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authorKarl Berry <karl@freefriends.org>2006-01-09 00:45:48 +0000
committerKarl Berry <karl@freefriends.org>2006-01-09 00:45:48 +0000
commit5dc602d16c5be2fd035b254ca23484a90aebd6dc (patch)
tree72efb15fba318cc2096a8cc6999ed3fa0bff317d /Master/texmf-dist/doc/xmltex
parentb4fc5f639874db951177ec539299d20908adb654 (diff)
doc 5
git-svn-id: svn://tug.org/texlive/trunk@81 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/xmltex')
-rw-r--r--Master/texmf-dist/doc/xmltex/base/englishutf16.xmlbin0 -> 194 bytes
-rw-r--r--Master/texmf-dist/doc/xmltex/base/russianutf8.xml7
-rw-r--r--Master/texmf-dist/doc/xmltex/passivetex/ChangeLog24
-rw-r--r--Master/texmf-dist/doc/xmltex/passivetex/Changes-2003-01150
-rw-r--r--Master/texmf-dist/doc/xmltex/passivetex/README.passivetex33
-rw-r--r--Master/texmf-dist/doc/xmltex/passivetex/index.html2771
-rw-r--r--Master/texmf-dist/doc/xmltex/passivetex/latextei-fo.xml647
-rw-r--r--Master/texmf-dist/doc/xmltex/passivetex/latextei.tex4
-rw-r--r--Master/texmf-dist/doc/xmltex/passivetex/latextei.xml972
-rw-r--r--Master/texmf-dist/doc/xmltex/passivetex/passivetex.xml388
-rw-r--r--Master/texmf-dist/doc/xmltex/passivetex/properties.xml592
-rw-r--r--Master/texmf-dist/doc/xmltex/passivetex/test.xml280
-rw-r--r--Master/texmf-dist/doc/xmltex/passivetex/xsa.xml14
13 files changed, 5882 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/xmltex/base/englishutf16.xml b/Master/texmf-dist/doc/xmltex/base/englishutf16.xml
new file mode 100644
index 00000000000..c51d565faf7
--- /dev/null
+++ b/Master/texmf-dist/doc/xmltex/base/englishutf16.xml
Binary files differ
diff --git a/Master/texmf-dist/doc/xmltex/base/russianutf8.xml b/Master/texmf-dist/doc/xmltex/base/russianutf8.xml
new file mode 100644
index 00000000000..735c9151641
--- /dev/null
+++ b/Master/texmf-dist/doc/xmltex/base/russianutf8.xml
@@ -0,0 +1,7 @@
+<документ атт="русский" >
+ <раздел>
+ <голова>Тест</голова>
+ Здравствуй Мир!
+ </раздел>
+</документ>
+
diff --git a/Master/texmf-dist/doc/xmltex/passivetex/ChangeLog b/Master/texmf-dist/doc/xmltex/passivetex/ChangeLog
new file mode 100644
index 00000000000..c95d5048a58
--- /dev/null
+++ b/Master/texmf-dist/doc/xmltex/passivetex/ChangeLog
@@ -0,0 +1,24 @@
+2001-06-19 Sebastian Rahtz <sebastian.rahtz@computing-services.oxford.ac.uk>
+
+ * passivetex.xml: releasing current version with broken tables
+
+2000-09-24 Sebastian Rahtz <sebastian.rahtz@oucs.ox.ac.uk>
+
+ * fotex.xmt: preserve value of "extent" attribute on
+ page-master-name basis, and use in \@outputpage
+
+2000-07-27 Sebastian Rahtz <sebastian.rahtz@oucs.ox.ac.uk>
+
+ * added break-after to FOEndBlock
+ * added FOlabel to fo:inline and fo:list-item
+
+2000-03-21 Sebastian Rahtz <sebastian.rahtz@computing-services.oxford.ac.uk>
+
+ * unicode.sty: changed mmasym to "if loaded", instead of "if exists"
+
+2000-01-13 Sebastian Rahtz <sebastian.rahtz@oucs.ox.ac.uk>
+
+ * mlnames.sty (subsection{Languages}): add
+ \languageshorthands{none} to all \selectlanguage lines
+
+
diff --git a/Master/texmf-dist/doc/xmltex/passivetex/Changes-2003-01 b/Master/texmf-dist/doc/xmltex/passivetex/Changes-2003-01
new file mode 100644
index 00000000000..a6491765fbe
--- /dev/null
+++ b/Master/texmf-dist/doc/xmltex/passivetex/Changes-2003-01
@@ -0,0 +1,150 @@
+1. Facilitating <fo:block span="all">
+FOTEX.XMT
+in \XMLelement{fo:block}: detect the span="all" attribute and if so, end
+multicol layout before (if present), and resume multicol layout (if there
+was one) after.
+FOTEX.STY
+new user-interface macros for loading nomulticols.sty if present, otherwise
+resorting to multicols, if present, otherwise defining a fake multicols
+environment. If nomulticols could not be loaded, care is taken that fo:block
+span="all" is disabled, otherwise the TeX run will fail.
+In \@outputpage, call refreshmulticols, which will possibly refresh the
+multicol layout.
+NOMULTICOL.STY
+new file, same functionality as MULTICOL.STY, but does not use an
+environment. With some extra macros to interrupt a multicolumnlayout. It is
+now possible to say
+
+begin multicol layout
+ start group
+ *1*
+ start group
+ end multicol layout *2*
+ start group
+ do something interesting
+ end group
+ begin multicol layout *4*
+ end group
+ *3*
+ end group
+end multicol layout
+
+CAVEAT 1: a lot of assignments of nomulticol have been made global, may be
+too much. For example, if something is set at point *1*, it should be
+restored at point *3*, but if this thing is also set by nomulticol, it will
+undergo a global change at point *2* and/or *4*, and hence will not be
+restored by TeX's grouping mechanism anymore.
+So may be it is needed to carefully discriminate between counts, dimens,
+boxes, and macros that are particular to multicol (the should be treated
+wholly globally), and the (La)TeX-quantities that are dependent on them, and
+they might be set locally.
+
+CAVEAT 2: care must be taken that nomulticol interacts well with an other
+change by me: every time a page is output, a fresh page setup will be
+computed, if necessary. After this page setup, the multicol environment must
+be refreshed (if it was in force). But refreshing should not occur twice in
+a row for the same page. Although it seems that I have succeeded in
+preventing this double refreshment, I still wonder why it can occur at the
+first place.
+2. Facilitating multiple special pages
+XSL-FO facilitates the specification of a sequence of special pages before
+an unbounded, repeating page sequence starts.
+PassiveTeX only allowed one special page, labelled First. I allow for the
+definition of a sequence of such pages, labelled Lead<counter>. In \@output
+page a counter keeps track of which Lead page should be set up. A page setup
+will be done if necessary.
+This change interacts with multicol, see previous item.
+Note also, that blank pages, caused by explicit page-breaks of number
+continuating properties, will be detected as blank pages, and hence react to
+the blank-or-not-blank attribute.
+3. Implementation of xsl-footnote-separator
+A rather crude implementation, by storing the static content of
+xsl-footnote-separator in the macro \footnoterule, and adjusting the
+\skip\footins too match the height+ depth of the new \footnoterule.
+4. Enabling footnotes in tables
+Footnotes in tables work. This is done by saving footnotes insides tables
+into a tokenlist \BoxedFootnotes, doing the corresponding \insert-s at the
+end of the table.
+
+CAVEAT: this is not reallly a nice implementation: if the table breaks
+across pages, the footnotetexts will not appear on the same page as the
+footnotemarks.
+5. Vertical align in tables
+If I work with an explicit line-height, the vertical space allocation for
+the first and last row of a table comes out wrong. Also, when there is a
+line-break inside a cell, the cell-height comes out too small. Something
+gets discarded. I have made some changes to the interlineskip (following the
+TeXBook definition of \offinterlineskip), in order to fix this, but I have
+not succeeded completely.
+6. Inheriting table-cell properties from table-column
+According to XSL-FO table-cells my inherit properties from corresponding
+table-columns by using
+att-x="from-column(att-x)"
+PassiveTeX only implements inheritance of column-width and column-number,
+without the need to use from-column("column-width").
+I have made only an adhoc improvement: text-align will be inherited from the
+column, and it happens automatically, without using from-column(text-align).
+I have done this with the Array implementation, used for column-width and
+column-number. More properties can added easily. It should not be too
+difficult to implement from-column(att-x) for a fixed set of attributes, but
+implementing this for all possible attributes is more difficult.
+7. vskip vs kern
+In the code for typesetting blocks, I have changed some vskips in kern,
+because I trust the kern better than te vskip (kerns will not be discarded,
+vskips might be, and I am not completely sure about the conditions).
+8. Bug in FOBoxedBlock
+There is some weird code at the start of \FOBoxedBlock (see comments in
+fotex.sty at that point).
+I have also added some \relax calls after assignments to be sure that the
+text after \fi etc is not gobbled up by the preceding assignment.
+9. Percenttests
+I have increased the use of percented attribute values. Also, \percenttest
+was not always able to see the % character, because it was still unexpanded
+when fed to it. I have changed that, so that any percent in the
+attributetext is surely expanded to a % with catcode 12 before being fed to
+percenttest.
+(Mostly % appears as an active char, and by means of a limitied-scope
+definition of % to be % with catcode 12, this case will be brought to meet
+the assumption).
+10. Overline
+I have added the overline formatting for inlines, but not nearly as nice as
+the underline of ulem.sty. I just needed it in simple cases, so I took the
+easy option.
+11. Pagenumber filtering
+The algorithm to filter page number sequences generated by indexes (a very
+nice feature of passivetex, by the way), had a few obvious mistakes. I have
+corrected them.
+12. Horizontal alignment
+There were still some problems with alignment, I made some corrections to
+\FOOutputblock in fotex.sty.
+See also mlnames.sty, definition of \Q@end
+13 Page breaks
+In \FONormalBlcok I found that a \penalty -\@M did not generate a page
+break, so I changed it to \newpage (a few times). (see also changes in
+\FOEndBlockTwo
+14 Sub- Superscript
+PassiveTeX adjusted the fontsize of sub/superscripts, but this should be
+governed by the fo-tree.
+So I adjusted \textsub/superscript in fotex.sty
+15 Dimensions of the page
+Page dimensions now work additive, more according to the XSL-FO spec.
+16 attribute="inherit"
+Now the inherit mechanism can also be triggered by the explicit value of
+"inherit". This was achieved by redefining a macro of xmltex: \XML@attrib@x
+(in fotex.xmt)
+17. fo:external-graphic
+scale-to-fit behaviour modified: scaled to the local container instead of
+the page (hsize, vsize instead of linewidth, textheight)
+18. fo:leader implemetation improved
+The code for fo:leader in xmt has been improved
+19. fo-retrieve-marker
+Some trivial improvements in the code of fo:retrieve-marker
+20. More unicode characters
+Added definitions for unicode &#x2000; and &#x2001 (em and n squares) in
+ucharacters.sty
+A. Nested fo:block in fo:table-cell
+Something goes wrong with <fo:table-cell><fo:block><fo:block>.
+The count \FOinTable records whether we are inside a table. But I think that
+it should also record wheter we are immediately below a <fo:table-cell> or
+deeper. But I have not found out what to do in the latter case ...
+
diff --git a/Master/texmf-dist/doc/xmltex/passivetex/README.passivetex b/Master/texmf-dist/doc/xmltex/passivetex/README.passivetex
new file mode 100644
index 00000000000..23061d7e5c1
--- /dev/null
+++ b/Master/texmf-dist/doc/xmltex/passivetex/README.passivetex
@@ -0,0 +1,33 @@
+PassiveTeX
+
+Sebastian Rahtz, February 10th 2000
+
+The files in this directory provide an implementation of XSL
+formatting objects. If an XSLT processor is used to write out XSL
+objects in serialized XML format, the result can be formatted using
+xmltex. In addition, an extended xmltex control file for TEI
+documents is provided.
+
+This package consists of the following files:
+
+The core xmltex `style' files for XSL FO XML:
+
+ fotex.xmt
+ fotex.sty
+
+A test file, containing TEI + MathML markup:
+
+ latextei.xml (original)
+ latextei-fo.xml (transformed to XSL FO)
+
+Support for direct formatting of TEI XML with xmltex
+
+ tei.xmt
+ latextei.tex (wrapper for xmltex of sample file)
+
+Some support files, shared with Jadetex:
+
+ unicode.sty
+ ucharacters.sty
+ mlnames.sty
+ dummyels.sty
diff --git a/Master/texmf-dist/doc/xmltex/passivetex/index.html b/Master/texmf-dist/doc/xmltex/passivetex/index.html
new file mode 100644
index 00000000000..367a991547d
--- /dev/null
+++ b/Master/texmf-dist/doc/xmltex/passivetex/index.html
@@ -0,0 +1,2771 @@
+
+<!DOCTYPE html
+ PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
+<html>
+ <!--THIS FILE IS GENERATED FROM AN XML MASTER.
+ DO NOT EDIT-->
+ <head>
+ <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+
+ <title>PassiveTeX</title>
+ <link rel="stylesheet" type="text/css" href="http://www.oucs.ox.ac.uk/stylesheets/tei-oucs.css">
+ </head>
+ <body><a name="TOP"></a><table class="header" width="100%">
+ <tr>
+ <td rowspan="3"><a target="_top" href="http://www.ox.ac.uk/"><img border="0" width="78" height="94" src="http://www.oucs.ox.ac.uk/icons/ncrest.gif" alt="Oxford University"></a></td>
+ <td align="left">
+ <h2 class="institution">Oxford University Computing Services</h2>
+ </td>
+ </tr>
+ <tr>
+ <td align="left">
+ <h1 class="maintitle">PassiveTeX</h1>
+ </td>
+ </tr>
+ </table>
+ <hr>
+
+
+
+
+
+
+ <h2>Contents</h2>
+ <ul class="toc">
+ <li class="toc">1. <a class="toc" href="#index-div-c16ab3b3b1">Summary</a></li>
+ <li class="toc">2. <a class="toc" href="#index-div-c16ab3b3b3">How does it work?</a></li>
+ <li class="toc">3. <a class="toc" href="#index-div-c16ab3b3b5">Installation</a></li>
+ <ul class="toc">
+ <li class="toc">3.1. <a class="toc" href="#index-div-c16ab3b3b5c11">LaTeX package dependencies</a></li>
+ </ul>
+ <li class="toc">4. <a class="toc" href="#index-div-c16ab3b3b7">Extensions</a></li>
+ <li class="toc">5. <a class="toc" href="#index-div-c16ab3b3b9">Notes on conformance to the XSL draft specification of November 2000</a></li>
+ <ul class="toc">
+ <li class="toc">5.1. <a class="toc" href="#index-div-c16ab3b3b9b9">Properties needed for basic conformance</a></li>
+ <li class="toc">5.2. <a class="toc" href="#index-div-c16ab3b3b9c11">Properties needed for full conformance</a></li>
+ <li class="toc">5.3. <a class="toc" href="#index-div-c16ab3b3b9c13">Properties needed for extended conformance</a></li>
+ </ul>
+ <li class="toc">6. <a class="toc" href="#index-div-c16ab3b3c11">Sample files</a></li>
+ <li class="toc">7. <a class="toc" href="#index-div-c16ab3b3c13">Concerns and problems</a></li>
+ <li class="toc">8. <a class="toc" href="#index-div-c16ab3b3c15">Things for LaTeX users to remember</a></li>
+ <li class="toc">9. <a class="toc" href="#index-div-c16ab3b3c17">Future directions</a></li>
+ </ul>
+
+ <div class="teidiv">
+ <h2><a name="index-div-c16ab3b3b1"></a>1. Summary
+ </h2>
+
+
+ <ul>
+ <li><a name="c16ab3b3b1b3b1"></a>
+ PassiveTeX is a library of TeX macros which can be used to process an XML
+ document which results from an XSL transformation to formatting objects.
