--- /dev/null
+#LyX 2.0.0svn created this file. For more info see http://www.lyx.org/
+\lyxformat 401
+\begin_document
+\begin_header
+\textclass ectaart
+\begin_preamble
+\RequirePackage[colorlinks,citecolor=blue,urlcolor=blue]{hyperref}
+\RequirePackage{hypernat}
+
+%% Local settings
+\startlocaldefs
+% These require a theorem-like module
+\numberwithin{equation}{section}
+\theoremstyle{plain}
+\endlocaldefs
+\end_preamble
+\options draft,pdftex
+\use_default_options false
+\begin_modules
+theorems-ams
+\end_modules
+\maintain_unincluded_children false
+\language english
+\inputencoding auto
+\fontencoding global
+\font_roman default
+\font_sans default
+\font_typewriter default
+\font_default_family default
+\use_xetex false
+\font_sc false
+\font_osf false
+\font_sf_scale 100
+\font_tt_scale 100
+
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\pdf_bookmarks true
+\pdf_bookmarksnumbered false
+\pdf_bookmarksopen false
+\pdf_bookmarksopenlevel 1
+\pdf_breaklinks false
+\pdf_pdfborder false
+\pdf_colorlinks true
+\pdf_backref false
+\pdf_pdfusetitle true
+\papersize default
+\use_geometry false
+\use_amsmath 1
+\use_esint 1
+\use_mhchem 1
+\use_mathdots 1
+\cite_engine natbib_authoryear
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\quotes_language english
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Title
+A Sample Document
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+protect
+\end_layout
+
+\end_inset
+
+
+\begin_inset Flex Thanks Reference
+status open
+
+\begin_layout Plain Layout
+T1
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout RunTitle
+A Sample Document
+\end_layout
+
+\begin_layout Thanks Text
+Footnote to the title with the `thankstext' command.
+\begin_inset Argument
+status open
+
+\begin_layout Plain Layout
+T1
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Authors Block
+\begin_inset Flex Author
+status open
+
+\begin_layout Plain Layout
+\begin_inset Flex Name (First Name)
+status open
+
+\begin_layout Plain Layout
+First
+\end_layout
+
+\end_inset
+
+
+\begin_inset Flex Name (Surname)
+status open
+
+\begin_layout Plain Layout
+Author
+\end_layout
+
+\end_inset
+
+
+\begin_inset Flex Thanks Reference
+status open
+
+\begin_layout Plain Layout
+a,t1
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Flex Author
+status open
+
+\begin_layout Plain Layout
+\begin_inset Flex Name (First Name)
+status open
+
+\begin_layout Plain Layout
+Second
+\end_layout
+
+\end_inset
+
+
+\begin_inset Flex Name (Surname)
+status open
+
+\begin_layout Plain Layout
+Author
+\end_layout
+
+\end_inset
+
+
+\begin_inset Flex Thanks Reference
+status open
+
+\begin_layout Plain Layout
+a
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Flex Author
+status open
+
+\begin_layout Plain Layout
+\begin_inset Flex Name (First Name)
+status open
+
+\begin_layout Plain Layout
+Third
+\end_layout
+
+\end_inset
+
+
+\begin_inset Flex Name (Surname)
+status open
+
+\begin_layout Plain Layout
+Author
+\end_layout
+
+\end_inset
+
+
+\begin_inset Flex Thanks Reference
+status open
+
+\begin_layout Plain Layout
+b
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Email
+first@somewhere.com
+\begin_inset Argument
+status open
+
+\begin_layout Plain Layout
+e1
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Email
+second@somewhere.com
+\begin_inset Argument
+status open
+
+\begin_layout Plain Layout
+e2
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Email
+third@somewhere.com
+\begin_inset Argument
+status open
+
+\begin_layout Plain Layout
+e3
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Web Address
+www.foo.com
+\begin_inset Argument
+status open
+
+\begin_layout Plain Layout
+u1
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Thanks Text
+Some comment
+\begin_inset Argument
+status open
+
+\begin_layout Plain Layout
+t1
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout RunAuthor
+F.
+ Author, S.
+ Author and T.
