1 #LyX 2.0.0svn created this file. For more info see http://www.lyx.org/
7 \RequirePackage[colorlinks,citecolor=blue,urlcolor=blue]{hyperref}
8 \RequirePackage{hypernat}
12 % These require a theorem-like module
13 \numberwithin{equation}{section}
18 \use_default_options false
22 \maintain_unincluded_children false
28 \font_typewriter default
29 \font_default_family default
37 \default_output_format default
39 \bibtex_command default
40 \index_command default
41 \paperfontsize default
45 \pdf_bookmarksnumbered false
46 \pdf_bookmarksopen false
47 \pdf_bookmarksopenlevel 1
59 \cite_engine natbib_authoryear
62 \paperorientation portrait
70 \paragraph_separation indent
71 \paragraph_indentation default
72 \quotes_language english
75 \paperpagestyle default
76 \tracking_changes false
89 \begin_layout Plain Layout
99 \begin_inset Flex Thanks Reference
102 \begin_layout Plain Layout
111 \begin_layout RunTitle
115 \begin_layout Thanks Text
116 Footnote to the title with the `thankstext' command.
117 \begin_inset Argument
120 \begin_layout Plain Layout
129 \begin_layout Authors Block
130 \begin_inset Flex Author
133 \begin_layout Plain Layout
134 \begin_inset Flex Name (First Name)
137 \begin_layout Plain Layout
144 \begin_inset Flex Name (Surname)
147 \begin_layout Plain Layout
154 \begin_inset Flex Thanks Reference
157 \begin_layout Plain Layout
169 \begin_inset Flex Author
172 \begin_layout Plain Layout
173 \begin_inset Flex Name (First Name)
176 \begin_layout Plain Layout
183 \begin_inset Flex Name (Surname)
186 \begin_layout Plain Layout
193 \begin_inset Flex Thanks Reference
196 \begin_layout Plain Layout
208 \begin_inset Flex Author
211 \begin_layout Plain Layout
212 \begin_inset Flex Name (First Name)
215 \begin_layout Plain Layout
222 \begin_inset Flex Name (Surname)
225 \begin_layout Plain Layout
232 \begin_inset Flex Thanks Reference
235 \begin_layout Plain Layout
251 \begin_inset Argument
254 \begin_layout Plain Layout
265 \begin_inset Argument
268 \begin_layout Plain Layout
279 \begin_inset Argument
282 \begin_layout Plain Layout
291 \begin_layout Web Address
293 \begin_inset Argument
296 \begin_layout Plain Layout
305 \begin_layout Thanks Text
307 \begin_inset Argument
310 \begin_layout Plain Layout
319 \begin_layout RunAuthor
326 \begin_layout Address
327 \begin_inset Argument
330 \begin_layout Plain Layout
336 Address of the First and Second authors, usually few lines long usually
337 few lines long usually few lines long
340 \begin_layout Address
341 \begin_inset Argument
344 \begin_layout Plain Layout
350 Address of the Third author, usually few lines long, usually few lines long
352 \begin_inset Flex Internet Address Reference
355 \begin_layout Plain Layout
364 \begin_layout Abstract
365 The abstract should summarize the contents of the paper.
366 It should be clear, descriptive, self-explanatory and not longer than 150
368 It should also be suitable for publication in abstracting services.
369 Please avoid using math formulas as much as possible.
372 \begin_layout Abstract
373 This is a sample input file.
374 Comparing it with the output it generates can show you how to produce a
375 simple document of your own.
379 \begin_layout Keyword
380 \begin_inset Flex Keyword
383 \begin_layout Plain Layout
390 \begin_inset Flex Keyword
393 \begin_layout Plain Layout
402 \begin_layout Section
406 \begin_layout Standard
407 The ends of words and sentences are marked by spaces.
408 It doesn't matter how many spaces you type; one is as good as 100.
409 The end of a line counts as a space.
412 \begin_layout Standard
413 One or more blank lines denote the end of a paragraph.
416 \begin_layout Standard
417 Since any number of consecutive spaces are treated like a single one, the
418 formatting of the input file makes no difference to TeX, but it makes a
420 When you use LaTeX, making your input file as easy to read as possible
421 will be a great help as you write your document and when you change it.
422 This sample file shows how you can add comments to your own input file.
425 \begin_layout Standard
426 Because printing is different from typewriting, there are a number of things
427 that you have to do differently when preparing an input file than if you
428 were just typing the document directly.
430 \begin_inset Quotes eld
434 \begin_inset Quotes erd
437 have to be handled specially, as do quotes within quotes:
438 \begin_inset Quotes eld
442 \begin_inset space \thinspace{}
446 \begin_inset Note Note
449 \begin_layout Plain Layout
450 Small space separates the double and single quote.
455 is what I just wrote, not `that'
456 \begin_inset space \thinspace{}
460 \begin_inset Quotes erd
466 \begin_layout Standard
467 Dashes come in three sizes: an intra-word dash, a medium dash for number
468 ranges like 1--2, and a punctuation dash---like this.