+
+ </li>
+ <li><a name="c16ab3b3b1b3b3"></a>
+ PassiveTeX provides a rapid development environment for experimenting
+ with XSL FO, using a reliable pre-existing formatter
+
+ </li>
+ <li><a name="c16ab3b3b1b3b5"></a>
+ Running PassiveTeX with the pdfTeX variant of TeX generates high-quality
+ PDF files in a single operation.
+
+ </li>
+ <li><a name="c16ab3b3b1b3b7"></a>
+ PassiveTeX shows how TeX can remain the formatter of choice for XML, while
+ hiding the details of its operation from the user.
+
+ </li>
+ </ul>
+
+ <p><a name="c16ab3b3b1b5"></a>
+ Available from <tt><a href="http://users.ox.ac.uk/~rahtz/passivetex/" target="_top">http://users.ox.ac.uk/~rahtz/passivetex/</a></tt>.
+ The current version is 1.4, 2000/12/11.
+
+ </p>
+
+ </div>
+
+ <div class="teidiv">
+ <h2><a name="index-div-c16ab3b3b3"></a>2. How does it work?
+ </h2>
+
+ <p><a name="c16ab3b3b3b2"></a>
+ PassiveTeX relies heavily on work by David Carlisle
+ (his namespace-aware XML parser written in
+ TeX, <tt>xmltex</tt>), and was developed from my
+ <a href="http://www.tug.org/applications/jadetex/" target="_top">JadeTeX</a>
+ macros for processing DSSSL via Jade.
+
+ </p>
+
+ <p><a name="c16ab3b3b3b4"></a>
+ Taking the XML version of the TEI Lite guidelines
+ (<a href="test/teiu5.xml" target="_top">teiu5.xml</a>, with DTD
+ <a href="test/teixlite.dtd" target="_top">teixlite.dtd</a>), we apply an XSL stylesheet
+ (see my page of <a href="http://users.ox.ac.uk/~rahtz/tei" target="_top">TEI style sheets</a>),
+ and run it through James Clark's XT XSL processor:
+ <pre>
+ java com.jclark.xsl.sax.Driver teiu5.xml tei.xsl teiu5.fo
+</pre>
+ (assuming you have <tt>xt.jar</tt>, <tt>xp.jar</tt> and <tt>sax.jar</tt>
+ on your CLASSPATH ). This creates the new XML file
+ <a href="test/teiu5.fo" target="_top">teiu5.fo</a>. We now run XMLTeX on this
+ <pre>
+ pdfxmltex teiu5.fo
+</pre>
+ which creates <a href="test/teiu5.pdf" target="_top">teiu5.pdf</a>. Voila!
+ Actually, we need to do
+ <pre>
+ pdfxmltex teiu5.fo
+</pre>
+ again, to resolve page-number references in the table of contents. For a comparison
+ with an HTML rendering of the same document (using XSL again),
+ see <a href="http://users.ox.ac.uk/~rahtz/tei/teiu5.html" target="_top">teiu5.html</a>
+ on my TEI page.
+ </p>
+
+ </div>
+
+ <div class="teidiv">
+ <h2><a name="index-div-c16ab3b3b5"></a>3. Installation
+ </h2>
+
+
+ <p><a name="c16ab3b3b5b3"></a>
+ The PassiveTeX macros should be downloaded (as a ZIP file,
+ <tt><a href="passivetex.zip" target="_top">passivetex.zip</a></tt>), unpacked, and installed in a TeX system (eg in
+ <tt>texmf/tex/latex/passivetex</tt>) in the normal place where you put
+ macros. Consult your local documentation or local expert if you do not know
+ how to install a new package; on a web2c-based system, don't forget to
+ run <tt>mktexlsr</tt> when you have the files in place,
+ to update the file lookup table.
+
+ </p>
+
+ <p><a name="c16ab3b3b5b5"></a>
+ What about that <tt>pdfxmltex</tt> command we saw in the last section?
+ You don't have it on your system? You need to download
+ <a href="ftp://ftp.tex.ac.uk/tex-archive/macros/xmltex/base.zip" target="_top">xmltex</a>
+ (that link gives you a ZIP archive of the system) and install it in the your TeX system.
+ It too is just a set of TeX macro packages.
+ Then you can use it on a file called (eg) <tt>teiu5.fo</tt> in one of two ways:
+
+ <ol>
+ <li><a name="c16ab3b3b5b5b7b1"></a>Build an <tt>xmltex</tt> format file for pdfTeX with
+ <pre>
+pdftex -ini "&amp;pdflatex" pdfxmltex.ini
+</pre>
+ and process your file with
+ <pre>
+pdflatex "&amp;pdfxmltex" teiu5.fo
+</pre>
+ Or,
+ </li>
+ <li><a name="c16ab3b3b5b5b7b3"></a>
+ Make a wrapper file called (eg) <tt>teiu5.tex</tt> looking like this:
+ <pre>
+\def\xmlfile{teiu5.fo}
+\input xmltex
+</pre>
+ and run pdfTeX on it as normal with
+ <pre>
+pdflatex teiu5.tex
+</pre>
+ </li>
+ </ol>
+ Do not worry, <tt>xmltex</tt> knows how to find the PassiveTeX macros as
+ it needs them. You will likely need to increase TeX memory
+ values (in the file <tt>texmf.cnf</tt> if you use a Web2c-based TeX);
+ I use:
+ <pre>
+main_memory = 2500000
+param_size = 1500
+stack_size = 1500
+hash_extra = 50000
+string_vacancies = 45000
+pool_free = 47500
+nest_size = 500
+save_size = 10000
+pool_size = 500000
+max_strings = 55000
+</pre>
+ </p>
+
+ <p><a name="c16ab3b3b5b7"></a>
+ For reference, the PassiveTeX package consists of the following files:
+
+ <ul>
+ <li><a name="c16ab3b3b5b7b1b1"></a>The core xmltex `style' files for XSL FO XML:
+ <pre>
+ fotex.xmt
+ fotex.sty
+</pre>
+ </li>
+ <li><a name="c16ab3b3b5b7b1b3"></a>
+ Support for direct formatting of TEI XML with xmltex
+ <pre>
+ tei.xmt
+ teixml.sty
+</pre>
+ </li>
+ <li><a name="c16ab3b3b5b7b1b5"></a>
+ Some support files, shared with JadeTeX:
+ <pre>
+ unicode.sty
+ ucharacters.sty
+ mlnames.sty
+ dummyels.sty
+</pre>
+ </li>
+ </ul>
+
+ </p>
+
+ <p><a name="c16ab3b3b5b9"></a>
+ NOTE: TeX has a limit
+ on the length of line it can read,
+ and some .fo files you generate may cause
+ TeX to die with an message about increasing buf_size.
+ If you get that, edit your
+ <tt>texmf.cnf</tt> file, increase the size of <tt>buf_size</tt> (mine is
+ 200000), and remake any format files.
+
+ </p>
+
+ <div class="teidiv">
+ <h3><a name="index-div-c16ab3b3b5c11"></a>3.1. LaTeX package dependencies
+ </h3>
+
+ <p><a name="c16ab3b3b5c11b2"></a>This setup assumes you have a decent modern TeX setup. The TeX Live 5 CD-ROM
+ is what I use, and it is up to date
+ (see <tt><a href="http://www.tug.org/texlive/" target="_top">http://www.tug.org/texlive/</a></tt>).
+
+ </p>
+
+ <p><a name="c16ab3b3b5c11b4"></a> Here is a
+ list of the packages loaded in a typical run of
+ PassiveTeX, with their version numbers where known:
+
+ <div align="center">
+ <table rules="all" border="1">
+
+ <tr>
+ <td> amsbsy.sty </td>
+ <td> 1999/11/29 v1.2d</td>
+ </tr>
+
+ <tr>
+ <td>amsfonts.sty </td>
+ <td> 1997/09/17 v2.2e</td>
+ </tr>
+
+ <tr>
+ <td> amsgen.sty </td>
+ <td> 1999/11/30 v2.0</td>
+ </tr>
+
+ <tr>
+ <td> amsmath.sty </td>
+ <td> 2000/03/29 v2.08 AMS math features</td>
+ </tr>
+
+ <tr>
+ <td> amsopn.sty </td>
+ <td> 1999/12/14 v2.01 operator names</td>
+ </tr>
+
+ <tr>
+ <td> amssymb.sty </td>
+ <td> 1996/11/03 v2.2b</td>
+ </tr>
+
+ <tr>
+ <td> amstext.sty </td>
+ <td> 1999/11/15 v2.0</td>
+ </tr>
+
+ <tr>
+ <td> array.sty </td>
+ <td> 1998/05/13 v2.3m Tabular extension package (FMi)</td>
+ </tr>
+
+ <tr>
+ <td> article.cls </td>
+ <td> 1999/09/10 v1.4a Standard LaTeX document class</td>
+ </tr>
+
+ <tr>
+ <td> bm.sty </td>
+ <td> 1999/07/05 v1.0g Bold Symbol Support (DPC/FMi)</td>
+ </tr>
+
+ <tr>
+ <td> color.sty </td>
+ <td> 1999/02/16 v1.0i Standard LaTeX Color (DPC)</td>
+ </tr>
+
+ <tr>
+ <td> fontenc.sty </td>
+ <td> (version not available)</td>
+ </tr>
+
+ <tr>
+ <td>graphics.sty </td>
+ <td> 1999/02/16 v1.0l Standard LaTeX Graphics (DPC,SPQR)</td>
+ </tr>
+
+ <tr>
+ <td>graphicx.sty </td>
+ <td> 1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR)</td>
+ </tr>
+
+ <tr>
+ <td> hpdftex.def </td>
+ <td> 2000/05/08 v6.70f Hyperref driver for pdfTeX</td>
+ </tr>
+
+ <tr>
+ <td>hyperref.sty </td>
+ <td> 2000/05/08 v6.70f Hypertext links for LaTeX</td>
+ </tr>
+
+ <tr>
+ <td> ifthen.sty </td>
+ <td> 1999/09/10 v1.1b Standard LaTeX ifthen package (DPC)</td>
+ </tr>
+
+ <tr>
+ <td> keyval.sty </td>
+ <td> 1999/03/16 v1.13 key=value parser (DPC)</td>
+ </tr>
+
+ <tr>
+ <td>longtable.sty </td>
+ <td> 1998/05/13 v4.09 Multi-page Table package (DPC)</td>
+ </tr>
+
+ <tr>
+ <td>multicol.sty </td>
+ <td> 1999/10/21 v1.5w multicolumn formatting (FMi)</td>
+ </tr>
+
+ <tr>
+ <td> nameref.sty </td>
+ <td> 2000/05/08 v2.18 Cross-referencing by name of section</td>
+ </tr>
+
+ <tr>
+ <td> ot1phv.fd </td>
+ <td> 2000/01/12 PSNFSS-v8.1 scalable font definitions for OT1/phv.</td>
+ </tr>
+
+ <tr>
+ <td> pd1enc.def </td>
+ <td> 2000/05/08 v6.70f Hyperref: PDFDocEncoding definition (HO)</td>
+ </tr>
+
+ <tr>
+ <td> pifont.sty </td>
+ <td> 2000/01/12 PSNFSS-v8.1 Pi font support (SPQR) </td>
+ </tr>
+
+ <tr>
+ <td>rotating.sty </td>
+ <td> 1997/09/26, v2.13 Rotation package</td>
+ </tr>
+
+ <tr>
+ <td> size10.clo </td>
+ <td> 1999/09/10 v1.4a Standard LaTeX file (size option)</td>
+ </tr>
+
+ <tr>
+ <td>stmaryrd.sty </td>
+ <td> 1994/03/03 St Mary's Road symbol package</td>
+ </tr>
+
+ <tr>
+ <td> t1enc.def </td>
+ <td> 1999/12/08 v1.9x Standard LaTeX file</td>
+ </tr>
+
+ <tr>
+ <td> t1phv.fd </td>
+ <td> 2000/01/12 PSNFSS-v8.1 scalable font definitions for T1/phv.</td>
+ </tr>
+
+ <tr>
+ <td> t1ptm.fd </td>
+ <td> 2000/01/12 PSNFSS-v8.1 font definitions for T1/ptm.</td>
+ </tr>
+
+ <tr>
+ <td> t2acmr.fd </td>
+ <td> 1999/01/07 v1.0 Computer Modern Cyrillic font definitions</td>
+ </tr>
+
+ <tr>
+ <td> t2aenc.def </td>
+ <td> 1999/11/29 v1.0c Cyrillic encoding definition file</td>
+ </tr>
+
+ <tr>
+ <td> t3enc.def </td>
+ <td> (version not available)</td>
+ </tr>
+
+ <tr>
+ <td>textcomp.sty </td>
+ <td> 1999/12/08 v1.9x Standard LaTeX package</td>
+ </tr>
+
+ <tr>
+ <td> times.sty </td>
+ <td> 2000/01/12 PSNFSS-v8.1 Times font as default roman (SPQR) </td>
+ </tr>
+
+ <tr>
+ <td> tipa.sty </td>
+ <td> 1996/06/10 TIPA version 1.0</td>
+ </tr>
+
+ <tr>
+ <td> trig.sty </td>
+ <td> 1999/03/16 v1.09 sin cos tan (DPC)</td>
+ </tr>
+
+ <tr>
+ <td> ts1cmr.fd </td>
+ <td> 1999/05/25 v2.5h Standard LaTeX font definitions</td>
+ </tr>
+
+ <tr>
+ <td> ts1enc.def </td>
+ <td> 1998/06/12 v3.0d (jk/car/fm) Standard LaTeX file</td>
+ </tr>
+
+ <tr>
+ <td> ts1ptm.fd </td>
+ <td> 2000/01/12 PSNFSS-v8.1 font definitions for TS1/ptm.</td>
+ </tr>
+
+ <tr>
+ <td> ulem.sty </td>
+ <td> 1997/04/21</td>
+ </tr>
+
+ <tr>
+ <td> umsa.fd </td>
+ <td> 1995/01/05 v2.2e AMS font definitions</td>
+ </tr>
+
+ <tr>
+ <td> umsb.fd </td>
+ <td> 1995/01/05 v2.2e AMS font definitions</td>
+ </tr>
+
+ <tr>
+ <td> upsy.fd </td>
+ <td> 2000/01/12 PSNFSS-v8.1 font definitions for U/psy.</td>
+ </tr>
+
+ <tr>
+ <td> upzd.fd </td>
+ <td> 2000/01/12 PSNFSS-v8.1 font definitions for U/pzd.</td>
+ </tr>
+
+ <tr>
+ <td> url.sty </td>
+ <td> 1999/03/28 ver 1.5x Verb mode for urls, etc.</td>
+ </tr>
+
+ <tr>
+ <td> Ustmry.fd </td>
+ <td> (version not available)</td>
+ </tr>
+
+ <tr>
+ <td> uwasy.fd </td>
+ <td> 1999/05/13 v1.0iWasy-2 symbol font definitions</td>
+ </tr>
+
+ <tr>
+ <td> wasysym.sty </td>
+ <td> 1999/05/13 v1.0i Wasy-2 symbol support package</td>
+ </tr>
+
+ </table>
+ </div>
+
+ </p>
+
+ </div>
+
+ </div>
+
+
+
+ <div class="teidiv">
+ <h2><a name="index-div-c16ab3b3b7"></a>4. Extensions
+ </h2>
+
+
+ <p><a name="c16ab3b3b7b3"></a>
+ PassiveTeX interprets MathML natively (elements must use the MathML namespace).