+ Author
+\end_layout
+
+\begin_layout Address
+\begin_inset Argument
+status open
+
+\begin_layout Plain Layout
+a
+\end_layout
+
+\end_inset
+
+Address of the First and Second authors, usually few lines long usually
+ few lines long usually few lines long
+\end_layout
+
+\begin_layout Address
+\begin_inset Argument
+status open
+
+\begin_layout Plain Layout
+b
+\end_layout
+
+\end_inset
+
+Address of the Third author, usually few lines long, usually few lines long
+
+\begin_inset Flex Internet Address Reference
+status open
+
+\begin_layout Plain Layout
+e3,u1
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Abstract
+The abstract should summarize the contents of the paper.
+ It should be clear, descriptive, self-explanatory and not longer than 150
+ words.
+ It should also be suitable for publication in abstracting services.
+ Please avoid using math formulas as much as possible.
+\end_layout
+
+\begin_layout Abstract
+This is a sample input file.
+ Comparing it with the output it generates can show you how to produce a
+ simple document of your own.
+
+\end_layout
+
+\begin_layout Keyword
+\begin_inset Flex Keyword
+status open
+
+\begin_layout Plain Layout
+sample
+\end_layout
+
+\end_inset
+
+
+\begin_inset Flex Keyword
+status open
+
+\begin_layout Plain Layout
+LaTeX2e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Ordinary text
+\end_layout
+
+\begin_layout Standard
+The ends of words and sentences are marked by spaces.
+ It doesn't matter how many spaces you type; one is as good as 100.
+ The end of a line counts as a space.
+\end_layout
+
+\begin_layout Standard
+One or more blank lines denote the end of a paragraph.
+\end_layout
+
+\begin_layout Standard
+Since any number of consecutive spaces are treated like a single one, the
+ formatting of the input file makes no difference to TeX, but it makes a
+ difference to you.
+ When you use LaTeX, making your input file as easy to read as possible
+ will be a great help as you write your document and when you change it.
+ This sample file shows how you can add comments to your own input file.
+\end_layout
+
+\begin_layout Standard
+Because printing is different from typewriting, there are a number of things
+ that you have to do differently when preparing an input file than if you
+ were just typing the document directly.
+ Quotation marks like
+\begin_inset Quotes eld
+\end_inset
+
+this
+\begin_inset Quotes erd
+\end_inset
+
+ have to be handled specially, as do quotes within quotes:
+\begin_inset Quotes eld
+\end_inset
+
+
+\begin_inset space \thinspace{}
+\end_inset
+
+`this'
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+Small space separates the double and single quote.
+\end_layout
+
+\end_inset
+
+ is what I just wrote, not `that'
+\begin_inset space \thinspace{}
+\end_inset
+
+
+\begin_inset Quotes erd
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Dashes come in three sizes: an intra-word dash, a medium dash for number
+ ranges like 1--2, and a punctuation dash---like this.
+\end_layout
+
+\begin_layout Standard
+A sentence-ending space should be larger than the space between words within
+ a sentence.
+ You sometimes have to type special commands in conjunction with punctuation
+ characters to get this right, as in the following sentence.
+ Gnats, gnus, etc.
+\begin_inset space \space{}
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+This makes an inter-word space.
+\end_layout
+
+\end_inset
+
+all begin with G\SpecialChar \@.
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+The end-of-sentence punctuation.
+\end_layout
+
+\end_inset
+
+You should check the spaces after periods when reading your output to make
+ sure you haven't forgotten any special cases.
+ Generating an ellipsis \SpecialChar \ldots{}
+
+\begin_inset space \space{}
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+Inter-word space needed because TeX ignores spaces after command names like
+
+\family typewriter
+
+\backslash
+ldots
+\family default
+ made from
+\family typewriter
+
+\backslash
+
+\family default
+ + letters.
+\end_layout
+
+\end_inset
+
+with the right spacing around the periods requires a special command.
+\end_layout
+
+\begin_layout Standard
+TeX
+\begin_inset space \space{}
+\end_inset
+
+interprets some common characters as commands, so you must type special
+ commands to generate them.
+ These characters include the following:
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+
+\backslash
+$
+\backslash
+&
+\backslash
+%
+\backslash
+#
+\backslash
+{ and~
+\backslash
+}.