471 \begin_layout Standard
472 A sentence-ending space should be larger than the space between words within
474 You sometimes have to type special commands in conjunction with punctuation
475 characters to get this right, as in the following sentence.
477 \begin_inset space \space{}
481 \begin_inset Note Note
484 \begin_layout Plain Layout
485 This makes an inter-word space.
490 all begin with G\SpecialChar \@.
492 \begin_inset Note Note
495 \begin_layout Plain Layout
496 The end-of-sentence punctuation.
501 You should check the spaces after periods when reading your output to make
502 sure you haven't forgotten any special cases.
503 Generating an ellipsis \SpecialChar \ldots{}
505 \begin_inset space \space{}
509 \begin_inset Note Note
512 \begin_layout Plain Layout
513 Inter-word space needed because TeX ignores spaces after command names like
531 with the right spacing around the periods requires a special command.
534 \begin_layout Standard
536 \begin_inset space \space{}
539 interprets some common characters as commands, so you must type special
540 commands to generate them.
541 These characters include the following:
542 \begin_inset Note Note
545 \begin_layout Plain Layout
561 \begin_layout Plain Layout
570 \begin_layout Standard
571 In printing, text is emphasized by using an
579 \begin_layout Plain Layout
589 \begin_inset Note Note
592 \begin_layout Plain Layout
599 command produces the tiny extra space that should be added between a slanted
600 and a following unslanted letter.
608 \begin_layout Emphasize
609 A long segment of text can also be emphasized in this way.
610 Text within such a segment given additional emphasis with
615 Italic type loses its ability to emphasize and become simply distracting
616 when used excessively.
620 \begin_layout Standard
621 It is sometimes necessary to prevent TeX
622 \begin_inset space \space{}
625 from breaking a line where it might otherwise do so.
626 This may be at a space, as between the
627 \begin_inset Quotes eld
631 \begin_inset Quotes erd
635 \begin_inset Quotes eld
639 \begin_inset Quotes erd
643 \begin_inset Quotes eld
651 \begin_inset Quotes erd
655 \begin_inset Note Note
658 \begin_layout Plain Layout
663 produces an unbreakable interword space.
668 or within a word---especially when the word is a symbol like
676 \begin_layout Plain Layout
685 that makes little sense when hyphenated across lines.
688 \begin_layout Standard
690 \begin_inset space \space{}
693 is good at typesetting mathematical formulas like
694 \begin_inset Formula \ensuremath{x-3y=7}
699 \begin_inset Formula \ensuremath{a_{1}>x^{2n}/y^{2n}>x'}
704 Remember that a letter like
705 \begin_inset Formula $x$
708 is a formula when it denotes a mathematical symbol, and should be treated
712 \begin_layout Section
716 \begin_layout Standard
721 \begin_layout Plain Layout
722 This is an example of a footnote.
731 \begin_layout Plain Layout
740 \begin_layout Section
744 \begin_layout Standard
745 Text is displayed by indenting it from the left margin.
746 Quotations are commonly displayed.
747 There are short quotations
751 This is a short a quotation.
752 It consists of a single paragraph of text.
753 There is no paragraph indentation.
757 \begin_layout Standard
762 \begin_layout Quotation
763 This is a longer quotation.
764 It consists of two paragraphs of text.
765 The beginning of each paragraph is indicated by an extra indentation.
768 \begin_layout Quotation
769 This is the second paragraph of the quotation.
770 It is just as dull as the first paragraph.
774 \begin_layout Standard
775 Another frequently-displayed structure is a list.
776 The following is an example of an
780 list, four levels deep.
784 \begin_layout Itemize
785 This is the first item of an itemized list.
786 Each item in the list is marked with a
787 \begin_inset Quotes eld
791 \begin_inset Quotes erd
795 The document style determines what kind of tick mark is used.
799 \begin_layout Itemize
800 This is the second item of the list.
801 It contains another list nested inside it.
802 The three inner lists are an
811 \begin_layout Itemize
812 This is the first item of an enumerated list that is nested within the itemized
817 \begin_layout Itemize
818 This is the second item of the inner list.
819 LaTeX allows you to nest lists deeper than you really should.
823 \begin_layout Standard
824 This is the rest of the second item of the outer list.
825 It is no more interesting than any other part of the item.
830 \begin_layout Itemize
831 This is the third item of the list.
835 \begin_layout Standard
836 The following is an example of an
840 list, four levels deep.