+ I also support a <tt>bookmark</tt> element in the
+ <tt>fotex</tt> namespace, used to make PDF bookmarks. Usage is like this:
+ <pre>
+&lt;xsl:template match="div2"&gt;
+ &lt;xsl:apply-templates select="head"/&gt;
+ &lt;fotex:bookmark
+ xmlns:fotex="http://www.tug.org/fotex"
+ fotex-bookmark-level="2"
+ fotex-bookmark-label="{@id}"&gt;
+ &lt;xsl:value-of select="head"/&gt;
+ &lt;/fotex:bookmark&gt;
+ &lt;/fo:block&gt;
+&lt;/xsl:template&gt;
+</pre>
+ </p>
+
+ </div>
+
+
+
+ <div class="teidiv">
+ <h2><a name="index-div-c16ab3b3b9"></a>5. Notes on conformance to the XSL draft specification of November 2000
+ </h2>
+
+
+
+ <p><a name="c16ab3b3b9b5"></a>
+ The following general limitations apply to most of the PassiveTeX
+ implementation of XSL FO:
+
+ <ol>
+ <li><a name="c16ab3b3b9b5b1b1"></a>The `px' unit is not recognised
+ </li>
+ <li><a name="c16ab3b3b9b5b1b3"></a>Absolute dimensions always work, but proportional ones
+ are often not recognized
+ </li>
+ <li><a name="c16ab3b3b9b5b1b5"></a>The functions allowed in attribute values are usually not
+ recognized
+ </li>
+ <li><a name="c16ab3b3b9b5b1b7"></a>There is no error checking at all, and all properies are
+ recognized; do not assume that they do anything...
+ </li>
+ </ol>
+
+ </p>
+
+ <p><a name="c16ab3b3b9b7"></a>
+ Most of the formatting objects are implemented more or less; the
+ following are not implemented at all:
+
+ <ol>
+ <li><a name="c16ab3b3b9b7b1b1"></a><tt>fo:bidi-override</tt></li>
+ <li><a name="c16ab3b3b9b7b1b3"></a><tt>fo:color-profile</tt></li>
+ <li><a name="c16ab3b3b9b7b1b5"></a><tt>fo:declarations</tt></li>
+ <li><a name="c16ab3b3b9b7b1b7"></a><tt>fo:initial-property-set</tt></li>
+ <li><a name="c16ab3b3b9b7b1b9"></a><tt>fo:instream-foreign-object</tt></li>
+ <li><a name="c16ab3b3b9b7b1c11"></a><tt>fo:multi-case</tt></li>
+ <li><a name="c16ab3b3b9b7b1c13"></a><tt>fo:multi-properties</tt></li>
+ <li><a name="c16ab3b3b9b7b1c15"></a><tt>fo:multi-property-set</tt></li>
+ <li><a name="c16ab3b3b9b7b1c17"></a><tt>fo:multi-switch</tt></li>
+ <li><a name="c16ab3b3b9b7b1c19"></a><tt>fo:multi-toggle</tt></li>
+ <li><a name="c16ab3b3b9b7b1c21"></a><tt>fo:region-end</tt></li>
+ <li><a name="c16ab3b3b9b7b1c23"></a><tt>fo:region-start</tt></li>
+ <li><a name="c16ab3b3b9b7b1c25"></a><tt>fo:table-footer</tt></li>
+ </ol>
+
+ </p>
+
+ <div class="teidiv">
+ <h3><a name="index-div-c16ab3b3b9b9"></a>5.1. Properties needed for basic conformance
+ </h3>
+
+ <p><a name="c16ab3b3b9b9b2"></a>
+
+ <div align="center">
+ <table rules="all" border="1">
+
+ <tr>
+ <td>alignment-adjust</td>
+ <td>auto | percentage | length | inherit</td>
+ <td>Basic</td>
+
+ <td>2. should be possible </td>
+ </tr>
+
+
+ <tr>
+ <td>azimuth</td>
+ <td>angle | [[ left-side | far-left | left | center-left | center | center-right | right | far-right | right-side
+ ] || behind ] | leftwards | rightwards | inherit
+ </td>
+ <td>Basic</td>
+
+ <td>4. N/A </td>
+ </tr>
+
+
+ <tr>
+ <td>background-color</td>
+ <td>color | transparent | inherit</td>
+ <td>Basic</td>
+ <td>3. does not really map in TeX </td>
+ </tr>
+
+
+ <tr>
+ <td>baseline-identifier</td>
+ <td>baseline | before-edge | text-before-edge | middle | after-edge
+ | text-after-edge | ideographic | alphabetic | hanging | mathematical
+ | inherit
+ </td>
+ <td>Basic</td>
+
+ <td>3. not at all sure where to start </td>
+ </tr>
+
+
+ <tr>
+ <td>baseline-shift</td>
+ <td>baseline | sub | super | percentage | length | inherit</td>
+ <td>Basic</td>
+
+ <td>1. basically works </td>
+ </tr>
+
+
+ <tr>
+ <td>block-progression-dimension</td>
+ <td>auto | length | percentage | length-range | inherit</td>
+ <td>Basic</td>
+
+ <td>3. do not really understand it </td>
+ </tr>
+
+
+ <tr>
+ <td>border-after-color</td>
+ <td>color | inherit</td>
+ <td>Basic</td>
+ <td>2. works for blocks (non-breaking) </td>
+ </tr>
+
+
+ <tr>
+ <td>border-after-style</td>
+ <td>border-style | inherit</td>
+ <td>Basic</td>
+ <td>2. works for blocks (non-breaking) </td>
+ </tr>
+
+
+ <tr>
+ <td>border-after-width</td>
+ <td>border-width | length-conditional | inherit</td>
+ <td>Basic</td>
+ <td>2. works for blocks (non-breaking) </td>
+ </tr>
+
+
+ <tr>
+ <td>border-before-color</td>
+ <td>color | inherit</td>
+ <td>Basic</td>
+ <td>2. works for blocks (non-breaking) </td>
+ </tr>
+
+
+ <tr>
+ <td>border-before-style</td>
+ <td>border-style | inherit</td>
+ <td>Basic</td>
+ <td>2. works for blocks (non-breaking) </td>
+ </tr>
+
+
+ <tr>
+ <td>border-before-width</td>
+ <td>border-width | length-conditional | inherit</td>
+ <td>Basic</td>
+ <td>2. works for blocks (non-breaking) </td>
+ </tr>
+
+
+ <tr>
+ <td>border-bottom-color</td>
+ <td>color | inherit</td>
+ <td>Basic</td>
+ <td>2. works for blocks (non-breaking) </td>
+ </tr>
+
+
+ <tr>
+ <td>border-bottom-style</td>
+ <td>border-style | inherit</td>
+ <td>Basic</td>
+ <td>1. used in places </td>
+ </tr>
+
+
+ <tr>
+ <td>border-bottom-width</td>
+ <td>border-width | inherit</td>
+ <td>Basic</td>
+ <td>2. works for blocks (non-breaking) </td>
+ </tr>
+
+
+ <tr>
+ <td>border-end-color</td>
+ <td>color | inherit</td>
+ <td>Basic</td>
+ <td>2. works for blocks (non-breaking) </td>
+ </tr>
+
+
+ <tr>
+ <td>border-end-style</td>
+ <td>border-style | inherit</td>
+ <td>Basic</td>
+ <td>2. works for blocks (non-breaking) </td>
+ </tr>
+
+
+ <tr>
+ <td>border-end-width</td>
+ <td>border-width | inherit</td>
+ <td>Basic</td>
+ <td>2. works for blocks (non-breaking) </td>
+ </tr>
+
+
+ <tr>
+ <td>border-left-color</td>
+ <td>color | inherit</td>
+ <td>Basic</td>
+ <td>2. works for blocks (non-breaking) </td>
+ </tr>
+
+
+ <tr>
+ <td>border-left-style</td>
+ <td>border-style | inherit</td>
+ <td>Basic</td>
+ <td>2. works for blocks (non-breaking) </td>
+ </tr>
+
+
+ <tr>
+ <td>border-left-width</td>
+ <td>border-width | inherit</td>
+ <td>Basic</td>
+ <td>2. works for blocks (non-breaking) </td>
+ </tr>
+
+
+ <tr>
+ <td>border-right-color</td>
+ <td>color | inherit</td>
+ <td>Basic</td>
+ <td>2. works for blocks (non-breaking) </td>
+ </tr>
+
+
+ <tr>
+ <td>border-right-style</td>
+ <td>border-style | inherit</td>
+ <td>Basic</td>
+ <td>2. works for blocks (non-breaking) </td>
+ </tr>
+
+
+ <tr>
+ <td>border-right-width</td>
+ <td>border-width | inherit</td>
+ <td>Basic</td>
+ <td>2. works for blocks (non-breaking) </td>
+ </tr>
+
+
+ <tr>
+ <td>border-start-color</td>
+ <td>color | inherit</td>
+ <td>Basic</td>
+ <td>2. works for blocks (non-breaking) </td>
+ </tr>
+
+
+ <tr>
+ <td>border-start-style</td>
+ <td>border-style | inherit</td>
+ <td>Basic</td>
+ <td>2. works for blocks (non-breaking) </td>
+ </tr>
+
+
+ <tr>
+ <td>border-start-width</td>
+ <td>border-width | inherit</td>
+ <td>Basic</td>
+ <td>2. works for blocks (non-breaking) </td>
+ </tr>
+
+
+ <tr>
+ <td>border-top-color</td>
+ <td>color | inherit</td>
+ <td>Basic</td>
+ <td>2. works for blocks (non-breaking) </td>
+ </tr>
+
+
+ <tr>
+ <td>border-top-style</td>
+ <td>border-style | inherit</td>
+ <td>Basic</td>
+ <td>1. used in places </td>
+ </tr>
+
+
+ <tr>
+ <td>border-top-width</td>
+ <td>border-width | inherit</td>
+ <td>Basic</td>
+ <td>2. works for blocks (non-breaking) </td>
+ </tr>
+
+
+ <tr>
+ <td>break-after</td>
+ <td>auto | column | page | even-page | odd-page | inherit</td>
+ <td>Basic</td>
+ <td>0. should be working </td>
+ </tr>
+
+
+ <tr>
+ <td>break-before</td>
+ <td>auto | column | page | even-page | odd-page | inherit</td>
+ <td>Basic</td>
+ <td>0. should be working </td>
+ </tr>
+
+
+ <tr>
+ <td>character</td>
+ <td>character</td>
+ <td>Basic</td>
+ <td>0. should be working </td>
+ </tr>
+
+
+ <tr>
+ <td>clip</td>
+ <td>shape | auto | inherit</td>
+ <td>Basic</td>
+ <td>2. theoretically possible </td>
+ </tr>
+
+
+ <tr>
+ <td>color</td>
+ <td>color | inherit</td>
+ <td>Basic</td>
+ <td>1. more or less complete </td>
+ </tr>
+
+
+ <tr>
+ <td>column-number</td>
+ <td>number</td>
+ <td>Basic</td>
+ <td>0. OK </td>
+ </tr>
+
+
+ <tr>
+ <td>column-width</td>
+ <td>length</td>
+ <td>Basic</td>
+ <td>0. OK </td>
+ </tr>
+
+
+ <tr>
+ <td>content-type</td>
+ <td>string | auto</td>
+ <td>Basic</td>
+ <td>4. N/A, I think </td>
+ </tr>
+
+
+ <tr>
+ <td>cue-after</td>
+ <td>uri | none | inherit </td>
+ <td>Basic</td>
+ <td>4. N/A </td>
+ </tr>
+
+
+ <tr>
+ <td>cue-before</td>
+ <td>uri | none | inherit </td>
+ <td>Basic</td>
+ <td>4. N/A </td>
+ </tr>
+
+
+ <tr>
+ <td>direction</td>
+ <td>ltr | rtl | inherit</td>
+ <td>Basic</td>
+ <td>3. waiting for extended TeX </td>
+ </tr>
+
+
+ <tr>
+ <td>display-align</td>
+ <td>auto | before | center | after | inherit</td>
+ <td>Basic</td>
+
+ <td>0. working </td>
+ </tr>
+
+
+ <tr>
+ <td>dominant-baseline</td>
+ <td>auto | autosense-script | no-change | reset-size | ideographic | alphabetic | hanging | mathematical
+ | inherit
+ </td>
+ <td>Basic</td>
+
+ <td>3. dont know where to begin </td>
+ </tr>
+
+
+ <tr>
+ <td>elevation</td>
+ <td>angle | below | level | above | higher | lower | inherit</td>
+ <td>Basic</td>
+
+ <td>4. N/A </td>
+ </tr>
+
+
+ <tr>
+ <td>end-indent</td>
+ <td>length | inherit</td>
+ <td>Basic</td>
+ <td>0. working </td>
+ </tr>
+
+
+ <tr>
+ <td>flow-name</td>
+ <td>name</td>
+ <td>Basic</td>
+ <td>0. working </td>
+ </tr>
+
+
+ <tr>
+ <td>font-family</td>
+ <td>[[ family-name | generic-family ],]* [family-name | generic-family] | inherit</td>
+ <td>Basic</td>
+
+ <td>1. more or less OK </td>
+ </tr>
+
+
+ <tr>
+ <td>font-size</td>
+ <td>absolute-size | relative-size | length | percentage | inherit</td>
+ <td>Basic</td>
+
+ <td>1. more or less all implemented </td>
+ </tr>
+
+
+ <tr>
+ <td>font-style</td>
+ <td>normal | italic | oblique | backslant | inherit</td>
+ <td>Basic</td>
+ <td>1. no oblique or backslant </td>
+ </tr>
+
+
+ <tr>
+ <td>font-variant</td>
+ <td>normal | small-caps | inherit</td>
+ <td>Basic</td>
+ <td>0. done </td>
+ </tr>
+
+
+ <tr>
+ <td>font-weight</td>
+ <td>normal | bold | bolder | lighter | 100 | 200 | 300 | 400 | 500 | 600 | 700 | 800 | 900 | inherit</td>
+ <td>Basic</td>
+
+ <td>1. normal and bold only at present, others to follow</td>
+ </tr>
+
+
+ <tr>
+ <td>format</td>
+ <td>string</td>
+ <td>Basic</td>
+ <td>3. dont want to think about it </td>
+ </tr>
+
+
+ <tr>
+ <td>grouping-separator</td>
+ <td>character</td>
+ <td>Basic</td>
+ <td>3. dont want to think about it </td>
+ </tr>
+
+
+ <tr>
+ <td>grouping-size</td>
+ <td>number</td>
+ <td>Basic</td>
+ <td>3. dont want to think about it </td>
+ </tr>
+
+
+ <tr>
+ <td>height</td>
+ <td>length | percentage | auto | inherit</td>
+ <td>Basic</td>
+ <td>2. should be OK, waiting for a need </td>
+ </tr>
+
+
+ <tr>
+ <td>id</td>
+ <td> id</td>
+ <td>Basic</td>
+ <td>0. used </td>
+ </tr>
+
+
+ <tr>
+ <td>initial-page-number</td>
+ <td>auto | auto-odd | auto-even | number | inherit</td>
+ <td>Basic</td>
+ <td>0. done </td>
+ </tr>
+
+
+ <tr>
+ <td>inline-progression-dimension</td>
+ <td>auto | length | percentage | length-range | inherit</td>
+ <td>Basic</td>
+
+ <td>3. have not considered at all </td>
+ </tr>
+
+
+ <tr>
+ <td>keep-with-next</td>
+ <td>keep | inherit</td>
+ <td>Basic</td>
+ <td>1. done in theory, not working 100%</td>
+ </tr>
+
+
+ <tr>
+ <td>keep-with-previous</td>
+ <td>keep | inherit</td>
+ <td>Basic</td>
+ <td>1. done in theory, not working 100% </td>
+ </tr>
+
+
+ <tr>
+ <td>leader-length</td>
+ <td>length-range | inherit</td>
+ <td>Basic</td>
+ <td>2. waiting to do soon </td>
+ </tr>
+
+
+ <tr>
+ <td>leader-pattern</td>
+ <td>space | rule | dots | use-content | inherit</td>
+ <td>Basic</td>
+ <td>2. waiting to do soon </td>
+ </tr>
+
+
+ <tr>
+ <td>letter-value</td>
+ <td>auto | alphabetic | traditional</td>
+ <td>Basic</td>
+ <td>3. dont want to think about it </td>
+ </tr>
+
+
+ <tr>
+ <td>line-height</td>
+ <td>normal | length | number | percentage | space | inherit</td>
+ <td>Basic</td>
+
+ <td>1. largely done </td>
+ </tr>
+
+
+ <tr>
+ <td>line-stacking-strategy</td>
+ <td>line-height | font-height | max-height | inherit</td>
+ <td>Basic</td>
+ <td>3. untouched </td>
+ </tr>
+
+
+ <tr>
+ <td>margin-bottom</td>
+ <td>margin-width | inherit</td>
+ <td>Basic</td>
+ <td>1. done in places </td>
+ </tr>
+
+
+ <tr>
+ <td>margin-left</td>