+\end_layout
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In printing, text is emphasized by using an
+\emph on
+italic
+\emph default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+/
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+ The
+\family typewriter
+
+\backslash
+/
+\family default
+ command produces the tiny extra space that should be added between a slanted
+ and a following unslanted letter.
+\end_layout
+
+\end_inset
+
+type style.
+\end_layout
+
+\begin_layout Emphasize
+A long segment of text can also be emphasized in this way.
+ Text within such a segment given additional emphasis with
+\emph on
+Roman
+\emph default
+ type.
+ Italic type loses its ability to emphasize and become simply distracting
+ when used excessively.
+
+\end_layout
+
+\begin_layout Standard
+It is sometimes necessary to prevent TeX
+\begin_inset space \space{}
+\end_inset
+
+from breaking a line where it might otherwise do so.
+ This may be at a space, as between the
+\begin_inset Quotes eld
+\end_inset
+
+Mr.
+\begin_inset Quotes erd
+\end_inset
+
+ and
+\begin_inset Quotes eld
+\end_inset
+
+Jones
+\begin_inset Quotes erd
+\end_inset
+
+ in
+\begin_inset Quotes eld
+\end_inset
+
+Mr.
+\begin_inset space ~
+\end_inset
+
+Jones
+\begin_inset Quotes erd
+\end_inset
+
+,
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+
+\family typewriter
+~
+\family default
+ produces an unbreakable interword space.
+\end_layout
+
+\end_inset
+
+or within a word---especially when the word is a symbol like
+\emph on
+itemnum
+\emph default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+/
+\end_layout
+
+\end_inset
+
+ that makes little sense when hyphenated across lines.
+\end_layout
+
+\begin_layout Standard
+TeX
+\begin_inset space \space{}
+\end_inset
+
+is good at typesetting mathematical formulas like
+\begin_inset Formula \ensuremath{x-3y=7}
+
+\end_inset
+
+ or
+\begin_inset Formula \ensuremath{a_{1}>x^{2n}/y^{2n}>x'}
+
+\end_inset
+
+.
+ Remember that a letter like
+\begin_inset Formula $x$
+\end_inset
+
+ is a formula when it denotes a mathematical symbol, and should be treated
+ as one.
+\end_layout
+
+\begin_layout Section
+Notes
+\end_layout
+
+\begin_layout Standard
+Footnotes
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+This is an example of a footnote.
+\end_layout
+
+\end_inset
+
+ pose no problem
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+And another one
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Displayed text
+\end_layout
+
+\begin_layout Standard
+Text is displayed by indenting it from the left margin.
+ Quotations are commonly displayed.
+ There are short quotations
+\end_layout
+
+\begin_layout Quote
+This is a short a quotation.
+ It consists of a single paragraph of text.
+ There is no paragraph indentation.
+
+\end_layout
+
+\begin_layout Standard
+and longer ones.
+
+\end_layout
+
+\begin_layout Quotation
+This is a longer quotation.
+ It consists of two paragraphs of text.
+ The beginning of each paragraph is indicated by an extra indentation.
+\end_layout
+
+\begin_layout Quotation
+This is the second paragraph of the quotation.
+ It is just as dull as the first paragraph.
+
+\end_layout
+
+\begin_layout Standard
+Another frequently-displayed structure is a list.
+ The following is an example of an
+\emph on
+itemized
+\emph default
+ list, four levels deep.
+
+\end_layout
+
+\begin_layout Itemize
+This is the first item of an itemized list.
+ Each item in the list is marked with a
+\begin_inset Quotes eld
+\end_inset
+
+tick
+\begin_inset Quotes erd
+\end_inset
+
+.
+ The document style determines what kind of tick mark is used.
+
+\end_layout
+
+\begin_layout Itemize
+This is the second item of the list.
+ It contains another list nested inside it.
+ The three inner lists are an
+\emph on
+itemized
+\emph default
+ list.
+
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+This is the first item of an enumerated list that is nested within the itemized
+ list.
+
+\end_layout
+
+\begin_layout Itemize
+This is the second item of the inner list.
+ LaTeX allows you to nest lists deeper than you really should.
+
+\end_layout
+
+\begin_layout Standard
+This is the rest of the second item of the outer list.
+ It is no more interesting than any other part of the item.
+
+\end_layout
+
+\end_deeper
+\begin_layout Itemize
+This is the third item of the list.
