Note
 status open
 
 \begin_layout Plain Layout
-
-\lang english
 TODO small note about cartesian multipoles, anapoles etc.
  (There should be some comparing paper that the Russians at META 2018 mentioned.)
 \end_layout
@@ -266,8 +248,6 @@ TODO small note about cartesian multipoles, anapoles etc.
 \end_layout
 
 \begin_layout Subsubsection
-
-\lang english
 T-matrix definition
 \end_layout
 
@@ -276,26 +256,18 @@ Absorbed power
 \end_layout
 
 \begin_layout Subsubsection
-
-\lang english
 T-matrix compactness, cutoff validity
 \end_layout
 
 \begin_layout Subsection
-
-\lang english
 Multiple scattering
 \end_layout
 
 \begin_layout Subsubsection
-
-\lang english
 Translation operator
 \end_layout
 
 \begin_layout Subsubsection
-
-\lang english
 Numerical complexity, comparison to other methods
 \end_layout
 
diff --git a/lepaper/infinite-old.lyx b/lepaper/infinite-old.lyx
index ffefe93..8e8296f 100644
--- a/lepaper/infinite-old.lyx
+++ b/lepaper/infinite-old.lyx
@@ -1,29 +1,37 @@
-#LyX 2.1 created this file. For more info see http://www.lyx.org/
-\lyxformat 474
+#LyX 2.4 created this file. For more info see https://www.lyx.org/
+\lyxformat 583
 \begin_document
 \begin_header
+\save_transient_properties true
+\origin unavailable
 \textclass article
 \use_default_options false
 \maintain_unincluded_children false
 \language english
 \language_package none
-\inputencoding auto
+\inputencoding utf8
 \fontencoding default
-\font_roman default
-\font_sans default
-\font_typewriter default
-\font_math auto
+\font_roman "default" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
 \font_default_family default
 \use_non_tex_fonts false
 \font_sc false
-\font_osf false
-\font_sf_scale 100
-\font_tt_scale 100
+\font_roman_osf false
+\font_sans_osf false
+\font_typewriter_osf false
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures true
 \graphics default
 \default_output_format default
 \output_sync 0
 \bibtex_command default
 \index_command default
+\float_placement class
+\float_alignment class
 \paperfontsize default
 \spacing single
 \use_hyperref false
@@ -48,6 +56,8 @@
 \suppress_date false
 \justification true
 \use_refstyle 0
+\use_minted 0
+\use_lineno 0
 \index Index
 \shortcut idx
 \color #008000
@@ -56,10 +66,14 @@
 \tocdepth 3
 \paragraph_separation indent
 \paragraph_indentation default
-\quotes_language english
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style english
+\dynamic_quotes 0
 \papercolumns 1
 \papersides 1
 \paperpagestyle default
+\tablestyle default
 \tracking_changes false
 \output_changes false
 \html_math_output 0
@@ -73,7 +87,7 @@
 Periodic systems and mode analysis
 \begin_inset CommandInset label
 LatexCommand label
-name "sub:Periodic-systems"
+name "subsec:Periodic-systems"
 
 \end_inset
 
@@ -160,6 +174,7 @@ reference "eq:multiple scattering per particle a"
 \begin_inset CommandInset citation
 LatexCommand cite
 key "linton_lattice_2010"
+literal "true"
 
 \end_inset
 
@@ -273,6 +288,7 @@ try points of the Brillouin zone can be found e.g.
 LatexCommand cite
 after "chapters 10–11"
 key "dresselhaus_group_2008"
+literal "true"
 
 \end_inset
 
@@ -323,6 +339,7 @@ We analyse the symmetries of the system in the same VSWF representation
 LatexCommand cite
 after "eq. (11.19)"
 key "dresselhaus_group_2008"
+literal "true"
 
 \end_inset
 
@@ -342,6 +359,7 @@ key "dresselhaus_group_2008"
 \begin_inset CommandInset citation
 LatexCommand cite
 key "schulz_point-group_1999"
+literal "true"
 
 \end_inset
 
@@ -359,6 +377,7 @@ key "schulz_point-group_1999"
 LatexCommand cite
 after "eq. (4.28)"
 key "dresselhaus_group_2008"
+literal "true"
 
 \end_inset
 
@@ -440,6 +459,7 @@ Each mode at the
 LatexCommand cite
 after "eq. (2.51)"
 key "dresselhaus_group_2008"
+literal "true"
 