+ <td>margin-width | inherit</td>
+ <td>Basic</td>
+ <td>1. done in places </td>
+ </tr>
+
+
+ <tr>
+ <td>margin-right</td>
+ <td>margin-width | inherit</td>
+ <td>Basic</td>
+ <td>1. done in places </td>
+ </tr>
+
+
+ <tr>
+ <td>margin-top</td>
+ <td>margin-width | inherit</td>
+ <td>Basic</td>
+ <td>1. done in places </td>
+ </tr>
+
+
+ <tr>
+ <td>master-name</td>
+ <td>name</td>
+ <td>Basic</td>
+ <td>0. ok </td>
+ </tr>
+
+
+ <tr>
+ <td>max-height</td>
+ <td>length | percentage | none | inherit </td>
+ <td>Basic</td>
+ <td>2. should be doable </td>
+ </tr>
+
+
+ <tr>
+ <td>max-width</td>
+ <td>length | percentage | none | inherit</td>
+ <td>Basic</td>
+ <td>2. should be doable </td>
+ </tr>
+
+
+ <tr>
+ <td>min-height</td>
+ <td>length | percentage | inherit </td>
+ <td>Basic</td>
+ <td>2. should be doable </td>
+ </tr>
+
+
+ <tr>
+ <td>min-width</td>
+ <td>length | percentage | inherit</td>
+ <td>Basic</td>
+ <td>2. should be doable </td>
+ </tr>
+
+
+ <tr>
+ <td>number-columns-repeated</td>
+ <td>number</td>
+ <td>Basic</td>
+
+ <td>2. doable in theory </td>
+ </tr>
+
+
+ <tr>
+ <td>number-columns-spanned</td>
+ <td>number</td>
+ <td>Basic</td>
+ <td>2. doable in theory </td>
+ </tr>
+
+
+ <tr>
+ <td>number-rows-spanned</td>
+ <td>number</td>
+ <td>Basic</td>
+ <td>2. doable in theory </td>
+ </tr>
+
+
+ <tr>
+ <td>orphans</td>
+ <td>integer | inherit</td>
+ <td>Basic</td>
+ <td>2. should be doable </td>
+ </tr>
+
+
+ <tr>
+ <td>overflow</td>
+ <td>visible | hidden | scroll | auto | inherit</td>
+ <td>Basic</td>
+ <td>2. theoretically </td>
+ </tr>
+
+
+ <tr>
+ <td>padding-after</td>
+ <td>padding-width | length-conditional | inherit</td>
+ <td>Basic</td>
+ <td>1. implemented crudely </td>
+ </tr>
+
+
+ <tr>
+ <td>padding-before</td>
+ <td>padding-width | length-conditional | inherit</td>
+ <td>Basic</td>
+ <td>1. implemented crudely </td>
+ </tr>
+
+
+ <tr>
+ <td>padding-bottom</td>
+ <td>padding-width | inherit</td>
+ <td>Basic</td>
+ <td>1. implemented crudely </td>
+ </tr>
+
+
+ <tr>
+ <td>padding-end</td>
+ <td>padding-width | inherit</td>
+ <td>Basic</td>
+ <td>1. implemented crudely </td>
+ </tr>
+
+
+ <tr>
+ <td>padding-left</td>
+ <td>padding-width | inherit</td>
+ <td>Basic</td>
+ <td>1. implemented crudely </td>
+ </tr>
+
+
+ <tr>
+ <td>padding-right</td>
+ <td>padding-width | inherit</td>
+ <td>Basic</td>
+ <td>1. implemented crudely </td>
+ </tr>
+
+
+ <tr>
+ <td>padding-start</td>
+ <td>padding-width | inherit</td>
+ <td>Basic</td>
+ <td>1. implemented crudely </td>
+ </tr>
+
+
+ <tr>
+ <td>padding-top</td>
+ <td>padding-width | inherit</td>
+ <td>Basic</td>
+ <td>1. implemented crudely </td>
+ </tr>
+
+
+ <tr>
+ <td>page-break-after</td>
+ <td>auto | always | avoid | left | right | inherit</td>
+ <td>Basic</td>
+ <td>1. Mostly implemented </td>
+ </tr>
+
+
+ <tr>
+ <td>page-break-before</td>
+ <td>auto | always | avoid | left | right | inherit</td>
+ <td>Basic</td>
+ <td>1. Mostly implemented </td>
+ </tr>
+
+
+ <tr>
+ <td>page-height</td>
+ <td>auto | indefinite | length | inherit</td>
+ <td>Basic</td>
+ <td>1. not all possibilities</td>
+ </tr>
+
+
+ <tr>
+ <td>page-width</td>
+ <td>auto | indefinite | length | inherit</td>
+ <td>Basic</td>
+ <td>1. not all possibilities</td>
+ </tr>
+
+
+ <tr>
+ <td>pause-after</td>
+ <td>time | percentage | inherit</td>
+ <td>Basic</td>
+ <td>4. N/A </td>
+ </tr>
+
+
+ <tr>
+ <td>pause-before</td>
+ <td>time | percentage | inherit</td>
+ <td>Basic</td>
+ <td>4. N/A </td>
+ </tr>
+
+
+ <tr>
+ <td>pitch</td>
+ <td>frequency | x-low | low | medium | high | x-high | inherit</td>
+ <td>Basic</td>
+
+ <td>4. N/A </td>
+ </tr>
+
+
+ <tr>
+ <td>pitch-range</td>
+ <td>number | inherit</td>
+ <td>Basic</td>
+ <td>4. N/A </td>
+ </tr>
+
+
+ <tr>
+ <td>play-during</td>
+ <td>uri mix? repeat? | auto | none | inherit </td>
+ <td>Basic</td>
+ <td>4. N/A </td>
+ </tr>
+
+
+ <tr>
+ <td>precedence</td>
+ <td>true | false | inherit</td>
+ <td>Basic</td>
+ <td>3. do not know where to start </td>
+ </tr>
+
+
+ <tr>
+ <td>provisional-distance-between-starts</td>
+ <td>length | inherit</td>
+ <td>Basic</td>
+ <td>1. does something, probably wrong </td>
+ </tr>
+
+
+ <tr>
+ <td>provisional-label-separation</td>
+ <td>length | inherit</td>
+ <td>Basic</td>
+ <td>1. does something, probably wrong </td>
+ </tr>
+
+
+ <tr>
+ <td>ref-id</td>
+ <td>idref | inherit</td>
+ <td>Basic</td>
+ <td>0. used in pagenumber </td>
+ </tr>
+
+
+ <tr>
+ <td>reference-orientation</td>
+ <td> 0 | 90 | 180 | 270 | -90 | -180 | -270 | inherit</td>
+ <td>Basic</td>
+ <td>2. doable for most objects </td>
+ </tr>
+
+
+ <tr>
+ <td>region-name</td>
+ <td>xsl-region-body | xsl-region-start | xsl-region-end | xsl-region-before | xsl-region-after | xsl-before-float-separator
+ | xsl-footnote-separator | name
+ </td>
+ <td>Basic</td>
+
+ <td>0. done </td>
+ </tr>
+
+
+ <tr>
+ <td>relative-align</td>
+ <td>before | baseline | inherit</td>
+ <td>Basic</td>
+
+ <td>3. have not got to grips with this </td>
+ </tr>
+
+
+ <tr>
+ <td>richness</td>
+ <td>number | inherit</td>
+ <td>Basic</td>
+ <td>4. N/A </td>
+ </tr>
+
+
+ <tr>
+ <td>role</td>
+ <td>string | none | inherit</td>
+ <td>Basic</td>
+ <td>4. N/A what should I do with it?</td>
+ </tr>
+
+
+ <tr>
+ <td>rule-style</td>
+ <td>none | dotted | dashed | solid | double | groove | ridge | inherit</td>
+ <td>Basic</td>
+
+ <td>1. done as far as possible </td>
+ </tr>
+
+
+ <tr>
+ <td>rule-thickness</td>
+ <td>length</td>
+ <td>Basic</td>
+ <td>0. done </td>
+ </tr>
+
+
+ <tr>
+ <td>source-document</td>
+ <td>uri+ | none | inherit</td>
+ <td>Basic</td>
+ <td>4. N/A not sure what to do with it</td>
+ </tr>
+
+
+ <tr>
+ <td>space-after</td>
+ <td>space | inherit</td>
+ <td>Basic</td>
+ <td>1. working more or less </td>
+ </tr>
+
+
+ <tr>
+ <td>space-before</td>
+ <td>space | inherit</td>
+ <td>Basic</td>
+ <td>1. working more or less </td>
+ </tr>
+
+
+ <tr>
+ <td>space-end</td>
+ <td>space | inherit</td>
+ <td>Basic</td>
+ <td>1. working more or less </td>
+ </tr>
+
+
+ <tr>
+ <td>space-start</td>
+ <td>space | inherit</td>
+ <td>Basic</td>
+ <td>1. working more or less </td>
+ </tr>
+
+
+ <tr>
+ <td>speak</td>
+ <td>normal | none | spell-out | inherit</td>
+ <td>Basic</td>
+ <td>4. N/A </td>
+ </tr>
+
+
+ <tr>
+ <td>speak-header</td>
+ <td>once | always | inherit</td>
+ <td>Basic</td>
+ <td>4. N/A </td>
+ </tr>
+
+
+ <tr>
+ <td>speak-numeral</td>
+ <td>digits | continuous | inherit</td>
+ <td>Basic</td>
+ <td>4. N/A </td>
+ </tr>
+
+
+ <tr>
+ <td>speak-punctuation</td>
+ <td>code | none | inherit</td>
+ <td>Basic</td>
+ <td>4. N/A </td>
+ </tr>
+
+
+ <tr>
+ <td>speech-rate</td>
+ <td>number | x-slow | slow | medium | fast | x-fast | faster | slower | inherit</td>
+ <td>Basic</td>
+
+ <td>4. N/A </td>
+ </tr>
+
+
+ <tr>
+ <td>src</td>
+ <td> uri | inherit</td>
+ <td>Basic</td>
+ <td>0. implemented </td>
+ </tr>
+
+
+ <tr>
+ <td>start-indent</td>
+ <td>length | inherit</td>
+ <td>Basic</td>
+ <td>0. done </td>
+ </tr>
+
+
+ <tr>
+ <td>stress</td>
+ <td>number | inherit</td>
+ <td>Basic</td>
+ <td>4. N/A </td>
+ </tr>
+
+
+ <tr>
+ <td>text-align</td>
+ <td>start | center | end | justify | inside | outside | left | right | string | inherit</td>
+ <td>Basic</td>
+
+ <td>0. done </td>
+ </tr>
+
+
+ <tr>
+ <td>text-indent</td>
+ <td>length | percentage | inherit</td>
+ <td>Basic</td>
+ <td>0. done </td>
+ </tr>
+
+
+ <tr>
+ <td>visibility</td>
+ <td>visible | hidden | collapse | inherit</td>
+ <td>Basic</td>
+ <td>2. I think can do this </td>
+ </tr>
+
+
+ <tr>
+ <td>voice-family</td>
+ <td>[[specific-voice | generic-voice ],]* [specific-voice | generic-voice ] | inherit</td>
+ <td>Basic</td>
+
+ <td>4. N/A </td>
+ </tr>
+
+
+ <tr>
+ <td>volume</td>
+ <td>number | percentage | silent | x-soft | soft | medium | loud | x-loud | inherit</td>
+ <td>Basic</td>
+
+ <td>4. N/A </td>
+ </tr>
+
+
+ <tr>
+ <td>widows</td>
+ <td>integer | inherit</td>
+ <td>Basic</td>
+ <td>2. should be doable </td>
+ </tr>
+
+
+ <tr>
+ <td>width</td>
+ <td>length | percentage | auto | inherit</td>
+ <td>Basic</td>
+ <td>2. should be OK, waiting for a need </td>
+ </tr>
+
+
+ <tr>
+ <td>wrap-option</td>
+ <td>no-wrap | wrap | inherit</td>
+ <td>Basic</td>
+ <td>0. should be working </td>
+ </tr>
+
+
+ <tr>
+ <td>writing-mode</td>
+ <td>lr-tb | rl-tb | tb-rl | lr | rl | tb | inherit</td>
+ <td>Basic</td>
+ <td>3. will need an extended TeX </td>
+ </tr>
+
+
+ <tr>
+ <td>z-index</td>
+ <td>auto | integer | inherit</td>
+ <td>Basic</td>
+ <td>3. dont know where to start </td>
+ </tr>
+
+ </table>
+ </div>
+
+ </p>
+
+ </div>
+
+
+
+ <div class="teidiv">
+ <h3><a name="index-div-c16ab3b3b9c11"></a>5.2. Properties needed for full conformance
+ </h3>
+
+ <p><a name="c16ab3b3b9c11b2"></a>
+
+ <div align="center">
+ <table rules="all" border="1">
+
+ <tr>
+ <td>absolute-position</td>
+ <td>auto | absolute | fixed | inherit</td>
+ <td>Complete</td>
+ <td>2. should be doable </td>
+ </tr>
+
+
+ <tr>
+ <td>background</td>
+ <td>[background-color || background-image
+ || background-repeat || background-attachment || background-position
+ | ]]inherit
+ </td>
+ <td>Complete</td>
+
+ <td>1. implemented but very fragile </td>
+ </tr>
+
+
+ <tr>
+ <td>background-position</td>
+ <td>[ [percentage | length ]{1,2} | [ [top | center | bottom] || [left | center | right] ] ] | inherit</td>
+ <td>Complete</td>
+
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>border</td>
+ <td>[ border-width || border-style || color ] | inherit</td>
+ <td>Complete</td>
+
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>border-bottom</td>
+ <td>[ border-top-width || border-style || color ] | inherit</td>
+ <td>Complete</td>
+
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>border-color</td>
+ <td>color{1,4} | transparent | inherit</td>
+ <td>Complete</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>border-left</td>
+ <td>[ border-top-width || border-style || color ] | inherit</td>
+ <td>Complete</td>
+
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>border-right</td>
+ <td>[ border-top-width || border-style || color ] | inherit</td>
+ <td>Complete</td>
+
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>border-spacing</td>
+ <td>length length? | inherit</td>
+ <td>Complete</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>border-style</td>
+ <td>border-style{1,4} | inherit</td>
+ <td>Complete</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>border-top</td>
+ <td>[ border-top-width || border-style || color ] | inherit</td>
+ <td>Complete</td>
+
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>border-width</td>
+ <td>border-width{1,4} | inherit</td>
+ <td>Complete</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>caption-side</td>
+ <td>before | after | start | end | top | bottom | left | right | inherit</td>
+ <td>Complete</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>cue</td>
+ <td>cue-before || cue-after | inherit</td>
+ <td>Complete</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>font</td>
+ <td>[ [ font-style || font-variant || font-weight ]? font-size [ / line-height]? font-family
+ ] | caption | icon | menu | message-box | small-caption | status-bar
+ | inherit
+ </td>
+ <td>Complete</td>
+
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>margin</td>
+ <td>margin-width{1,4} | inherit </td>
+ <td>Complete</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>padding</td>
+ <td>padding-width{1,4} | inherit</td>
+ <td>Complete</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>page-break-inside</td>
+ <td>avoid | auto | inherit</td>
+ <td>Complete</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>pause</td>
+ <td>[time | percentage]{1,2} | inherit</td>
+ <td>Complete</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>position</td>
+ <td>static | relative | absolute | fixed | inherit</td>
+ <td>Complete</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>size</td>
+ <td>length{1,2} | auto | landscape | portrait | inherit</td>
+ <td>Complete</td>
+
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>vertical-align</td>
+ <td>baseline | middle | sub | super | text-top | text-bottom | percentage | length | top | bottom | inherit</td>