+
+\end_layout
+
+\begin_layout Standard
+The following is an example of an
+\emph on
+enumerated
+\emph default
+ list, four levels deep.
+
+\end_layout
+
+\begin_layout Enumerate
+This is the first item of an enumerated list.
+ Each item in the list is marked with a
+\begin_inset Quotes eld
+\end_inset
+
+tick
+\begin_inset Quotes erd
+\end_inset
+
+.
+ The document style determines what kind of tick mark is used.
+
+\end_layout
+
+\begin_layout Enumerate
+This is the second item of the list.
+ It contains another list nested inside it.
+ The three inner lists are an
+\emph on
+enumerated
+\emph default
+ list.
+
+\end_layout
+
+\begin_deeper
+\begin_layout Enumerate
+This is the first item of an enumerated list that is nested within the enumerate
+d list.
+
+\end_layout
+
+\begin_layout Enumerate
+This is the second item of the inner list.
+ LaTeX allows you to nest lists deeper than you really should.
+
+\end_layout
+
+\begin_layout Standard
+This is the rest of the second item of the outer list.
+ It is no more interesting than any other part of the item.
+
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+This is the third item of the list.
+
+\end_layout
+
+\begin_layout Standard
+The following is an example of a
+\emph on
+description
+\emph default
+ list.
+
+\end_layout
+
+\begin_layout Description
+Cow Highly intelligent animal that can produce milk out of grass.
+
+\end_layout
+
+\begin_layout Description
+Horse Less intelligent animal renowned for its legs.
+
+\end_layout
+
+\begin_layout Description
+Human being Not so intelligent animal that thinks that it can think.
+
+\end_layout
+
+\begin_layout Standard
+You can even display poetry.
+
+\end_layout
+
+\begin_layout Verse
+There is an environment for verse
+\begin_inset Newline newline
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+The
+\family typewriter
+
+\backslash
+
+\backslash
+
+\family default
+ command separates lines within a stanza.
+ One or more blank lines separate stanzas.
+\end_layout
+
+\end_inset
+
+ Whose features some poets will curse.
+
+\end_layout
+
+\begin_layout Verse
+For instead of making
+\begin_inset Newline newline
+\end_inset
+
+ Them do
+\emph on
+all
+\emph default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+/
+\end_layout
+
+\end_inset
+
+ line breaking,
+\begin_inset Newline newline
+\end_inset
+
+ It allows them to put too many words on a line when they'd rather be forced
+ to be terse.
+
+\end_layout
+
+\begin_layout Standard
+Mathematical formulas may also be displayed.
+ A displayed formula is one-line long; multiline formulas require special
+ formatting instructions.
+
+\begin_inset Formula \[
+x'+y^{2}=z_{i}^{2}\]
+
+\end_inset
+
+ Don't start a paragraph with a displayed equation, nor make one a paragraph
+ by itself.
+\end_layout
+
+\begin_layout Standard
+Example of a theorem:
+\end_layout
+
+\begin_layout Theorem
+All conjectures are interesting, but some conjectures are more interesting
+ than others.
+
+\end_layout
+
+\begin_layout Proof
+Obvious.
+\end_layout
+
+\begin_layout Section
+Tables and figures
+\end_layout
+
+\begin_layout Standard
+Cross reference to labelled table: As you can see in Table
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sphericcase"
+
+\end_inset
+
+ on page
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset CommandInset ref
+LatexCommand pageref
+reference "sphericcase"
+
+\end_inset
+
+ and also in Table
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "parset"
+
+\end_inset
+
+ on page
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset CommandInset ref
+LatexCommand pageref
+reference "parset"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float table
+wide true
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+The spherical case (
+\begin_inset Formula $I_{1}=0$
+\end_inset
+
+,
+\begin_inset Formula $I_{2}=0$
+\end_inset
+
+).
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset CommandInset label
+LatexCommand label
+name "sphericcase"
+
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="13" columns="6">
+<features tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0">
+<column alignment="right" valignment="top" width="0">
+<column alignment="right" valignment="top" width="0">
+<column alignment="right" valignment="top" width="0">
+<column alignment="right" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Equil.