844 \begin_layout Enumerate
845 This is the first item of an enumerated list.
846 Each item in the list is marked with a
847 \begin_inset Quotes eld
851 \begin_inset Quotes erd
855 The document style determines what kind of tick mark is used.
859 \begin_layout Enumerate
860 This is the second item of the list.
861 It contains another list nested inside it.
862 The three inner lists are an
871 \begin_layout Enumerate
872 This is the first item of an enumerated list that is nested within the enumerate
877 \begin_layout Enumerate
878 This is the second item of the inner list.
879 LaTeX allows you to nest lists deeper than you really should.
883 \begin_layout Standard
884 This is the rest of the second item of the outer list.
885 It is no more interesting than any other part of the item.
890 \begin_layout Enumerate
891 This is the third item of the list.
895 \begin_layout Standard
896 The following is an example of a
904 \begin_layout Description
905 Cow Highly intelligent animal that can produce milk out of grass.
909 \begin_layout Description
910 Horse Less intelligent animal renowned for its legs.
914 \begin_layout Description
915 Human being Not so intelligent animal that thinks that it can think.
919 \begin_layout Standard
920 You can even display poetry.
925 There is an environment for verse
926 \begin_inset Newline newline
930 \begin_inset Note Note
933 \begin_layout Plain Layout
942 command separates lines within a stanza.
943 One or more blank lines separate stanzas.
948 Whose features some poets will curse.
953 For instead of making
954 \begin_inset Newline newline
965 \begin_layout Plain Layout
975 \begin_inset Newline newline
978 It allows them to put too many words on a line when they'd rather be forced
983 \begin_layout Standard
984 Mathematical formulas may also be displayed.
985 A displayed formula is one-line long; multiline formulas require special
986 formatting instructions.
988 \begin_inset Formula \[
993 Don't start a paragraph with a displayed equation, nor make one a paragraph
997 \begin_layout Standard
998 Example of a theorem:
1001 \begin_layout Theorem
1002 All conjectures are interesting, but some conjectures are more interesting
1011 \begin_layout Section
1015 \begin_layout Standard
1016 Cross reference to labelled table: As you can see in Table
1017 \begin_inset space ~
1021 \begin_inset CommandInset ref
1023 reference "sphericcase"
1028 \begin_inset space ~
1032 \begin_inset CommandInset ref
1033 LatexCommand pageref
1034 reference "sphericcase"
1039 \begin_inset space ~
1043 \begin_inset CommandInset ref
1050 \begin_inset space ~
1054 \begin_inset CommandInset ref
1055 LatexCommand pageref
1063 \begin_layout Standard
1064 \begin_inset Float table
1069 \begin_layout Plain Layout
1070 \begin_inset Caption
1072 \begin_layout Plain Layout
1073 The spherical case (
1074 \begin_inset Formula $I_{1}=0$
1078 \begin_inset Formula $I_{2}=0$
1089 \begin_layout Plain Layout
1090 \begin_inset CommandInset label
1097 \begin_inset Tabular
1098 <lyxtabular version="3" rows="13" columns="6">
1099 <features tabularvalignment="middle">
1100 <column alignment="center" valignment="top" width="0">
1101 <column alignment="right" valignment="top" width="0">
1102 <column alignment="right" valignment="top" width="0">
1103 <column alignment="right" valignment="top" width="0">
1104 <column alignment="right" valignment="top" width="0">
1105 <column alignment="center" valignment="top" width="0">
1107 <cell alignment="center" valignment="top" topline="true" usebox="none">
1110 \begin_layout Plain Layout
1117 <cell alignment="none" valignment="top" topline="true" usebox="none">
1120 \begin_layout Plain Layout
1126 <cell alignment="none" valignment="top" topline="true" usebox="none">
1129 \begin_layout Plain Layout
1135 <cell alignment="none" valignment="top" topline="true" usebox="none">
1138 \begin_layout Plain Layout
1144 <cell alignment="none" valignment="top" topline="true" usebox="none">
1147 \begin_layout Plain Layout
1153 <cell alignment="none" valignment="top" topline="true" usebox="none">
1156 \begin_layout Plain Layout
1164 <cell alignment="center" valignment="top" usebox="none">
1167 \begin_layout Plain Layout
1173 <cell multicolumn="1" alignment="none" valignment="top" usebox="none" special="c">