 \end_inset
 
diff --git a/lepaper/infinite.lyx b/lepaper/infinite.lyx
index a91c95c..620e64c 100644
--- a/lepaper/infinite.lyx
+++ b/lepaper/infinite.lyx
@@ -1,5 +1,5 @@
-#LyX 2.3 created this file. For more info see http://www.lyx.org/
-\lyxformat 544
+#LyX 2.4 created this file. For more info see https://www.lyx.org/
+\lyxformat 583
 \begin_document
 \begin_header
 \save_transient_properties true
@@ -7,27 +7,31 @@
 \textclass article
 \use_default_options true
 \maintain_unincluded_children false
-\language finnish
+\language english
 \language_package default
-\inputencoding auto
-\fontencoding global
+\inputencoding utf8
+\fontencoding auto
 \font_roman "default" "TeX Gyre Pagella"
 \font_sans "default" "default"
 \font_typewriter "default" "default"
 \font_math "auto" "auto"
 \font_default_family default
-\use_non_tex_fonts true
+\use_non_tex_fonts false
 \font_sc false
-\font_osf true
+\font_roman_osf true
+\font_sans_osf false
+\font_typewriter_osf false
 \font_sf_scale 100 100
 \font_tt_scale 100 100
 \use_microtype false
 \use_dash_ligatures true
 \graphics default
-\default_output_format pdf4
+\default_output_format default
 \output_sync 0
 \bibtex_command default
 \index_command default
+\float_placement class
+\float_alignment class
 \paperfontsize default
 \spacing single
 \use_hyperref true
@@ -63,6 +67,7 @@
 \justification true
 \use_refstyle 1
 \use_minted 0
+\use_lineno 0
 \index Index
 \shortcut idx
 \color #008000
@@ -73,11 +78,12 @@
 \paragraph_indentation default
 \is_math_indent 0
 \math_numbering_side default
-\quotes_style swedish
+\quotes_style english
 \dynamic_quotes 0
 \papercolumns 1
 \papersides 1
 \paperpagestyle default
+\tablestyle default
 \tracking_changes false
 \output_changes false
 \html_math_output 0
@@ -92,14 +98,10 @@ Infinite periodic systems
 \end_layout
 
 \begin_layout Subsection
-
-\lang english
 Formulation of the problem
 \end_layout
 
 \begin_layout Standard
-
-\lang english
 Assume a system of compact EM scatterers in otherwise homogeneous and isotropic
  medium, and assume that the system, i.e.
  both the medium and the scatterers, have linear response.
@@ -139,14 +141,10 @@ where
 \end_layout
 
 \begin_layout Standard
-
-\lang english
 ...
 \end_layout
 
 \begin_layout Standard
-
-\lang english
 \begin_inset Formula 
 \[
 \sum_{β}(\delta_{αβ}-T_{α}S_{α\leftarrowβ})A_{β}=T_{α}P_{0α}.
@@ -158,14 +156,10 @@ where
 \end_layout
 
 \begin_layout Standard
-
-\lang english
 Now suppose that the scatterers constitute an infinite lattice
 \end_layout
 
 \begin_layout Standard
-
-\lang english
 \begin_inset Formula 
 \[
 \sum_{\vect bβ}(\delta_{\vect{ab}}\delta_{αβ}-T_{\vect aα}S_{\vect aα\leftarrow\vect bβ})A_{\vect bβ}=T_{\vect aα}P_{0\vect aα}.
@@ -225,14 +219,10 @@ W_{\alpha\beta}(\vect k)\equiv\sum_{\vect b}S_{\vect 0α\leftarrow\vect bβ}e^{i
 \end_layout
 
 \begin_layout Subsection
-
-\lang english
 Computing the Fourier sum of the translation operator
 \end_layout
 
 \begin_layout Standard
-
-\lang english
 The problem evaluating 
 \begin_inset CommandInset ref
 LatexCommand eqref
@@ -241,7 +231,7 @@ reference "eq:W definition"
 \end_inset
 
  is the asymptotic behaviour of the translation operator, 
-\begin_inset Formula $S_{\vect0α\leftarrow\vect bβ}\sim\left|\vect r_{\vect b}\right|^{-1}e^{ik_{0}\left|\vect r_{\vect b}\right|}$
+\begin_inset Formula $S_{\vect 0α\leftarrow\vect bβ}\sim\left|\vect r_{\vect b}\right|^{-1}e^{ik_{0}\left|\vect r_{\vect b}\right|}$
 \end_inset
 
  that makes the convergence of the sum quite problematic for any 
@@ -253,8 +243,6 @@ reference "eq:W definition"
 status open
 