+ <td>Complete</td>
+
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>white-space</td>
+ <td>normal | pre | nowrap | inherit</td>
+ <td>Complete</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>xml:lang</td>
+ <td>country-language | inherit</td>
+ <td>Complete</td>
+ <td>2. not done yet, but will be </td>
+ </tr>
+
+ </table>
+ </div>
+
+ </p>
+
+ </div>
+
+
+ <div class="teidiv">
+ <h3><a name="index-div-c16ab3b3b9c13"></a>5.3. Properties needed for extended conformance
+ </h3>
+
+ <p><a name="c16ab3b3b9c13b2"></a>
+
+ <div align="center">
+ <table rules="all" border="1">
+
+ <tr>
+ <td>table-layout</td>
+ <td>auto | fixed | inherit</td>
+ <td>Extended.Fallback: fixed</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>background-attachment</td>
+ <td>scroll | fixed | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td>2. I can see where I might start </td>
+ </tr>
+
+
+ <tr>
+ <td>background-image</td>
+ <td>uri | none | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td>2. I can see where I might start </td>
+ </tr>
+
+
+ <tr>
+ <td>background-position-horizontal</td>
+ <td>percentage | length | left | center | right | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+
+ <td>2. I can see where I might start </td>
+ </tr>
+
+
+ <tr>
+ <td>background-position-vertical</td>
+ <td>percentage | length | top | center | bottom | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+
+ <td>2. I can see where I might start </td>
+ </tr>
+
+
+ <tr>
+ <td>border-collapse</td>
+ <td>collapse | separate | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>border-separation</td>
+ <td>length-bp-ip-direction | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>column-count</td>
+ <td>number | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td>0. implemented </td>
+ </tr>
+
+
+ <tr>
+ <td>content-height</td>
+ <td>auto | length | percentage | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td>1. done for graphics </td>
+ </tr>
+
+
+ <tr>
+ <td>content-width</td>
+ <td>auto | length | percentage | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td>1. done for graphics </td>
+ </tr>
+
+
+ <tr>
+ <td>country</td>
+ <td>none | country | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td>2. waiting to find a use for it </td>
+ </tr>
+
+
+ <tr>
+ <td>empty-cells</td>
+ <td>show | hide | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>ends-row</td>
+ <td>yes | no</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>font-height-override-after</td>
+ <td>use-font-metrics | length | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td>3. need extended TeX </td>
+ </tr>
+
+
+ <tr>
+ <td>font-height-override-before</td>
+ <td>use-font-metrics | length | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td>3. need extended TeX </td>
+ </tr>
+
+
+ <tr>
+ <td>font-size-adjust</td>
+ <td>number | none | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td>2. doable, I think </td>
+ </tr>
+
+
+ <tr>
+ <td>font-stretch</td>
+ <td>normal | wider | narrower | ultra-condensed | extra-condensed | condensed | semi-condensed | semi-expanded |
+ expanded | extra-expanded | ultra-expanded |inherit
+ </td>
+ <td>Extended.Fallback: Initial value</td>
+
+ <td>0. should be OK </td>
+ </tr>
+
+
+ <tr>
+ <td>glyph-orientation-horizontal</td>
+ <td>angle | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td>3. need extended TeX </td>
+ </tr>
+
+
+ <tr>
+ <td>glyph-orientation-vertical</td>
+ <td>auto | angle | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td>3. need extended TeX </td>
+ </tr>
+
+
+ <tr>
+ <td>hyphenate</td>
+ <td>false | true | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td>0. done </td>
+ </tr>
+
+
+ <tr>
+ <td>keep-together</td>
+ <td>keep | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>language</td>
+ <td>none | language | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td>0. done, if underlying TeX system OK </td>
+ </tr>
+
+
+ <tr>
+ <td>last-line-end-indent</td>
+ <td>length | percentage | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>leader-alignment</td>
+ <td>none | reference-area | page | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>leader-pattern-width</td>
+ <td>use-font-metrics | length | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>letter-spacing</td>
+ <td>normal | length | space | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td>2. doable in limited circumstances </td>
+ </tr>
+
+
+ <tr>
+ <td>line-height-shift-adjustment</td>
+ <td>consider-shifts | disregard-shifts | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>linefeed-treatment</td>
+ <td>ignore | preserve | treat-as-space | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td>2. doable, if tiresome </td>
+ </tr>
+
+
+ <tr>
+ <td>relative-position</td>
+ <td>auto | static | relative | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>scaling</td>
+ <td>uniform | non-uniform | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td>0. ok </td>
+ </tr>
+
+
+ <tr>
+ <td>scaling-method</td>
+ <td>auto | integer-pixels | resample-any-method | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td>4. N/A, I think </td>
+ </tr>
+
+
+ <tr>
+ <td>score-spaces</td>
+ <td>true | false | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td>3. dont think I can do this </td>
+ </tr>
+
+
+ <tr>
+ <td>space-treatment</td>
+ <td>ignore | preserve | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td>0. seems to work </td>
+ </tr>
+
+
+ <tr>
+ <td>span</td>
+ <td>none | all | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td>3. proving hard </td>
+ </tr>
+
+
+ <tr>
+ <td>starts-row</td>
+ <td>yes |
+ no
+ </td>
+ <td>Extended.Fallback: Initial value</td>
+
+ <td>0. works</td>
+ </tr>
+
+
+ <tr>
+ <td>suppress-at-line-break</td>
+ <td>auto | suppress | retain | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>table-omit-footer-at-break</td>
+ <td>yes | no</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>table-omit-header-at-break</td>
+ <td>yes | no</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>text-align-last</td>
+ <td>relative | start | center | end | justify | inside | outside | left | right | string | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+
+ <td>1. works, usually </td>
+ </tr>
+
+
+ <tr>
+ <td>text-decoration</td>
+ <td>none | [ [ underline | no-underline] || [ overline | no-overline ] || [ line-through | no-line-through ] || [ blink | no-blink
+ ] ]
+
+ | inherit
+ </td>
+ <td>Extended.Fallback: Initial value</td>
+
+ <td>1. done for some possibilities, not all </td>
+ </tr>
+
+
+ <tr>
+ <td>text-shadow</td>
+ <td>none | [color || length length length? ,]* [color || length length length?] | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>text-transform</td>
+ <td>capitalize | uppercase | lowercase | none | </td>
+ <td>Extended.Fallback: Initial value</td>
+ <td>2. doable </td>
+ </tr>
+
+
+ <tr>
+ <td>treat-as-word-space</td>
+ <td>auto | yes | no | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>white-space-collapse</td>
+ <td>false | true | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td>0. Done </td>
+ </tr>
+
+
+ <tr>
+ <td>word-spacing</td>
+ <td>normal | length | space | inherit</td>
+ <td>Extended.Fallback: Initial value</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>bottom</td>
+ <td>length | percentage | auto | inherit</td>
+ <td>Extended.Fallback: N/A due to fallback for absolute-position, relative-position</td>
+ <td>2. doable, I think </td>
+ </tr>
+
+
+ <tr>
+ <td>left</td>
+ <td>length | percentage | auto | inherit</td>
+ <td>Extended.Fallback: N/A due to fallback for absolute-position, relative-position</td>
+ <td>2. doable, I think </td>
+ </tr>
+
+
+ <tr>
+ <td>right</td>
+ <td>length | percentage | auto | inherit</td>
+ <td>Extended.Fallback: N/A due to fallback for absolute-position, relative-position</td>
+ <td>2. doable, I think </td>
+ </tr>
+
+
+ <tr>
+ <td>top</td>
+ <td>length | percentage | auto | inherit</td>
+ <td>Extended.Fallback: N/A due to fallback for absolute-position, relative-position</td>
+ <td>2. doable, I think </td>
+ </tr>
+
+
+ <tr>
+ <td>column-gap</td>
+ <td>length | percentage | inherit</td>
+ <td>Extended.Fallback: N/A due to fallback for column-count</td>
+ <td>1. implemented (not for all value types) </td>
+ </tr>
+
+
+ <tr>
+ <td>hyphenation-character</td>
+ <td>character | inherit</td>
+ <td>Extended.Fallback: N/A due to fallback for hyphenate</td>
+ <td>3. need to think about how to do this </td>
+ </tr>
+
+
+ <tr>
+ <td>hyphenation-keep</td>
+ <td>auto | column | page | inherit</td>
+ <td>Extended.Fallback: N/A due to fallback for hyphenate</td>
+ <td>3. not sure how to do this </td>
+ </tr>
+
+
+ <tr>
+ <td>hyphenation-ladder-count</td>
+ <td>no-limit | number | inherit</td>
+ <td>Extended.Fallback: N/A due to fallback for hyphenate</td>
+ <td>3. I dont see how to do this </td>
+ </tr>
+
+
+ <tr>
+ <td>hyphenation-push-character-count</td>
+ <td>number | inherit</td>
+ <td>Extended.Fallback: N/A due to fallback for hyphenate</td>
+ <td>2. I think this maps in TeX </td>
+ </tr>
+
+
+ <tr>
+ <td>hyphenation-remain-character-count</td>
+ <td>number | inherit</td>
+ <td>Extended.Fallback: N/A due to fallback for hyphenate</td>
+ <td>2. I think this maps in TeX </td>
+ </tr>
+
+
+ <tr>
+ <td>color-profile-name</td>
+ <td>name | inherit</td>
+ <td>Extended.Fallback: N/A use fallback for fo:color-profile</td>
+ <td>3. would need a lot of thought </td>
+ </tr>
+
+
+ <tr>
+ <td>rendering-intent</td>
+ <td>auto | perceptual | relative-colorimetric | saturation | absolute-colorimetric | inherit</td>
+ <td>Extended.Fallback: N/A use fallback for fo:color-profile</td>
+ <td>3. not sure how to do this </td>
+ </tr>
+
+
+ <tr>
+ <td>clear</td>
+ <td>start | end | left | right | both | none | inherit</td>
+ <td>Extended.Fallback: N/A use fallback for fo:float</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>float</td>
+ <td>before | start | end | left | right | none | inherit</td>
+ <td>Extended.Fallback: N/A use fallback for fo:float</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>marker-class-name</td>
+ <td>name</td>
+ <td>Extended.Fallback: N/A use fallback for fo:marker</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>active-state</td>
+ <td>link | visited | active | hover | focus</td>
+ <td>Extended.Fallback: N/A use fallback for fo:multi-properties</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>auto-restore</td>
+ <td>yes | no</td>
+ <td>Extended.Fallback: N/A use fallback for fo:multi-switch</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>case-name</td>
+ <td>name</td>
+ <td>Extended.Fallback: N/A use fallback for fo:multi-switch</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>case-title</td>
+ <td>string</td>
+ <td>Extended.Fallback: N/A use fallback for fo:multi-switch</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>starting-state</td>
+ <td>show | hide</td>
+ <td>Extended.Fallback: N/A use fallback for fo:multi-switch</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>switch-to</td>
+ <td>xsl-preceding | xsl-following | xsl-any | name[ name]*</td>
+ <td>Extended.Fallback: N/A use fallback for fo:multi-switch</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>extent</td>
+ <td>length | percentage | inherit</td>
+ <td>Extended.Fallback: N/A use fallback for fo:region-before, fo:region-after, fo:region-start, and fo:region-end</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>blank-or-not-blank</td>
+ <td>blank | not-blank | any | inherit</td>
+ <td>Extended.Fallback: N/A use fallback for fo:repeatable-page-master-alternatives</td>
+ <td>3. dont want to think about it </td>
+ </tr>
+
+
+ <tr>
+ <td>odd-or-even</td>
+ <td>odd | even | any | inherit</td>
+ <td>Extended.Fallback: N/A use fallback for fo:repeatable-page-master-alternatives</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>page-position</td>
+ <td>first | last | rest | any | inherit</td>
+ <td>Extended.Fallback: N/A use fallback for fo:repeatable-page-master-alternatives</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>maximum-repeats</td>