1176 \begin_layout Plain Layout
1177 \begin_inset Formula $x$
1185 <cell multicolumn="1" alignment="none" valignment="top" usebox="none" special="c">
1188 \begin_layout Plain Layout
1189 \begin_inset Formula $y$
1197 <cell multicolumn="1" alignment="none" valignment="top" usebox="none" special="c">
1200 \begin_layout Plain Layout
1201 \begin_inset Formula $z$
1209 <cell multicolumn="1" alignment="none" valignment="top" usebox="none" special="c">
1212 \begin_layout Plain Layout
1213 \begin_inset Formula $C$
1221 <cell alignment="center" valignment="top" usebox="none">
1224 \begin_layout Plain Layout
1232 <cell alignment="center" valignment="top" topline="true" usebox="none">
1235 \begin_layout Plain Layout
1236 \begin_inset Formula $~~L_{1}$
1244 <cell alignment="right" valignment="top" topline="true" usebox="none">
1247 \begin_layout Plain Layout
1248 \begin_inset Formula $-$
1256 <cell alignment="right" valignment="top" topline="true" usebox="none">
1259 \begin_layout Plain Layout
1265 <cell alignment="right" valignment="top" topline="true" usebox="none">
1268 \begin_layout Plain Layout
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1277 \begin_layout Plain Layout
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1286 \begin_layout Plain Layout
1294 <cell alignment="center" valignment="top" usebox="none">
1297 \begin_layout Plain Layout
1298 \begin_inset Formula $~~L_{2}$
1306 <cell alignment="right" valignment="top" usebox="none">
1309 \begin_layout Plain Layout
1315 <cell alignment="right" valignment="top" usebox="none">
1318 \begin_layout Plain Layout
1324 <cell alignment="right" valignment="top" usebox="none">
1327 \begin_layout Plain Layout
1333 <cell alignment="right" valignment="top" usebox="none">
1336 \begin_layout Plain Layout
1342 <cell alignment="center" valignment="top" usebox="none">
1345 \begin_layout Plain Layout
1353 <cell alignment="center" valignment="top" usebox="none">
1356 \begin_layout Plain Layout
1357 \begin_inset Formula $~~L_{3}$
1365 <cell alignment="right" valignment="top" usebox="none">
1368 \begin_layout Plain Layout
1374 <cell alignment="right" valignment="top" usebox="none">
1377 \begin_layout Plain Layout
1383 <cell alignment="right" valignment="top" usebox="none">
1386 \begin_layout Plain Layout
1392 <cell alignment="right" valignment="top" usebox="none">
1395 \begin_layout Plain Layout
1396 \begin_inset Formula $-$
1404 <cell alignment="center" valignment="top" usebox="none">
1407 \begin_layout Plain Layout
1415 <cell alignment="center" valignment="top" usebox="none">
1418 \begin_layout Plain Layout
1419 \begin_inset Formula $~~L_{4}$
1427 <cell alignment="right" valignment="top" usebox="none">
1430 \begin_layout Plain Layout
1436 <cell alignment="right" valignment="top" usebox="none">
1439 \begin_layout Plain Layout
1445 <cell alignment="right" valignment="top" usebox="none">
1448 \begin_layout Plain Layout
1449 \begin_inset Formula $-$
1457 <cell alignment="right" valignment="top" usebox="none">
1460 \begin_layout Plain Layout
1466 <cell alignment="center" valignment="top" usebox="none">
1469 \begin_layout Plain Layout
1477 <cell alignment="center" valignment="top" usebox="none">
1480 \begin_layout Plain Layout
1481 \begin_inset Formula $~~L_{5}$
1489 <cell alignment="right" valignment="top" usebox="none">
1492 \begin_layout Plain Layout
1498 <cell alignment="right" valignment="top" usebox="none">
1501 \begin_layout Plain Layout
1507 <cell alignment="right" valignment="top" usebox="none">
1510 \begin_layout Plain Layout
1511 \begin_inset Formula $-$
1519 <cell alignment="right" valignment="top" usebox="none">
1522 \begin_layout Plain Layout
1528 <cell alignment="center" valignment="top" usebox="none">
1531 \begin_layout Plain Layout
1539 <cell alignment="center" valignment="top" usebox="none">
1542 \begin_layout Plain Layout
1543 \begin_inset Formula $~~L_{6}$
1551 <cell alignment="right" valignment="top" usebox="none">
1554 \begin_layout Plain Layout
1560 <cell alignment="right" valignment="top" usebox="none">
1563 \begin_layout Plain Layout
1569 <cell alignment="right" valignment="top" usebox="none">
1572 \begin_layout Plain Layout
1578 <cell alignment="right" valignment="top" usebox="none">
1581 \begin_layout Plain Layout
1587 <cell alignment="center" valignment="top" usebox="none">