 \begin_layout Plain Layout
-
-\lang english
 Note that 
 \begin_inset Formula $d$
 \end_inset
@@ -274,8 +262,6 @@ Note that
 \end_layout
 
 \begin_layout Standard
-
-\lang english
 Let us re-express the sum in 
 \begin_inset CommandInset ref
 LatexCommand eqref
@@ -284,11 +270,14 @@ reference "eq:W definition"
 \end_inset
 
  in terms of integral with a delta comb
+\begin_inset FormulaMacro
+\renewcommand{\basis}[1]{\mathfrak{#1}}
+\end_inset
+
+
 \end_layout
 
 \begin_layout Standard
-
-\lang english
 \begin_inset Formula 
 \begin{equation}
 W_{\alpha\beta}(\vect k)=\int\ud^{d}\vect r\dc{\basis u}(\vect r)S(\vect r_{\alpha}\leftarrow\vect r+\vect r_{\beta})e^{i\vect k\cdot\vect r}.\label{eq:W integral}
@@ -338,7 +327,7 @@ translation operator for spherical waves originating in
 \end_inset
 
  is in fact a function of a single 3d argument, 
-\begin_inset Formula $S(\vect r_{\alpha}\leftarrow\vect r+\vect r_{\beta})=S(\vect0\leftarrow\vect r+\vect r_{\beta}-\vect r_{\alpha})=S(-\vect r-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect0)=S(-\vect r-\vect r_{\beta}+\vect r_{\alpha})$
+\begin_inset Formula $S(\vect r_{\alpha}\leftarrow\vect r+\vect r_{\beta})=S(\vect 0\leftarrow\vect r+\vect r_{\beta}-\vect r_{\alpha})=S(-\vect r-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect 0)=S(-\vect r-\vect r_{\beta}+\vect r_{\alpha})$
 \end_inset
 
 .
@@ -352,7 +341,7 @@ reference "eq:W integral"
  can be rewritten as
 \begin_inset Formula 
 \[
-W_{\alpha\beta}(\vect k)=\left(2\pi\right)^{\frac{d}{2}}\uaft{(\dc{\basis u}S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect0))\left(\vect k\right)}
+W_{\alpha\beta}(\vect k)=\left(2\pi\right)^{\frac{d}{2}}\uaft{(\dc{\basis u}S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect 0))\left(\vect k\right)}
 \]
 
 \end_inset
@@ -377,10 +366,10 @@ reference "eq:Dirac comb uaFt"
  for the Fourier transform of Dirac comb)
 \begin_inset Formula 
 \begin{eqnarray}
-W_{\alpha\beta}(\vect k) & = & \left(\left(\uaft{\dc{\basis u}}\right)\ast\left(\uaft{S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect0)}\right)\right)(\vect k)\nonumber \\
- & = & \frac{\left|\det\recb{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\left(\dc{\recb{\basis u}}^{(d)}\ast\left(\uaft{S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect0)}\right)\right)\left(\vect k\right)\nonumber \\
- & = & \frac{\left|\det\rec{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\sum_{\vect K\in\recb{\basis u}\ints^{d}}\left(\uaft{S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect0)}\right)\left(\vect k-\vect K\right)\label{eq:W sum in reciprocal space}\\
- & = & \frac{\left|\det\rec{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\sum_{\vect K\in\recb{\basis u}\ints^{d}}e^{i\left(\vect k-\vect K\right)\cdot\left(-\vect r_{\beta}+\vect r_{\alpha}\right)}\left(\uaft{S(\vect{\bullet}\leftarrow\vect0)}\right)\left(\vect k-\vect K\right)\nonumber 
+W_{\alpha\beta}(\vect k) & = & \left(\left(\uaft{\dc{\basis u}}\right)\ast\left(\uaft{S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect 0)}\right)\right)(\vect k)\nonumber \\
+ & = & \frac{\left|\det\recb{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\left(\dc{\recb{\basis u}}^{(d)}\ast\left(\uaft{S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect 0)}\right)\right)\left(\vect k\right)\nonumber \\
+ & = & \frac{\left|\det\rec{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\sum_{\vect K\in\recb{\basis u}\ints^{d}}\left(\uaft{S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect 0)}\right)\left(\vect k-\vect K\right)\label{eq:W sum in reciprocal space}\\
+ & = & \frac{\left|\det\rec{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\sum_{\vect K\in\recb{\basis u}\ints^{d}}e^{i\left(\vect k-\vect K\right)\cdot\left(-\vect r_{\beta}+\vect r_{\alpha}\right)}\left(\uaft{S(\vect{\bullet}\leftarrow\vect 0)}\right)\left(\vect k-\vect K\right)\nonumber 
 \end{eqnarray}
 