+ <td>number | no-limit | inherit</td>
+ <td>Extended.Fallback: N/A use fallback for fo:repeatable-page-master-reference and fo:repeatable-page-master-alternatives</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>retrieve-boundary</td>
+ <td>page | page-sequence | document</td>
+ <td>Extended.Fallback: N/A use fallback for fo:retrieve-marker</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>retrieve-class-name</td>
+ <td>name</td>
+ <td>Extended.Fallback:
+ N/A use fallback for fo:retrieve-marker
+ </td>
+ <td>1. works usually </td>
+ </tr>
+
+
+ <tr>
+ <td>retrieve-position</td>
+ <td>first-starting-within-page | first-including-carryover | last-starting-within-page | last-ending-within-page</td>
+ <td>Extended.Fallback: N/A use fallback for fo:retrieve-marker</td>
+
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>destination-placement-offset</td>
+ <td>length</td>
+ <td>Extended.Fallback: N/A use fallback for fo:simple-link</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>external-destination</td>
+ <td>uri-reference</td>
+ <td>Extended.Fallback:
+ N/A use fallback for fo:simple-link
+ </td>
+ <td>0. works ok </td>
+ </tr>
+
+
+ <tr>
+ <td>indicate-destination</td>
+ <td>yes |
+ no
+ </td>
+ <td>Extended.Fallback: N/A use fallback for
+ fo:simple-link
+ </td>
+ <td>1. should work </td>
+ </tr>
+
+
+ <tr>
+ <td>internal-destination</td>
+ <td>null string |
+ idref
+ </td>
+ <td>Extended.Fallback: N/A use fallback for
+ fo:simple-link
+ </td>
+ <td>0. works </td>
+ </tr>
+
+
+ <tr>
+ <td>show-destination</td>
+ <td>replace | new</td>
+ <td>Extended.Fallback: N/A use fallback for fo:simple-link</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>force-page-count</td>
+ <td>auto | even | odd | end-on-even | end-on-odd | no-force | inherit</td>
+ <td>Extended.Fallback: no-force</td>
+
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>background-repeat</td>
+ <td>repeat | repeat-x | repeat-y | no-repeat | inherit</td>
+ <td>Extended.Fallback: no-repeat</td>
+ <td> </td>
+ </tr>
+
+
+ <tr>
+ <td>script</td>
+ <td>none | auto | script | inherit</td>
+ <td>Extended.Fallback: none</td>
+ <td>4. dont know what to do with it </td>
+ </tr>
+
+
+ <tr>
+ <td>unicode-bidi</td>
+ <td>normal | embed | bidi-override | inherit</td>
+ <td>Extended.Fallback: See prose</td>
+ <td> </td>
+
+ </tr>
+
+ </table>
+ </div>
+
+ </p>
+
+ </div>
+
+
+ </div>
+
+
+ <div class="teidiv">
+ <h2><a name="index-div-c16ab3b3c11"></a>6. Sample files
+ </h2>
+
+
+ <p><a name="c16ab3b3c11b3"></a>
+
+ <ul>
+ <li><a name="c16ab3b3c11b3b1b1"></a> The TEI Lite description (<a href="test/teiu5.xml" target="_top">teiu5.xml</a>) converted PDF as <a href="test/teiu5.pdf" target="_top">teiu5.pdf</a></li>
+ <li><a name="c16ab3b3c11b3b1b3"></a> A TEI test file (<a href="test/exercise.xml" target="_top">exercise.xml</a>)
+ converted to PDF as <a href="test/exercise.pdf" target="_top">exercise.pdf</a></li>
+ <li><a name="c16ab3b3c11b3b1b5"></a> A physics paper (<a href="test/latextei.xml" target="_top">latextei.xml</a>) containing a fair
+ amount of MathML markup, originally
+ translated from LaTeX into XML.
+ It is used extensively as an example in the
+ <a href="http://cseng.awl.com/bookpage.taf?ISBN=0-201-43311-7&amp;ptype=0&amp;catid=&amp;navmin=&amp;ctype=author&amp;catpage=&amp;seriesid=" target="_top">LaTeX Web Companion</a>.
+ Here we see it
+ converted to <a href="test/latextei.pdf" target="_top">latextei.pdf</a> using
+ <a href="test/latextei.xsl" target="_top">test/latextei.xsl</a></li>
+ <li><a name="c16ab3b3c11b3b1b7"></a> James Tauber prepared a simple XSL spec (<a href="test/darkness.xsl" target="_top">darkness.xsl</a>) for Joseph Conrad's
+ <a href="test/darkness.xml" target="_top"><em>Heart of
+ Darkness</em></a>, which I ran to PDF as <a href="test/darkness.pdf" target="_top">darkness.pdf</a></li>
+ </ul>
+
+ </p>
+
+ </div>
+
+
+ <div class="teidiv">
+ <h2><a name="index-div-c16ab3b3c13"></a>7. Concerns and problems
+ </h2>
+
+
+ <p><a name="c16ab3b3c13b3"></a>
+ Some points to bear in mind
+
+ <ol>
+ <li><a name="c16ab3b3c13b3b1b1"></a> Obviously, the XSL FO spec is still a draft.
+ And this system is not conforming
+ precisely to the current draft.
+ </li>
+ <li><a name="c16ab3b3c13b3b1b3"></a> This is an experiment system to check whether the
+ idea works. Expect something more polished eventually.
+ </li>
+ <li><a name="c16ab3b3c13b3b1b5"></a> You need a modern TeX setup (like
+ <a href="http://www.tug.org/teTeX/" target="_top">teTeX</a> or
+ <a href="http://www.tug.org/texlive/" target="_top">TeX Live</a>)
+ to get to grips with it.
+ </li>
+ <li><a name="c16ab3b3c13b3b1b7"></a> Quite a few flow objects and characteristics are not dealt with yet.
+ I will add support for more things as needed or requested.
+ </li>
+ <li><a name="c16ab3b3c13b3b1b9"></a> I do not have any objective check that what I think XSL FOs are
+ supposed to do is actually right :-}
+ </li>
+ <li><a name="c16ab3b3c13b3b1c11"></a> I have only worked so far with the TEI Lite (XML version) and
+ Docbook DTDs, and probably misinterpreted half of what they say.
+ </li>
+ </ol>
+
+ </p>
+
+ </div>
+
+
+ <div class="teidiv">
+ <h2><a name="index-div-c16ab3b3c15"></a>8. Things for LaTeX users to remember
+ </h2>
+
+
+ <p><a name="c16ab3b3c15b3"></a>
+
+ <ul>
+ <li><a name="c16ab3b3c15b3b1b1"></a> No use is made of LaTeX high-level constructs. No sections,
+ no lists, no cross-refs, no bibliographies; on the other hand,
+ some extensions in the <tt>fotex:</tt> namespace are supported
+ (eg to get Acrobat bookmarks)
+
+ </li>
+ <li><a name="c16ab3b3c15b3b1b3"></a> XSL FO's underlying character set is Unicode; by default,
+ entities are mapped to their Unicode position;
+
+ </li>
+ <li><a name="c16ab3b3c15b3b1b5"></a> All vertical and horizontal space is explicit in the
+ specification
+
+ </li>
+ <li><a name="c16ab3b3c15b3b1b7"></a> Page and line breaking is left to TeX: the rest is up to you.
+
+ </li>
+ </ul>
+
+ </p>
+
+ </div>
+
+
+ <div class="teidiv">
+ <h2><a name="index-div-c16ab3b3c17"></a>9. Future directions
+ </h2>
+
+
+ <p><a name="c16ab3b3c17b3"></a>
+
+ <ul>
+ <li><a name="c16ab3b3c17b3b1b1"></a>Complete the MathML handling
+ </li>
+ <li><a name="c16ab3b3c17b3b1b3"></a>Handle more variety in property values (eg colors, fonts)
+ </li>
+ <li><a name="c16ab3b3c17b3b1b5"></a>Deal with more complex tables
+ </li>
+ <li><a name="c16ab3b3c17b3b1b7"></a>Support SVG. How?
+
+ <ul>
+ <li><a name="c16ab3b3c17b3b1b7b1b1"></a>By direct intepretation and mapping to raw PDF
+ </li>
+ <li><a name="c16ab3b3c17b3b1b7b1b3"></a>By translation to MetaPost, and spawning a MetaPost process
+ </li>
+ <li><a name="c16ab3b3c17b3b1b7b1b5"></a>By pre-processing to existing TeX graphics languages
+ </li>
+ </ul>
+ In any case, SVG fragments need to be recognized directly to perform in-line
+ graphical functions (setting text at an angle?)
+
+ </li>
+ <li><a name="c16ab3b3c17b3b1b9"></a>Use Unicode-based TeX variant (Omega) to handle non-Latin material
+ more naturally
+ </li>
+ </ul>
+
+ </p>
+
+ <p><a name="c16ab3b3c17b5"></a>
+ I will be very glad to discuss details with anyone. Contact me (Sebastian Rahtz) as
+ <a href="mailto:sebastian.rahtz@oucs.ox.ac.uk" target="_top">sebastian.rahtz@oucs.ox.ac.uk</a>
+
+ </p>
+
+ </div>
+
+ <hr>
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+ <address>Date: November 2000
+ (revised 2000/12/11)
+ &nbsp;Author: .
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+ <!--Generated
+ using an XSLT version 1 stylesheet
+ based on http://www.oucs.ox.ac.uk/stylesheets/teihtml.xsl
+ processed using:
+ `SAXON 5.5.1 from Michael Kay of ICL'
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@@ -0,0 +1,647 @@
+<?xml version="1.0" encoding="utf-8"?>
+<fo:root xmlns:fo="http://www.w3.org/XSL/Format/1.0" xmlns:fop="http://www.jtauber.com/fop" xmlns:fotex="http://www.tug.org/fotex"><fo:layout-master-set><fo:simple-page-master page-master-name="left" margin-top="75pt" margin-bottom="100pt" margin-left="80pt" margin-right="150pt"><fo:region-body margin-bottom="24pt" margin-top="24pt"/><fo:region-after extent="25pt"/><fo:region-before extent="25pt"/></fo:simple-page-master><fo:simple-page-master page-master-name="right" margin-top="75pt" margin-bottom="100pt" margin-left="80pt" margin-right="150pt"><fo:region-body margin-bottom="24pt" margin-top="24pt"/><fo:region-after extent="25pt"/><fo:region-before extent="25pt"/></fo:simple-page-master><fo:simple-page-master page-master-name="first" margin-top="75pt" margin-bottom="100pt" margin-left="80pt" margin-right="150pt"><fo:region-body margin-bottom="24pt" margin-top="24pt"/><fo:region-after extent="25pt"/><fo:region-before extent="25pt"/></fo:simple-page-master></fo:layout-master-set><fo:page-sequence><fo:static-content flow-name="xsl-after"/><fo:static-content flow-name="xsl-before"/><fo:sequence-specification><fo:sequence-specifier-single page-master="right"/></fo:sequence-specification><fo:flow>
+ <fo:block font-size="18pt" space-after="8pt" text-align-last="centered">
+ Simulation of Energy Loss Straggling
+ </fo:block>
+ <fo:block space-after="6pt" font-size="14pt" text-align-last="centered"><fo:inline-sequence font-style="italic">Maria Physicist</fo:inline-sequence></fo:block>
+ <fo:block space-after="6pt" font-size="16pt" text-align-last="centered">January 17, 1999</fo:block>
+ </fo:flow></fo:page-sequence><fo:page-sequence initial-page-number="1"><fo:sequence-specification><fo:sequence-specifier-alternating page-master-first="first" page-master-odd="right" page-master-even="left"/></fo:sequence-specification><fo:static-content flow-name="xsl-after" fop:master="right"><fo:block font-size="10pt"><fo:inline-rule rule-thickness="0pt"/><fo:page-number/></fo:block></fo:static-content><fo:static-content flow-name="xsl-after" fop:master="left"><fo:block font-size="10pt"><fo:page-number/><fo:inline-rule rule-thickness="0pt"/></fo:block></fo:static-content><fo:static-content flow-name="xsl-before" fop:master="right"><fo:block text-align-last="centered" font-size="10pt"><!--Running Head: title-->Simulation of Energy Loss Straggling</fo:block></fo:static-content><fo:static-content flow-name="xsl-before" fop:master="left"><fo:block text-align-last="centered" font-size="10pt"><!--Running Head: author-->Maria Physicist</fo:block></fo:static-content><fo:static-content flow-name="xsl-before" fop:master="first"/><fo:static-content flow-name="xsl-after" fop:master="first"><fo:block font-size="10pt"><fo:inline-rule rule-thickness="0pt"/><fo:page-number/><fo:inline-rule rule-thickness="0pt"/></fo:block></fo:static-content><fo:flow font-family="Times Roman" font-size="10pt"> <fo:block keep-with-next="true" id="intro" text-align="start" font-size="18pt" text-indent="-3em" font-weight="bold" space-after="6pt" space-before.optimum="12pt">1. Introduction<fotex:bookmark fotex-bookmark-level="0" fotex-bookmark-label="intro">1. Introduction</fotex:bookmark></fo:block> <fo:block font-size="10pt" text-align="justified">Due to
+the statistical nature of ionisation energy loss, large fluctuations
+can occur in the amount of energy deposited by a particle traversing
+an absorber element. Continuous processes such as multiple scattering
+and energy loss play a relevant role in the longitudinal and lateral
+development of electromagnetic and hadronic showers, and in the case
+of sampling calorimeters the measured resolution can be significantly
+affected by such fluctuations in their active layers. The description
+of ionisation fluctuations is characterised by the significance
+parameter <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi></fotex:inlinemath>, which is
+proportional to the ratio of mean energy loss to the maximum allowed
+energy transfer in a single collision with an atomic electron
+ <fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"> <mi>κ</mi><mo>=</mo>
+<mfrac>
+ <mrow><mi>ξ</mi></mrow>
+ <mrow>
+ <msub><mi>E</mi><mi>max</mi></msub>
+ </mrow>
+</mfrac>
+</mrow>
+</fotex:displaymath>
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>max</mi></msub></fotex:inlinemath> is the
+maximum transferable energy in a single collision with an atomic electron.