1590 \begin_layout Plain Layout
1598 <cell alignment="center" valignment="top" usebox="none">
1601 \begin_layout Plain Layout
1602 \begin_inset Formula $~~L_{7}$
1610 <cell alignment="right" valignment="top" usebox="none">
1613 \begin_layout Plain Layout
1619 <cell alignment="right" valignment="top" usebox="none">
1622 \begin_layout Plain Layout
1628 <cell alignment="right" valignment="top" usebox="none">
1631 \begin_layout Plain Layout
1632 \begin_inset Formula $-$
1640 <cell alignment="right" valignment="top" usebox="none">
1643 \begin_layout Plain Layout
1649 <cell alignment="center" valignment="top" usebox="none">
1652 \begin_layout Plain Layout
1660 <cell alignment="center" valignment="top" usebox="none">
1663 \begin_layout Plain Layout
1664 \begin_inset Formula $~~L_{8}$
1672 <cell alignment="right" valignment="top" usebox="none">
1675 \begin_layout Plain Layout
1681 <cell alignment="right" valignment="top" usebox="none">
1684 \begin_layout Plain Layout
1690 <cell alignment="right" valignment="top" usebox="none">
1693 \begin_layout Plain Layout
1694 \begin_inset Formula $-$
1702 <cell alignment="right" valignment="top" usebox="none">
1705 \begin_layout Plain Layout
1711 <cell alignment="center" valignment="top" usebox="none">
1714 \begin_layout Plain Layout
1722 <cell alignment="center" valignment="top" usebox="none">
1725 \begin_layout Plain Layout
1726 \begin_inset Formula $~~L_{9}$
1734 <cell alignment="right" valignment="top" usebox="none">
1737 \begin_layout Plain Layout
1743 <cell alignment="right" valignment="top" usebox="none">
1746 \begin_layout Plain Layout
1747 \begin_inset Formula $-$
1755 <cell alignment="right" valignment="top" usebox="none">
1758 \begin_layout Plain Layout
1759 \begin_inset Formula $-$
1767 <cell alignment="right" valignment="top" usebox="none">
1770 \begin_layout Plain Layout
1776 <cell alignment="center" valignment="top" usebox="none">
1779 \begin_layout Plain Layout
1787 <cell alignment="center" valignment="top" usebox="none">
1790 \begin_layout Plain Layout
1791 \begin_inset Formula $~~L_{10}$
1799 <cell alignment="right" valignment="top" usebox="none">
1802 \begin_layout Plain Layout
1808 <cell alignment="right" valignment="top" usebox="none">
1811 \begin_layout Plain Layout
1817 <cell alignment="right" valignment="top" usebox="none">
1820 \begin_layout Plain Layout
1821 \begin_inset Formula $-$
1829 <cell alignment="right" valignment="top" usebox="none">
1832 \begin_layout Plain Layout
1838 <cell alignment="center" valignment="top" usebox="none">
1841 \begin_layout Plain Layout
1849 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1852 \begin_layout Plain Layout
1853 \begin_inset Formula $~~L_{11}$
1861 <cell alignment="right" valignment="top" bottomline="true" usebox="none">
1864 \begin_layout Plain Layout
1870 <cell alignment="right" valignment="top" bottomline="true" usebox="none">
1873 \begin_layout Plain Layout
1874 \begin_inset Formula $-$
1882 <cell alignment="right" valignment="top" bottomline="true" usebox="none">
1885 \begin_layout Plain Layout
1886 \begin_inset Formula $-$
1894 <cell alignment="right" valignment="top" bottomline="true" usebox="none">
1897 \begin_layout Plain Layout
1903 <cell alignment="center" valignment="top" bottomline="true" usebox="none">
1906 \begin_layout Plain Layout
1925 \begin_layout Standard
1926 A major point of difference lies in the value of the specific production
1928 \begin_inset Formula $\pi$
1931 for large values of the specific growth rate
1932 \begin_inset Formula $\mu$
1936 Already in the early publications
1937 \begin_inset CommandInset citation
1943 it appeared that high glucose concentrations in the production phase are
1944 well correlated with a low penicillin yield (the `glucose effect').
1945 It has been confirmed recently
1946 \begin_inset CommandInset citation
1952 that high glucose concentrations inhibit the synthesis of the enzymes of
1953 the penicillin pathway, but not the actual penicillin biosynthesis.
1954 In other words, glucose represses (and not inhibits) the penicillin biosynthesi
1958 \begin_layout Standard
1959 These findings do not contradict the results of
1960 \begin_inset CommandInset citation
1967 \begin_inset CommandInset citation
1973 which were obtained for continuous culture fermentations.