 \end_inset
@@ -390,8 +379,6 @@ W_{\alpha\beta}(\vect k) & = & \left(\left(\uaft{\dc{\basis u}}\right)\ast\left(
 status open
 
 \begin_layout Plain Layout
-
-\lang english
 Factor 
 \begin_inset Formula $\left(2\pi\right)^{\frac{d}{2}}$
 \end_inset
@@ -424,8 +411,6 @@ whole
 \end_layout
 
 \begin_layout Standard
-
-\lang english
 However, Fourier transform is linear, so we can in principle separate 
 \begin_inset Formula $S$
 \end_inset
@@ -486,8 +471,8 @@ reference "eq:W sum in reciprocal space"
 \begin_inset Formula 
 \begin{eqnarray}
 W_{\alpha\beta}\left(\vect k\right) & = & W_{\alpha\beta}^{\textup{S}}\left(\vect k\right)+W_{\alpha\beta}^{\textup{L}}\left(\vect k\right)\nonumber \\
-W_{\alpha\beta}^{\textup{S}}\left(\vect k\right) & = & \sum_{\vect R\in\basis u\ints^{d}}S^{\textup{S}}(\vect0\leftarrow\vect R+\vect r_{\beta}-\vect r_{\alpha})e^{i\vect k\cdot\vect R}\label{eq:W Short definition}\\
-W_{\alpha\beta}^{\textup{L}}\left(\vect k\right) & = & \frac{\left|\det\rec{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\sum_{\vect K\in\recb{\basis u}\ints^{d}}\left(\uaft{S^{\textup{L}}(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect0)}\right)\left(\vect k-\vect K\right)\label{eq:W Long definition}
+W_{\alpha\beta}^{\textup{S}}\left(\vect k\right) & = & \sum_{\vect R\in\basis u\ints^{d}}S^{\textup{S}}(\vect 0\leftarrow\vect R+\vect r_{\beta}-\vect r_{\alpha})e^{i\vect k\cdot\vect R}\label{eq:W Short definition}\\
+W_{\alpha\beta}^{\textup{L}}\left(\vect k\right) & = & \frac{\left|\det\rec{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\sum_{\vect K\in\recb{\basis u}\ints^{d}}\left(\uaft{S^{\textup{L}}(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect 0)}\right)\left(\vect k-\vect K\right)\label{eq:W Long definition}
 \end{eqnarray}
 
 \end_inset
diff --git a/lepaper/intro.lyx b/lepaper/intro.lyx
index 63172d3..f802303 100644
--- a/lepaper/intro.lyx
+++ b/lepaper/intro.lyx
@@ -1,5 +1,5 @@
-#LyX 2.3 created this file. For more info see http://www.lyx.org/
-\lyxformat 544
+#LyX 2.4 created this file. For more info see https://www.lyx.org/
+\lyxformat 583
 \begin_document
 \begin_header
 \save_transient_properties true
@@ -7,27 +7,31 @@
 \textclass article
 \use_default_options true
 \maintain_unincluded_children false
-\language finnish
+\language english
 \language_package default
-\inputencoding auto
-\fontencoding global
+\inputencoding utf8
+\fontencoding auto
 \font_roman "default" "TeX Gyre Pagella"
 \font_sans "default" "default"
 \font_typewriter "default" "default"
 \font_math "auto" "auto"
 \font_default_family default
-\use_non_tex_fonts true
+\use_non_tex_fonts false
 \font_sc false
-\font_osf true
+\font_roman_osf true
+\font_sans_osf false
+\font_typewriter_osf false
 \font_sf_scale 100 100
 \font_tt_scale 100 100
 \use_microtype false
 \use_dash_ligatures true
 \graphics default
-\default_output_format pdf4
+\default_output_format default
 \output_sync 0
 \bibtex_command default
 \index_command default
+\float_placement class
+\float_alignment class
 \paperfontsize default
 \spacing single
 \use_hyperref true
@@ -63,6 +67,7 @@
 \justification true
 \use_refstyle 1
 \use_minted 0
+\use_lineno 0
 \index Index
 \shortcut idx
 \color #008000
@@ -73,11 +78,12 @@
 \paragraph_indentation default
 \is_math_indent 0
 \math_numbering_side default
-\quotes_style swedish
+\quotes_style english
 \dynamic_quotes 0
 \papercolumns 1
 \papersides 1
 \paperpagestyle default
+\tablestyle default
 \tracking_changes false
 \output_changes false
 \html_math_output 0