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="none" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="none" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="none" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="none" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="none" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Points
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="1" alignment="none" valignment="top" usebox="none" special="c">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $x$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="1" alignment="none" valignment="top" usebox="none" special="c">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $y$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="1" alignment="none" valignment="top" usebox="none" special="c">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $z$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="1" alignment="none" valignment="top" usebox="none" special="c">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $C$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+S
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $~~L_{1}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $-$
+\end_inset
+
+2.485252241
+\end_layout
+
+\end_inset
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+
+\begin_layout Plain Layout
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+\end_inset
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+<cell alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
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+\end_layout
+
+\end_inset
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+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $~~L_{2}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_inset
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+
+\end_inset
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+<cell alignment="right" valignment="top" usebox="none">
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+
+\begin_layout Plain Layout
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+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
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+
+\begin_layout Plain Layout
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+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+S
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $~~L_{3}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0.009869059
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
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+
+\begin_layout Plain Layout
+4.756386544
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $-$
+\end_inset
+
+0.000057922
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+U
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $~~L_{4}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_layout
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+\end_inset
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+<cell alignment="right" valignment="top" usebox="none">
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+
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+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $-$
+\end_inset
+
+0.007021459
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+U
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $~~L_{5}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_layout
+
+\end_inset
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+<cell alignment="right" valignment="top" usebox="none">
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+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_inset
+
+0.212446624
+\end_layout
+
+\end_inset
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+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+U
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $~~L_{6}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_inset
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+<cell alignment="right" valignment="top" usebox="none">
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+<cell alignment="right" valignment="top" usebox="none">
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+<cell alignment="right" valignment="top" usebox="none">
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+\end_inset
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+<cell alignment="center" valignment="top" usebox="none">
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+
+\begin_layout Plain Layout
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+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $~~L_{7}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
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+<cell alignment="right" valignment="top" usebox="none">
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+
+\end_inset
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+<cell alignment="right" valignment="top" usebox="none">
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+
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+<cell alignment="center" valignment="top" usebox="none">
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+
+\begin_layout Plain Layout
+U
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $~~L_{8}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+
+\end_inset
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+<cell alignment="right" valignment="top" usebox="none">
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+
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+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
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+
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+\end_inset
+
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+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
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+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+U
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $~~L_{9}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
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+
+\begin_layout Plain Layout
+\begin_inset Formula $-$
+\end_inset
+
+0.421735658
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $-$
+\end_inset
+
+0.093667445
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+9.241525367
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+U
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $~~L_{10}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+1.472523232
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+1.393484549
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $-$
+\end_inset
+
+0.083801333
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+6.733436505
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+U
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $~~L_{11}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $-$
+\end_inset
+
+1.393484549
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $-$
+\end_inset
+
+0.083801333
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+6.733436505
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+U
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+A major point of difference lies in the value of the specific production
+ rate
+\begin_inset Formula $\pi$
+\end_inset
+
+ for large values of the specific growth rate
+\begin_inset Formula $\mu$
+\end_inset
+
+.
+ Already in the early publications
+\begin_inset CommandInset citation
+LatexCommand cite
+key "r1,r2,r3"
+
+\end_inset
+
+ it appeared that high glucose concentrations in the production phase are
+ well correlated with a low penicillin yield (the `glucose effect').
+ It has been confirmed recently
+\begin_inset CommandInset citation
+LatexCommand cite
+key "r1,r2,r3,r4"
+
+\end_inset
+
+ that high glucose concentrations inhibit the synthesis of the enzymes of
+ the penicillin pathway, but not the actual penicillin biosynthesis.
+ In other words, glucose represses (and not inhibits) the penicillin biosynthesi
+s.
+\end_layout
+
+\begin_layout Standard
+These findings do not contradict the results of
+\begin_inset CommandInset citation
+LatexCommand cite
+key "r1"
+
+\end_inset
+
+ and of
+\begin_inset CommandInset citation
+LatexCommand cite
+key "r4"
+
+\end_inset
+
+ which were obtained for continuous culture fermentations.