1974 Because for high values of the specific growth rate
1975 \begin_inset Formula $\mu$
1978 it is most likely (as shall be discussed below) that maintenance metabolism
1979 occurs, it can be shown that in steady state continuous culture conditions,
1981 \begin_inset Formula $\mu$
1984 described by a Monod kinetics
1985 \begin_inset Formula \begin{equation}
1986 C_{s}=K_{M}\frac{\mu/\mu_{x}}{1-\mu/\mu_{x}}\label{cs}\end{equation}
1990 Pirt & Rhigelato determined
1991 \begin_inset Formula $\pi$
1995 \begin_inset Formula $\mu$
1999 \begin_inset Formula $0.023$
2003 \begin_inset Formula $0.086$
2007 \begin_inset Formula $^{-1}$
2011 They also reported a value
2012 \begin_inset Formula $\mu_{x}\approx0.095$
2016 \begin_inset Formula $^{-1}$
2019 , so that for their experiments
2020 \begin_inset Formula $\mu/\mu_{x}$
2024 \begin_inset Formula $0.24$
2028 \begin_inset Formula $0.9$
2033 \begin_inset Formula $K_{M}$
2038 \begin_inset CommandInset ref
2045 \begin_inset Formula $K_{M}=1$
2049 \begin_inset CommandInset citation
2055 , one finds with the above equation
2056 \begin_inset Formula $0.3<C_{s}<9$
2060 This agrees well with the work of
2061 \begin_inset CommandInset citation
2067 , who reported that penicillin biosynthesis repression only occurs at glucose
2069 \begin_inset Formula $C_{s}=10$
2073 The conclusion is that the glucose concentrations in the experiments of
2074 Pirt & Rhigelato probably were too low for glucose repression to be detected.
2075 The experimental data published by Ryu & Hospodka are not detailed sufficiently
2076 to permit a similar analysis.
2079 \begin_layout Standard
2080 \begin_inset Float table
2085 \begin_layout Plain Layout
2089 \begin_layout Plain Layout
2099 \begin_inset Caption
2101 \begin_layout Plain Layout
2102 Parameter sets used by Bajpai & Reuß
2103 \begin_inset space \space{}
2114 \begin_layout Plain Layout
2115 \begin_inset CommandInset label
2122 \begin_inset Tabular
2123 <lyxtabular version="3" rows="10" columns="4">
2124 <features tabularvalignment="middle">
2125 <column alignment="left" valignment="top" width="0">
2126 <column alignment="right" valignment="top" width="0">
2127 <column alignment="left" valignment="top" width="0">
2128 <column alignment="left" valignment="top" width="0">
2130 <cell multicolumn="1" alignment="none" valignment="top" topline="true" usebox="none" special="l">
2133 \begin_layout Plain Layout
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2144 \begin_layout Plain Layout
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2153 \begin_layout Plain Layout
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2166 \begin_layout Plain Layout
2176 <cell alignment="left" valignment="top" topline="true" usebox="none">
2179 \begin_layout Plain Layout
2180 \begin_inset Formula $\mu_{x}$
2188 <cell alignment="right" valignment="top" topline="true" usebox="none">
2191 \begin_layout Plain Layout
2193 \begin_inset Formula $^{-1}$
2201 <cell alignment="left" valignment="top" topline="true" usebox="none">
2204 \begin_layout Plain Layout
2210 <cell alignment="left" valignment="top" topline="true" usebox="none">
2213 \begin_layout Plain Layout
2221 <cell alignment="left" valignment="top" usebox="none">
2224 \begin_layout Plain Layout
2225 \begin_inset Formula $K_{x}$
2233 <cell alignment="right" valignment="top" usebox="none">
2236 \begin_layout Plain Layout
2242 <cell alignment="left" valignment="top" usebox="none">
2245 \begin_layout Plain Layout
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2254 \begin_layout Plain Layout
2262 <cell alignment="left" valignment="top" usebox="none">
2265 \begin_layout Plain Layout
2266 \begin_inset Formula $\mu_{p}$
2274 <cell alignment="right" valignment="top" usebox="none">
2277 \begin_layout Plain Layout
2283 <cell alignment="left" valignment="top" usebox="none">
2286 \begin_layout Plain Layout
2292 <cell alignment="left" valignment="top" usebox="none">
2295 \begin_layout Plain Layout
2303 <cell alignment="left" valignment="top" usebox="none">
2306 \begin_layout Plain Layout
2307 \begin_inset Formula $K_{p}$
2315 <cell alignment="right" valignment="top" usebox="none">
2318 \begin_layout Plain Layout
2324 <cell alignment="left" valignment="top" usebox="none">
2327 \begin_layout Plain Layout
2333 <cell alignment="left" valignment="top" usebox="none">
2336 \begin_layout Plain Layout
2344 <cell alignment="left" valignment="top" usebox="none">