+<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML">
+ <msub><mi>E</mi><mi>max</mi></msub><mo>=</mo> <mfrac><mrow><mn>2</mn><msub><mi>m</mi><mrow><mi>e</mi></mrow></msub><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><msup><mi>γ</mi><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>1</mn><mo>+</mo><mn>2</mn><mi>γ</mi><msub><mi>m</mi><mrow><mi>e</mi></mrow></msub><mo>/</mo><msub><mi>m</mi><mrow><mi>x</mi></mrow></msub><mo>+</mo><msup><mfenced open="(" close=")"><msub><mi>m</mi><mrow><mi>e</mi></mrow></msub><mo>/</mo><msub><mi>m</mi><mrow><mi>x</mi></mrow></msub> </mfenced><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo>,</mo>
+</mrow></fotex:displaymath> where
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">γ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mrow><mi>x</mi></mrow></msub></fotex:inlinemath>,
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi></fotex:inlinemath> is energy and
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mrow><mi>x</mi></mrow></msub></fotex:inlinemath> the mass of the
+incident particle, <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">-</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>γ</mi><mrow><mn>2</mn></mrow></msup></fotex:inlinemath>
+and <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mrow><mi>e</mi></mrow></msub></fotex:inlinemath> is the
+electron mass. <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">ξ</mi></fotex:inlinemath>
+comes from the Rutherford scattering crosss section and is defined as:
+ <fotex:eqnarray><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">ξ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>2</mn><mi>π</mi><msup><mi>z</mi><mrow><mn>2</mn></mrow></msup><msup><mi>e</mi><mrow><mn>4</mn></mrow></msup><msub><mi>N</mi><mrow><mi>A</mi><mi>v</mi></mrow></msub><mi>Z</mi><mi>ρ</mi><mi>δ</mi><mi>x</mi></mrow><mrow><msub><mi>m</mi><mrow><mi>e</mi></mrow></msub><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup><mi>A</mi></mrow></mfrac> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">5</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">3</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">4</mn> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>z</mi><mrow><mn>2</mn></mrow></msup></mrow><mrow><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Z</mi></mrow><mrow><mi>A</mi></mrow></mfrac><mi xmlns="http://www.w3.org/1998/Math/MathML">ρ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi><mspace width="12pt" xmlns="http://www.w3.org/1998/Math/MathML"/><mi xmlns="http://www.w3.org/1998/Math/MathML">keV </mi><mo xmlns="http://www.w3.org/1998/Math/MathML">,</mo> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/>
+</fotex:subeqn></fotex:eqnarray>
+where
+</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt"><fo:inline-included-container><fo:table id="N610"><fo:table-body><fo:table-row><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">z</mi></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>charge of the incident particle </fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mrow><mi>A</mi><mi>v</mi></mrow></msub></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>Avogadro's number </fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">Z</mi></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>atomic number of the material</fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">A</mi></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>atomic weight of the material </fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">ρ</mi></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>density </fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>thickness of the material </fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence> </fo:inline-sequence></fo:table-cell></fo:table-row></fo:table-body></fo:table></fo:inline-included-container>
+</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt"><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi></fotex:inlinemath>
+measures the contribution of the collisions with energy transfer close to
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>max</mi></msub></fotex:inlinemath>. For a given absorber,
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi></fotex:inlinemath> tends towards large
+values if <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi></fotex:inlinemath> is large
+and/or if <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">β</mi></fotex:inlinemath> is small.
+Likewise, <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi></fotex:inlinemath> tends
+towards zero if <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi></fotex:inlinemath> is
+small and/or if <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">β</mi></fotex:inlinemath>
+approaches 1.
+</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">The value of <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi></fotex:inlinemath>
+distinguishes two regimes which occur in the description of ionisation fluctuations
+:
+</fo:block><fo:list-block font-size="10pt" margin-right="10pt" space-before.optimum="10pt" space-after.optimum="10pt" margin-left="15pt"><fo:list-item><fo:list-item-label><fo:block margin-right="2.5pt" text-align="centered">•</fo:block></fo:list-item-label><fo:list-item-body><fo:block font-weight="normal">
+<fo:block font-size="10pt" text-align="justified">A
+large
+number
+of
+collisions
+involving
+the
+loss
+of
+all
+or
+most
+of
+the
+incident
+particle
+energy
+during
+the
+traversal
+of
+an
+absorber.
+</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">As
+the
+total
+energy
+transfer
+is
+composed
+of
+a
+multitude
+of
+small
+energy
+losses,
+we
+can
+apply
+the
+central
+limit
+theorem
+and
+describe
+the
+fluctuations
+by
+a
+Gaussian
+distribution.
+This
+case
+is
+applicable
+to
+non-relativistic
+particles
+and
+is
+described
+by
+the
+inequality
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">&gt;</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn></fotex:inlinemath>
+(i.e.
+when
+the
+mean
+energy
+loss
+in
+the
+absorber
+is
+greater
+than
+the
+maximum
+energy
+transfer
+in
+a
+single
+collision).
+</fo:block></fo:block></fo:list-item-body></fo:list-item><fo:list-item><fo:list-item-label><fo:block margin-right="2.5pt" text-align="centered">•</fo:block></fo:list-item-label><fo:list-item-body><fo:block font-weight="normal">
+<fo:block font-size="10pt" text-align="justified">Particles
+traversing
+thin
+counters
+and
+incident
+electrons
+under
+any
+conditions.
+</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">The
+relevant
+inequalities
+and
+distributions
+are
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">&lt;</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">&lt;</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn></fotex:inlinemath>,
+Vavilov
+distribution,
+and
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">&lt;</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn></fotex:inlinemath>,
+Landau
+distribution.</fo:block></fo:block></fo:list-item-body></fo:list-item></fo:list-block>
+<fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">An additional regime is defined by the contribution of the collisions
+with low energy transfer which can be estimated with the relation
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">ξ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mrow><mn>0</mn></mrow></msub></fotex:inlinemath>,
+where <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mrow><mn>0</mn></mrow></msub></fotex:inlinemath>
+is the mean ionisation potential of the atom. Landau theory assumes that
+the number of these collisions is high, and consequently, it has a restriction
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">ξ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mrow><mn>0</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">≫</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn></fotex:inlinemath>. In <fo:inline-sequence font-family="Computer-Modern-Typewriter">GEANT</fo:inline-sequence> (see
+URL <fo:inline-sequence font-family="Computer-Modern-Typewriter" color="green"><fo:simple-link external-destination="http://wwwinfo.cern.ch/asdoc/geant/geantall.html">http://wwwinfo.cern.ch/asdoc/geant/geantall.html</fo:simple-link></fo:inline-sequence>), the limit of Landau theory has
+been set at <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">ξ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mrow><mn>0</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">5</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn></fotex:inlinemath>.
+Below this limit special models taking into account the atomic structure of the material are
+used. This is important in thin layers and gaseous materials. Figure <fo:inline-sequence color="green"><fo:simple-link internal-destination="fg:phys332-1">1</fo:simple-link></fo:inline-sequence> shows the behaviour
+of <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">ξ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mrow><mn>0</mn></mrow></msub></fotex:inlinemath> as
+a function of the layer thickness for an electron of 100 keV and 1 GeV of kinetic
+energy in Argon, Silicon and Uranium.
+</fo:block>
+<fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt"><fo:float id="fg:phys332-1"><fo:block text-align-last="centered"><fo:display-graphic href="phys332-1"/></fo:block><fo:block text-align-last="centered">Figure 1. The variable <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">ξ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mrow><mn>0</mn></mrow></msub></fotex:inlinemath>
+can be used to measure the validity range of the Landau
+theory. It depends on the type and energy of the particle,
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">Z</mi></fotex:inlinemath>,
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">A</mi></fotex:inlinemath>
+and the ionisation potential of the material and the layer thickness. </fo:block></fo:float></fo:block>
+<fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">In the following sections, the different theories and models for the energy loss
+fluctuation are described. First, the Landau theory and its limitations are discussed,
+and then, the Vavilov and Gaussian straggling functions and the methods in the thin
+layers and gaseous materials are presented.
+</fo:block>
+
+<fo:block keep-with-next="true" id="sec:phys332-1" text-align="start" font-size="18pt" text-indent="-3em" font-weight="bold" space-after="6pt" space-before.optimum="12pt">2. Landau theory<fotex:bookmark fotex-bookmark-level="0" fotex-bookmark-label="sec:phys332-1">2. Landau theory</fotex:bookmark></fo:block>
+
+<fo:block font-size="10pt" text-align="justified">For a particle of mass <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mrow><mi>x</mi></mrow></msub></fotex:inlinemath> traversing
+a thickness of material <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi></fotex:inlinemath>,
+the Landau probability distribution may be written in terms of the universal Landau
+function <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">φ</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>λ</mi><mo>)</mo></mrow></fotex:inlinemath>
+as<fo:inline-sequence color="green"><fo:simple-link internal-destination="bib-LAND"> [1]</fo:simple-link></fo:inline-sequence>:
+ <fotex:eqnarray><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">f</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>ε</mi><mo>,</mo><mi>δ</mi><mi>x</mi><mo>)</mo></mrow> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn></mrow><mrow><mi>ξ</mi></mrow></mfrac><mi xmlns="http://www.w3.org/1998/Math/MathML">φ</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>λ</mi><mo>)</mo></mrow> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/>
+</fotex:subeqn></fotex:eqnarray>
+where
+ <fotex:eqnarray><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">φ</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>λ</mi><mo>)</mo></mrow> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mi>π</mi><mi>i</mi></mrow></mfrac><msubsup xmlns="http://www.w3.org/1998/Math/MathML"><mo>∫</mo>
+ <mrow><mi>c</mi><mo>+</mo><mi>i</mi><mi>∞</mi></mrow><mrow><mi>c</mi><mo>-</mo><mi>i</mi><mi>∞</mi></mrow></msubsup><mo xmlns="http://www.w3.org/1998/Math/MathML">exp</mo><mfenced open="(" close=")" xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>ln</mo><mi>u</mi><mo>+</mo><mi>λ</mi><mi>u</mi></mfenced><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">u</mi><mspace width="2cm" xmlns="http://www.w3.org/1998/Math/MathML"/><mi xmlns="http://www.w3.org/1998/Math/MathML">c</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">≥</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/>
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML">
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">λ</mi> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ε</mi><mo>-</mo><munderover accent="true"><mo>̄</mo><mi>ε</mi><mrow/></munderover></mrow><mrow><mi>ξ</mi></mrow></mfrac> <mo xmlns="http://www.w3.org/1998/Math/MathML">-</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">γ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">′</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">-</mo><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo xmlns="http://www.w3.org/1998/Math/MathML">-</mo><mo xmlns="http://www.w3.org/1998/Math/MathML">ln</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ξ</mi></mrow><mrow><msub><mi>E</mi><mi>max</mi></msub></mrow></mfrac> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/>
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML">
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">γ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">′</mi> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">4</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">2</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">2</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">7</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">8</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">4</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">-</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">γ</mi> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/>
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML">
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">γ</mi> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">5</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">7</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">7</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">2</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">5</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mtext xmlns="http://www.w3.org/1998/Math/MathML">(Eulers constant)</mtext> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/>
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML">
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><munderover accent="true" xmlns="http://www.w3.org/1998/Math/MathML"><mo>̄</mo><mi>ε</mi><mrow/></munderover> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mtext xmlns="http://www.w3.org/1998/Math/MathML">average energy loss</mtext> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/>
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML">
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">ε</mi> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mtext xmlns="http://www.w3.org/1998/Math/MathML">actual energy loss</mtext> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/>
+</fotex:subeqn></fotex:eqnarray>
+</fo:block>
+<fo:block keep-with-next="true" id="N1783" text-align="start" font-size="14pt" text-indent="-3em" font-weight="bold" space-after="3pt" space-before.optimum="9pt">2.1. Restrictions<fotex:bookmark fotex-bookmark-level="1" fotex-bookmark-label="N1783">2.1. Restrictions</fotex:bookmark></fo:block>
+
+<fo:block font-size="10pt" text-align="justified">The Landau formalism makes two restrictive assumptions :
+</fo:block><fo:list-block font-size="10pt" margin-right="10pt" space-before.optimum="10pt" space-after.optimum="10pt" margin-left="15pt"><fo:list-item><fo:list-item-label><fo:block margin-right="2.5pt" text-align="centered">•</fo:block></fo:list-item-label><fo:list-item-body><fo:block font-weight="normal">
+<fo:block font-size="10pt" text-align="justified">The
+typical
+energy
+loss
+is
+small
+compared
+to
+the
+maximum
+energy
+loss
+in
+a
+single
+collision.
+This
+restriction
+is
+removed
+in
+the
+Vavilov
+theory
+(see
+section
+<fo:inline-sequence color="green"><fo:simple-link internal-destination="vavref">3 (Vavilov theory)</fo:simple-link></fo:inline-sequence>).