+ Because for high values of the specific growth rate
+\begin_inset Formula $\mu$
+\end_inset
+
+ it is most likely (as shall be discussed below) that maintenance metabolism
+ occurs, it can be shown that in steady state continuous culture conditions,
+ and with
+\begin_inset Formula $\mu$
+\end_inset
+
+ described by a Monod kinetics
+\begin_inset Formula \begin{equation}
+C_{s}=K_{M}\frac{\mu/\mu_{x}}{1-\mu/\mu_{x}}\label{cs}\end{equation}
+
+\end_inset
+
+ Pirt & Rhigelato determined
+\begin_inset Formula $\pi$
+\end_inset
+
+ for
+\begin_inset Formula $\mu$
+\end_inset
+
+ between
+\begin_inset Formula $0.023$
+\end_inset
+
+ and
+\begin_inset Formula $0.086$
+\end_inset
+
+ h
+\begin_inset Formula $^{-1}$
+\end_inset
+
+.
+ They also reported a value
+\begin_inset Formula $\mu_{x}\approx0.095$
+\end_inset
+
+ h
+\begin_inset Formula $^{-1}$
+\end_inset
+
+, so that for their experiments
+\begin_inset Formula $\mu/\mu_{x}$
+\end_inset
+
+ is in the range of
+\begin_inset Formula $0.24$
+\end_inset
+
+ to
+\begin_inset Formula $0.9$
+\end_inset
+
+.
+ Substituting
+\begin_inset Formula $K_{M}$
+\end_inset
+
+ in Eq.
+ (
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "cs"
+
+\end_inset
+
+) by the value
+\begin_inset Formula $K_{M}=1$
+\end_inset
+
+ g/L as used by
+\begin_inset CommandInset citation
+LatexCommand cite
+key "r1"
+
+\end_inset
+
+, one finds with the above equation
+\begin_inset Formula $0.3<C_{s}<9$
+\end_inset
+
+ g/L.
+ This agrees well with the work of
+\begin_inset CommandInset citation
+LatexCommand cite
+key "r4"
+
+\end_inset
+
+, who reported that penicillin biosynthesis repression only occurs at glucose
+ concentrations from
+\begin_inset Formula $C_{s}=10$
+\end_inset
+
+ g/L on.
+ The conclusion is that the glucose concentrations in the experiments of
+ Pirt & Rhigelato probably were too low for glucose repression to be detected.
+ The experimental data published by Ryu & Hospodka are not detailed sufficiently
+ to permit a similar analysis.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float table
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+centering
+\end_layout
+
+\end_inset
+
+
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Parameter sets used by Bajpai & Reuß
+\begin_inset space \space{}
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset CommandInset label
+LatexCommand label
+name "parset"
+
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="4">
+<features tabularvalignment="middle">
+<column alignment="left" valignment="top" width="0">
+<column alignment="right" valignment="top" width="0">
+<column alignment="left" valignment="top" width="0">
+<column alignment="left" valignment="top" width="0">
+<row>
+<cell multicolumn="1" alignment="none" valignment="top" topline="true" usebox="none" special="l">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\shape italic
+parameter
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="2" alignment="center" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="left" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\shape italic
+Set 1
+\shape default
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="left" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\shape italic
+Set 2
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mu_{x}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+[h
+\begin_inset Formula $^{-1}$
+\end_inset
+
+]
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="left" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0.092
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="left" valignment="top" topline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0.11
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $K_{x}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+[g/g DM]
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="left" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0.15
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="left" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0.006
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\mu_{p}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+[g/g DM h]
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="left" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0.005
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="left" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0.004
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $K_{p}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+[g/L]
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="left" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0.0002
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="left" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0.0001
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $K_{i}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+[g/L]
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="left" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0.1
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="left" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0.1
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $Y_{x/s}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+[g DM/g]
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="left" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0.45
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="left" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0.47
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $Y_{p/s}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+[g/g]
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="left" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0.9
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="left" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+1.2
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $k_{h}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+[h
+\begin_inset Formula $^{-1}$
+\end_inset
+
+]
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="left" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0.04
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="left" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0.01
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="left" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $m_{s}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="right" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+[g/g DM h]
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="left" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0.014
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="left" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0.029
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Bajpai & Reuß
+\begin_inset space \space{}
+\end_inset
+
+decided to disregard the differences between time constants for the two
+ regulation mechanisms (glucose repression or inhibition) because of the
+ relatively very long fermentation times, and therefore proposed a Haldane
+ expression for
+\begin_inset Formula $\pi$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+It is interesting that simulations with the
+\begin_inset CommandInset citation
+LatexCommand cite
+key "r4"
+
+\end_inset
+
+ model for the initial conditions given by these authors indicate that,
+ when the remaining substrate is fed at a constant rate, a considerable
+ and unrealistic amount of penicillin is produced when the glucose concentration
+ is still very high
+\begin_inset CommandInset citation
+LatexCommand cite
+key "r2,r3,r4"
+
+\end_inset
+
+ Simulations with the Bajpai & Reuß
+\begin_inset space \space{}
+\end_inset
+
+model correctly predict almost no penicillin production in similar conditions.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+figuur 1
+\end_layout
+
+\end_inset
+
+
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+fbox{
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+vbox
+\end_layout
+
+\end_inset
+
+ to6pc
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+{
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+hsize
+\end_layout
+
+\end_inset
+
+4cm
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset VSpace vfill
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Caption
+
+\begin_layout Plain Layout
+\begin_inset Argument
+status collapsed
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+
+Pathway of the penicillin G biosynthesis.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset CommandInset label
+LatexCommand label
+name "penG"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Sample of cross-reference to figure.