2347 \begin_layout Plain Layout
2348 \begin_inset Formula $K_{i}$
2356 <cell alignment="right" valignment="top" usebox="none">
2359 \begin_layout Plain Layout
2365 <cell alignment="left" valignment="top" usebox="none">
2368 \begin_layout Plain Layout
2374 <cell alignment="left" valignment="top" usebox="none">
2377 \begin_layout Plain Layout
2385 <cell alignment="left" valignment="top" usebox="none">
2388 \begin_layout Plain Layout
2389 \begin_inset Formula $Y_{x/s}$
2397 <cell alignment="right" valignment="top" usebox="none">
2400 \begin_layout Plain Layout
2406 <cell alignment="left" valignment="top" usebox="none">
2409 \begin_layout Plain Layout
2415 <cell alignment="left" valignment="top" usebox="none">
2418 \begin_layout Plain Layout
2426 <cell alignment="left" valignment="top" usebox="none">
2429 \begin_layout Plain Layout
2430 \begin_inset Formula $Y_{p/s}$
2438 <cell alignment="right" valignment="top" usebox="none">
2441 \begin_layout Plain Layout
2447 <cell alignment="left" valignment="top" usebox="none">
2450 \begin_layout Plain Layout
2456 <cell alignment="left" valignment="top" usebox="none">
2459 \begin_layout Plain Layout
2467 <cell alignment="left" valignment="top" usebox="none">
2470 \begin_layout Plain Layout
2471 \begin_inset Formula $k_{h}$
2479 <cell alignment="right" valignment="top" usebox="none">
2482 \begin_layout Plain Layout
2484 \begin_inset Formula $^{-1}$
2492 <cell alignment="left" valignment="top" usebox="none">
2495 \begin_layout Plain Layout
2501 <cell alignment="left" valignment="top" usebox="none">
2504 \begin_layout Plain Layout
2512 <cell alignment="left" valignment="top" bottomline="true" usebox="none">
2515 \begin_layout Plain Layout
2516 \begin_inset Formula $m_{s}$
2524 <cell alignment="right" valignment="top" bottomline="true" usebox="none">
2527 \begin_layout Plain Layout
2533 <cell alignment="left" valignment="top" bottomline="true" usebox="none">
2536 \begin_layout Plain Layout
2542 <cell alignment="left" valignment="top" bottomline="true" usebox="none">
2545 \begin_layout Plain Layout
2564 \begin_layout Standard
2566 \begin_inset space \space{}
2569 decided to disregard the differences between time constants for the two
2570 regulation mechanisms (glucose repression or inhibition) because of the
2571 relatively very long fermentation times, and therefore proposed a Haldane
2573 \begin_inset Formula $\pi$
2579 \begin_layout Standard
2580 It is interesting that simulations with the
2581 \begin_inset CommandInset citation
2587 model for the initial conditions given by these authors indicate that,
2588 when the remaining substrate is fed at a constant rate, a considerable
2589 and unrealistic amount of penicillin is produced when the glucose concentration
2591 \begin_inset CommandInset citation
2597 Simulations with the Bajpai & Reuß
2598 \begin_inset space \space{}
2601 model correctly predict almost no penicillin production in similar conditions.
2604 \begin_layout Standard
2605 \begin_inset Note Note
2608 \begin_layout Plain Layout
2615 \begin_inset Float figure
2620 \begin_layout Plain Layout
2624 \begin_layout Plain Layout
2637 \begin_layout Plain Layout
2650 \begin_layout Plain Layout
2661 \begin_layout Plain Layout
2671 \begin_inset space \hfill{}
2675 \begin_inset VSpace vfill
2682 \begin_layout Plain Layout
2693 \begin_layout Plain Layout
2701 \begin_inset Caption
2703 \begin_layout Plain Layout
2704 \begin_inset Argument
2707 \begin_layout Plain Layout
2713 Pathway of the penicillin G biosynthesis.
2721 \begin_layout Plain Layout
2722 \begin_inset CommandInset label
2736 \begin_layout Standard
2737 Sample of cross-reference to figure.
2739 \begin_inset space ~
2743 \begin_inset CommandInset ref
2749 shows that is not easy to get something on paper.
2752 \begin_layout Section
2756 \begin_layout Subsection
2760 \begin_layout Standard
2761 Carr-Goldstein based their model on balancing methods and biochemical know\SpecialChar \-
2763 The original model (1980) contained an equation for the oxygen dynamics
2764 which has been omitted in a second paper (1981).
2765 This simplified model shall be discussed here.
2768 \begin_layout Subsubsection
2772 \begin_layout Standard
2773 Carr-Goldstein based their model on balancing methods and biochemical know\SpecialChar \-
2775 The original model (1980) contained an equation for the oxygen dynamics
2776 which has been omitted in a second paper (1981).
2777 This simplified model shall be discussed here.
2780 \begin_layout Section
2781 Equations and the like
2784 \begin_layout Standard
2786 \begin_inset Formula \begin{equation}
2787 C_{s}=K_{M}\frac{\mu/\mu_{x}}{1-\mu/\mu_{x}}\label{ccs}\end{equation}
2794 \begin_layout Standard
2798 \begin_layout Standard
2799 \begin_inset Formula \begin{equation}
2800 G=\frac{P_{{\rm opt}}-P_{{\rm ref}}}{P_{{\rm ref}}}\mbox{\ }100\mbox{\ }(\%)\end{equation}
2807 \begin_layout Standard
2808 Two equation arrays:
2811 \begin_layout Standard
2812 \begin_inset Formula \begin{eqnarray}
2813 \frac{dS}{dt} & = & -\sigma X+s_{F}F\\
2814 \frac{dX}{dt} & = & \mu X\\
2815 \frac{dP}{dt} & = & \pi X-k_{h}P\\
2816 \frac{dV}{dt} & = & F
2824 \begin_layout Standard
2828 \begin_layout Standard
2829 \begin_inset Formula \begin{eqnarray}
2830 \mu_{{\rm substr}} & = & \mu_{x}\frac{C_{s}}{K_{x}C_{x}+C_{s}}\\
2831 \mu & = & \mu_{{\rm substr}}-Y_{x/s}(1-H(C_{s}))(m_{s}+\pi/Y_{p/s})\\
2832 \sigma & = & \mu_{{\rm substr}}/Y_{x/s}+H(C_{s})(m_{s}+\pi/Y_{p/s})
2840 \begin_layout Section
2845 \begin_layout Standard
2846 \begin_inset CommandInset label
2852 We consider a sequence of queueing systems indexed by
2853 \begin_inset Formula $n$
2857 It is assumed that each system is composed of
2858 \begin_inset Formula $J$
2861 stations, indexed by
2862 \begin_inset Formula $1$
2866 \begin_inset Formula $J$
2870 \begin_inset Formula $K$
2873 customer classes, indexed by
2874 \begin_inset Formula $1$
2878 \begin_inset Formula $K$
2882 Each customer class has a fixed route through the network of stations.
2884 \begin_inset Formula $k$
2888 \begin_inset Formula $k=1,\ldots,K$
2891 , arrive to the system according to a renewal process, independently of
2892 the arrivals of the other customer classes.
2893 These customers move through the network, never visiting a station more
2894 than once, until they eventually exit the system.
2897 \begin_layout Subsection
2901 \begin_layout Standard
2902 However, different customer classes may visit stations in different orders;
2903 the system is not necessarily
2904 \begin_inset Quotes eld
2908 \begin_inset Quotes erd
2914 \begin_inset Formula $k$
2919 in as the sequence of servers they encounter along their way through the
2920 network and denote it by
2921 \begin_inset Formula \begin{equation}
2922 \mathcal{P}=\bigl(j_{k,1},j_{k,2},\dots,j_{k,m(k)}\bigr).\label{path}\end{equation}
2929 \begin_layout Standard
2930 Sample of cross-reference to the formula
2931 \begin_inset CommandInset ref
2938 \begin_inset CommandInset ref
2947 \begin_layout Section*
2951 \begin_layout Standard
2952 And this is an acknowledgements section with a heading that was produced
2954 \begin_inset Formula $\backslash$
2958 Thank you all for helping me writing this LaTeX
2959 \begin_inset space \space{}
2965 \begin_layout Bibliography
2966 \labelwidthstring References
2967 \begin_inset CommandInset bibitem
2968 LatexCommand bibitem
2969 label "\\protect\\citeauthoryear{Billingsley, P.}{1999}"
2982 Convergence of Probability Measures
2988 \begin_layout Bibliography
2989 \labelwidthstring References
2990 \begin_inset CommandInset bibitem
2991 LatexCommand bibitem
2992 label "\\protect\\citeauthoryear{Bourbaki, N.}{1966}"
3012 Addison--Wesley, Reading, MA.
3015 \begin_layout Bibliography
3016 \labelwidthstring References
3017 \begin_inset CommandInset bibitem
3018 LatexCommand bibitem
3019 label "\\protect\\citeauthoryear{Ethier, S. N. and Kurtz, T. G.}{1985}"
3039 Markov Processes: Characterization and Convergence
3045 \begin_layout Bibliography
3046 \labelwidthstring References
3047 \begin_inset CommandInset bibitem
3048 LatexCommand bibitem
3049 label "\\protect\\citeauthoryear{Prokhorov, Yu.}{1956}"
3060 Convergence of random processes and limit theorems in probability theory.
3074 \begin_layout Bibliography
3075 \labelwidthstring References
3076 \begin_inset CommandInset bibitem
3077 LatexCommand bibitem
3078 label "\\protect\\citeauthoryear{Prokhorov, Yu.}{1957}"
3084 \begin_inset Flex By Same Author (bib)
3087 \begin_layout Plain Layout
3094 Convergence of random processes and limit theorems in probability theory