+ Figure
+\begin_inset space ~
+\end_inset
+
+
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "penG"
+
+\end_inset
+
+ shows that is not easy to get something on paper.
+\end_layout
+
+\begin_layout Section
+Headings
+\end_layout
+
+\begin_layout Subsection
+Subsection
+\end_layout
+
+\begin_layout Standard
+Carr-Goldstein based their model on balancing methods and biochemical know\SpecialChar \-
+ledge.
+ The original model (1980) contained an equation for the oxygen dynamics
+ which has been omitted in a second paper (1981).
+ This simplified model shall be discussed here.
+\end_layout
+
+\begin_layout Subsubsection
+Subsubsection
+\end_layout
+
+\begin_layout Standard
+Carr-Goldstein based their model on balancing methods and biochemical know\SpecialChar \-
+ledge.
+ The original model (1980) contained an equation for the oxygen dynamics
+ which has been omitted in a second paper (1981).
+ This simplified model shall be discussed here.
+\end_layout
+
+\begin_layout Section
+Equations and the like
+\end_layout
+
+\begin_layout Standard
+Two equations:
+\begin_inset Formula \begin{equation}
+C_{s}=K_{M}\frac{\mu/\mu_{x}}{1-\mu/\mu_{x}}\label{ccs}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+and
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{equation}
+G=\frac{P_{{\rm opt}}-P_{{\rm ref}}}{P_{{\rm ref}}}\mbox{\ }100\mbox{\ }(\%)\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Two equation arrays:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{eqnarray}
+\frac{dS}{dt} & = & -\sigma X+s_{F}F\\
+\frac{dX}{dt} & = & \mu X\\
+\frac{dP}{dt} & = & \pi X-k_{h}P\\
+\frac{dV}{dt} & = & F
+\end{eqnarray}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+and,
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{eqnarray}
+\mu_{{\rm substr}} & = & \mu_{x}\frac{C_{s}}{K_{x}C_{x}+C_{s}}\\
+\mu & = & \mu_{{\rm substr}}-Y_{x/s}(1-H(C_{s}))(m_{s}+\pi/Y_{p/s})\\
+\sigma & = & \mu_{{\rm substr}}/Y_{x/s}+H(C_{s})(m_{s}+\pi/Y_{p/s})
+\end{eqnarray}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+\start_of_appendix
+Appendix section
+\end_layout
+
+\begin_layout Standard
+\begin_inset CommandInset label
+LatexCommand label
+name "app"
+
+\end_inset
+
+ We consider a sequence of queueing systems indexed by
+\begin_inset Formula $n$
+\end_inset
+
+.
+ It is assumed that each system is composed of
+\begin_inset Formula $J$
+\end_inset
+
+ stations, indexed by
+\begin_inset Formula $1$
+\end_inset
+
+ through
+\begin_inset Formula $J$
+\end_inset
+
+, and
+\begin_inset Formula $K$
+\end_inset
+
+ customer classes, indexed by
+\begin_inset Formula $1$
+\end_inset
+
+ through
+\begin_inset Formula $K$
+\end_inset
+
+.
+ Each customer class has a fixed route through the network of stations.
+ Customers in class
+\begin_inset Formula $k$
+\end_inset
+
+,
+\begin_inset Formula $k=1,\ldots,K$
+\end_inset
+
+, arrive to the system according to a renewal process, independently of
+ the arrivals of the other customer classes.
+ These customers move through the network, never visiting a station more
+ than once, until they eventually exit the system.
+\end_layout
+
+\begin_layout Subsection
+Appendix subsection
+\end_layout
+
+\begin_layout Standard
+However, different customer classes may visit stations in different orders;
+ the system is not necessarily
+\begin_inset Quotes eld
+\end_inset
+
+feed-forward.
+\begin_inset Quotes erd
+\end_inset
+
+ We define the
+\emph on
+path of class
+\begin_inset Formula $k$
+\end_inset
+
+ customers
+\emph default
+ in as the sequence of servers they encounter along their way through the
+ network and denote it by
+\begin_inset Formula \begin{equation}
+\mathcal{P}=\bigl(j_{k,1},j_{k,2},\dots,j_{k,m(k)}\bigr).\label{path}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Sample of cross-reference to the formula
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "path"
+
+\end_inset
+
+ in Appendix
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "app"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section*
+Acknowledgements
+\end_layout
+
+\begin_layout Standard
+And this is an acknowledgements section with a heading that was produced
+ by the
+\begin_inset Formula $\backslash$
+\end_inset
+
+section* command.
+ Thank you all for helping me writing this LaTeX
+\begin_inset space \space{}
+\end_inset
+
+sample file.
+\end_layout
+
+\begin_layout Bibliography
+\labelwidthstring References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "\\protect\\citeauthoryear{Billingsley, P.}{1999}"
+key "r1"
+
+\end_inset
+
+
+\shape smallcaps
+Billingsley, P.
+
+\shape default
+ (1999).
+
+\shape italic
+Convergence of Probability Measures
+\shape default
+, 2nd ed.
+ Wiley, New York.
+\end_layout
+
+\begin_layout Bibliography
+\labelwidthstring References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "\\protect\\citeauthoryear{Bourbaki, N.}{1966}"
+key "r2"
+
+\end_inset
+
+
+\shape smallcaps
+Bourbaki, N.
+
+\shape default
+ (1966).
+
+\shape italic
+General Topology
+\shape default
+
+\series bold
+1
+\series default
+.
+ Addison--Wesley, Reading, MA.
+\end_layout
+
+\begin_layout Bibliography
+\labelwidthstring References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "\\protect\\citeauthoryear{Ethier, S. N. and Kurtz, T. G.}{1985}"
+key "r3"
+
+\end_inset
+
+
+\shape smallcaps
+Ethier, S.
+ N.
+
+\shape default
+ and
+\shape smallcaps
+Kurtz, T.
+ G.
+
+\shape default
+ (1985).
+
+\shape italic
+Markov Processes: Characterization and Convergence
+\shape default
+.
+ Wiley, New York.
+\end_layout
+
+\begin_layout Bibliography
+\labelwidthstring References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "\\protect\\citeauthoryear{Prokhorov, Yu.}{1956}"
+key "r4"
+
+\end_inset
+
+
+\shape smallcaps
+Prokhorov, Yu.
+
+\shape default
+ (1956).
+ Convergence of random processes and limit theorems in probability theory.
+
+\shape italic
+Theory Probab.
+ Appl.
+
+\shape default
+
+\series bold
+1
+\series default
+ 157--214.
+\end_layout
+
+\begin_layout Bibliography
+\labelwidthstring References
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "\\protect\\citeauthoryear{Prokhorov, Yu.}{1957}"
+key "r5"
+
+\end_inset
+
+
+\begin_inset Flex By Same Author (bib)
+status open
+
+\begin_layout Plain Layout
+Prokhorov, Yu.
+\end_layout
+
+\end_inset
+
+ (1957).
+ Convergence of random processes and limit theorems in probability theory
+ II.
+
+\shape italic
+Theory Probab.
+ Appl.
+
+\shape default
+
+\series bold
+2
+\series default
+ 157--214.
+\end_layout
+
+\end_body
+\end_document
projects / lyx.git / commitdiff