+</fo:block></fo:block></fo:list-item-body></fo:list-item><fo:list-item><fo:list-item-label><fo:block margin-right="2.5pt" text-align="centered">•</fo:block></fo:list-item-label><fo:list-item-body><fo:block font-weight="normal">
+<fo:block font-size="10pt" text-align="justified">The
+typical
+energy
+loss
+in
+the
+absorber
+should
+be
+large
+compared
+to
+the
+binding
+energy
+of
+the
+most
+tightly
+bound
+electron.
+For
+gaseous
+detectors,
+typical
+energy
+losses
+are
+a
+few
+keV
+which
+is
+comparable
+to
+the
+binding
+energies
+of
+the
+inner
+electrons.
+In
+such
+cases
+a
+more
+sophisticated
+approach
+which
+accounts
+for
+atomic
+energy
+levels<fo:inline-sequence color="green"><fo:simple-link internal-destination="bib-TALM"> [4]</fo:simple-link></fo:inline-sequence>
+is
+necessary
+to
+accurately
+simulate
+data
+distributions.
+In
+<fo:inline-sequence font-family="Computer-Modern-Typewriter">GEANT</fo:inline-sequence>,
+a
+parameterised
+model
+by
+L.
+Urbán
+is
+used
+(see
+section
+<fo:inline-sequence color="green"><fo:simple-link internal-destination="urban">5 (Urbán model)</fo:simple-link></fo:inline-sequence>).</fo:block></fo:block></fo:list-item-body></fo:list-item></fo:list-block>
+<fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">In addition, the average value of the Landau distribution is infinite.
+Summing the Landau fluctuation obtained to the average energy from the
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi></fotex:inlinemath>
+tables, we obtain a value which is larger than the one coming from the table. The
+probability to sample a large value is small, so it takes a large number of steps
+(extractions) for the average fluctuation to be significantly larger than zero. This
+introduces a dependence of the energy loss on the step size which can affect
+calculations.
+</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">A solution to this has been to introduce a limit on the value of the
+variable sampled by the Landau distribution in order to keep the average
+fluctuation to 0. The value obtained from the <fo:inline-sequence font-family="Computer-Modern-Typewriter">GLANDO</fo:inline-sequence> routine is:
+<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML">
+ <mi>δ</mi><mi>d</mi><mi>E</mi><mo>/</mo><mi>d</mi><mi>x</mi><mo>=</mo><mi>ε</mi><mo>-</mo><munderover accent="true"><mo>̄</mo><mi>ε</mi><mrow/></munderover><mo>=</mo><mi>ξ</mi><mrow><mo>(</mo><mi>λ</mi><mo>-</mo><mi>γ</mi><mi>′</mi><mo>+</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo>+</mo><mo>ln</mo> <mfrac><mrow><mi>ξ</mi></mrow><mrow><msub><mi>E</mi><mi>max</mi></msub></mrow></mfrac> <mo>)</mo></mrow>
+</mrow></fotex:displaymath>
+In order for this to have average 0, we must impose that:
+<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML">
+ <munderover accent="true"><mo>̄</mo><mi>λ</mi><mrow/></munderover><mo>=</mo><mo>-</mo><mi>γ</mi><mi>′</mi><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo>-</mo><mo>ln</mo> <mfrac><mrow><mi>ξ</mi></mrow><mrow><msub><mi>E</mi><mi>max</mi></msub></mrow></mfrac>
+</mrow></fotex:displaymath>
+</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">This is realised introducing a <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mrow><mtext>max</mtext></mrow></msub><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><munderover accent="true"><mo>̄</mo><mi>λ</mi><mrow/></munderover><mo>)</mo></mrow></fotex:inlinemath>
+such that if only values of <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">λ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">≤</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mrow><mtext>max</mtext></mrow></msub></fotex:inlinemath>
+are accepted, the average value of the distribution is
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><munderover accent="true" xmlns="http://www.w3.org/1998/Math/MathML"><mo>̄</mo><mi>λ</mi><mrow/></munderover></fotex:inlinemath>.
+</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">A parametric fit to the universal Landau distribution has been performed, with following result:
+<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML">
+ <msub><mi>λ</mi><mrow><mtext>max</mtext></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>6</mn><mn>0</mn><mn>7</mn><mn>1</mn><mn>5</mn><mo>+</mo><mn>1</mn><mo>.</mo><mn>1</mn><mn>9</mn><mn>3</mn><mn>4</mn><munderover accent="true"><mo>̄</mo><mi>λ</mi><mrow/></munderover><mo>+</mo><mrow><mo>(</mo><mn>0</mn><mo>.</mo><mn>6</mn><mn>7</mn><mn>7</mn><mn>9</mn><mn>4</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn><mn>5</mn><mn>2</mn><mn>3</mn><mn>8</mn><mn>2</mn><munderover accent="true"><mi>λ</mi><mrow/><mo>̄</mo></munderover><mo>)</mo></mrow><mo>exp</mo><mrow><mo>(</mo><mn>0</mn><mo>.</mo><mn>9</mn><mn>4</mn><mn>7</mn><mn>5</mn><mn>3</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>7</mn><mn>4</mn><mn>4</mn><mn>4</mn><mn>2</mn><munderover accent="true"><mi>λ</mi><mrow/><mo>̄</mo></munderover><mo>)</mo></mrow>
+</mrow></fotex:displaymath> only values
+smaller than <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mrow><mtext>max</mtext></mrow></msub></fotex:inlinemath>
+are accepted, otherwise the distribution is resampled.
+</fo:block>
+
+
+<fo:block keep-with-next="true" id="vavref" text-align="start" font-size="18pt" text-indent="-3em" font-weight="bold" space-after="6pt" space-before.optimum="12pt">3. Vavilov theory<fotex:bookmark fotex-bookmark-level="0" fotex-bookmark-label="vavref">3. Vavilov theory</fotex:bookmark></fo:block>
+
+<fo:block font-size="10pt" text-align="justified">Vavilov<fo:inline-sequence color="green"><fo:simple-link internal-destination="bib-VAVI"> [5]</fo:simple-link></fo:inline-sequence> derived a more accurate straggling distribution by introducing the kinematic
+limit on the maximum transferable energy in a single collision, rather than using
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>max</mi></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">∞</mi></fotex:inlinemath>. Now
+we can write<fo:inline-sequence color="green"><fo:simple-link internal-destination="bib-SCH1"> [2]</fo:simple-link></fo:inline-sequence>:
+ <fotex:eqnarray><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">f</mi> <mfenced open="(" close=")" xmlns="http://www.w3.org/1998/Math/MathML"><mi>ε</mi><mo>,</mo><mi>δ</mi><mi>s</mi></mfenced> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn></mrow><mrow><mi>ξ</mi></mrow></mfrac><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>φ</mi><mrow><mi>v</mi></mrow></msub> <mfenced open="(" close=")" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>λ</mi><mrow><mi>v</mi></mrow></msub><mo>,</mo><mi>κ</mi><mo>,</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup></mfenced> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/>
+</fotex:subeqn></fotex:eqnarray>
+where
+ <fotex:eqnarray><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>φ</mi><mrow><mi>v</mi></mrow></msub> <mfenced open="(" close=")" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>λ</mi><mrow><mi>v</mi></mrow></msub><mo>,</mo><mi>κ</mi><mo>,</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup></mfenced> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mi>π</mi><mi>i</mi></mrow></mfrac><msubsup xmlns="http://www.w3.org/1998/Math/MathML"><mo>∫</mo>
+ <mrow><mi>c</mi><mo>+</mo><mi>i</mi><mi>∞</mi></mrow><mrow><mi>c</mi><mo>-</mo><mi>i</mi><mi>∞</mi></mrow></msubsup><mi xmlns="http://www.w3.org/1998/Math/MathML">φ</mi><mfenced open="(" close=")" xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></mfenced><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mrow><mi>λ</mi><mi>s</mi></mrow></msup><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">s</mi><mspace width="2cm" xmlns="http://www.w3.org/1998/Math/MathML"/><mi xmlns="http://www.w3.org/1998/Math/MathML">c</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">≥</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/>
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML">
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">φ</mi><mfenced open="(" close=")" xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></mfenced> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mo xmlns="http://www.w3.org/1998/Math/MathML">exp</mo><mfenced open="[" close="]" xmlns="http://www.w3.org/1998/Math/MathML"><mi>κ</mi><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mi>γ</mi><mo>)</mo></mrow></mfenced><mo xmlns="http://www.w3.org/1998/Math/MathML">exp</mo><mfenced open="[" close="]" xmlns="http://www.w3.org/1998/Math/MathML"><mi>ψ</mi> <mfenced open="(" close=")"><mi>s</mi></mfenced></mfenced><mo xmlns="http://www.w3.org/1998/Math/MathML">,</mo> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/>
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML">
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">ψ</mi> <mfenced open="(" close=")" xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></mfenced> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mi xmlns="http://www.w3.org/1998/Math/MathML">s</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">ln</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">+</mo><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>s</mi><mo>+</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mi>κ</mi><mo>)</mo></mrow><mfenced open="[" close="]" xmlns="http://www.w3.org/1998/Math/MathML"><mo>ln</mo><mrow><mo>(</mo><mi>s</mi><mo>/</mo><mi>κ</mi><mo>)</mo></mrow><mo>+</mo><msub><mi>E</mi><mrow>
+<mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>s</mi><mo>/</mo><mi>κ</mi><mo>)</mo></mrow></mfenced><mo xmlns="http://www.w3.org/1998/Math/MathML">-</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mrow><mo>-</mo><mi>s</mi><mo>/</mo><mi>κ</mi></mrow></msup><mo xmlns="http://www.w3.org/1998/Math/MathML">,</mo> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/>
+</fotex:subeqn></fotex:eqnarray>
+and
+ <fotex:eqnarray><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>1</mn></mrow></msub><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>z</mi><mo>)</mo></mrow> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msubsup xmlns="http://www.w3.org/1998/Math/MathML"> <mo>∫</mo>
+ <mrow><mi>∞</mi></mrow><mrow><mi>z</mi></mrow></msubsup><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mrow><mo>-</mo><mi>t</mi></mrow></msup><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">t</mi><mspace width="1cm" xmlns="http://www.w3.org/1998/Math/MathML"/><mtext xmlns="http://www.w3.org/1998/Math/MathML">(the exponential integral)</mtext> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/>
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML">
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mrow><mi>v</mi></mrow></msub> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi><mfenced open="[" close="]" xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>ε</mi><mo>-</mo><munderover accent="true"><mo>̄</mo><mi>ε</mi><mrow/></munderover></mrow><mrow><mi>ξ</mi></mrow></mfrac> <mo>-</mo><mi>γ</mi><mi>′</mi><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup></mfenced> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/>
+</fotex:subeqn></fotex:eqnarray>
+</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">The Vavilov parameters are simply related to the Landau parameter by
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mrow><mi>L</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mrow><mi>v</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">-</mo><mo xmlns="http://www.w3.org/1998/Math/MathML">ln</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi></fotex:inlinemath>. It can be shown that
+as <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">→</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn></fotex:inlinemath>, the distribution of
+the variable <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mrow><mi>L</mi></mrow></msub></fotex:inlinemath> approaches
+that of Landau. For <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">≤</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">.</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn></fotex:inlinemath>
+the two distributions are already practically identical. Contrary to what many textbooks
+report, the Vavilov distribution <fo:inline-sequence font-style="italic">does not</fo:inline-sequence> approximate the Landau distribution for small
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi></fotex:inlinemath>, but rather the
+distribution of <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mrow><mi>L</mi></mrow></msub></fotex:inlinemath>
+defined above tends to the distribution of the true
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">λ</mi></fotex:inlinemath> from
+the Landau density function. Thus the routine <fo:inline-sequence font-family="Computer-Modern-Typewriter">GVAVIV</fo:inline-sequence> samples the variable
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mrow><mi>L</mi></mrow></msub></fotex:inlinemath> rather
+than <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi><mrow><mi>v</mi></mrow></msub></fotex:inlinemath>.
+For <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">≥</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn></fotex:inlinemath>
+the Vavilov distribution tends to a Gaussian distribution (see next section).
+</fo:block>
+
+<fo:block keep-with-next="true" id="N3325" text-align="start" font-size="18pt" text-indent="-3em" font-weight="bold" space-after="6pt" space-before.optimum="12pt">4. Gaussian Theory<fotex:bookmark fotex-bookmark-level="0" fotex-bookmark-label="N3325">4. Gaussian Theory</fotex:bookmark></fo:block>
+
+<fo:block font-size="10pt" text-align="justified">Various conflicting forms have been proposed for Gaussian straggling functions, but most
+of these appear to have little theoretical or experimental basis. However, it has been shown<fo:inline-sequence color="green"><fo:simple-link internal-destination="bib-SELT"> [3]</fo:simple-link></fo:inline-sequence>
+that for <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">κ</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">≥</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn></fotex:inlinemath>
+the Vavilov distribution can be replaced by a Gaussian of the form:
+ <fotex:eqnarray><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">f</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>ε</mi><mo>,</mo><mi>δ</mi><mi>s</mi><mo>)</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">≈</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn></mrow><mrow><mi>ξ</mi><msqrt><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mrow><mi>κ</mi></mrow></mfrac> <mfenced open="(" close=")"><mn>1</mn><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><mn>2</mn></mfenced></msqrt></mrow></mfrac><mo xmlns="http://www.w3.org/1998/Math/MathML">exp</mo><mfenced open="[" close="]" xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mrow><mo>(</mo><mi>ε</mi><mo>-</mo><munderover accent="true"><mo>̄</mo><mi>ε</mi><mrow/></munderover><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn></mrow></mfrac> <mfrac><mrow><mi>κ</mi></mrow><mrow><msup><mi>ξ</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mn>1</mn><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><mn>2</mn><mo>)</mo></mrow></mrow></mfrac></mfenced> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/>
+</fotex:subeqn></fotex:eqnarray>
+thus implying
+ <fotex:eqnarray><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">mean</mi> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <munderover accent="true" xmlns="http://www.w3.org/1998/Math/MathML"><mo>̄</mo><mi>ε</mi><mrow/></munderover> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/>
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML">
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mrow><mn>2</mn></mrow></msup> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>ξ</mi><mrow><mn>2</mn></mrow></msup></mrow><mrow><mi>κ</mi></mrow></mfrac> <mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>1</mn><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><mn>2</mn><mo>)</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">ξ</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mi>
+max</mi></mrow></msub><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>1</mn><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><mn>2</mn><mo>)</mo></mrow> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/>
+</fotex:subeqn></fotex:eqnarray>
+</fo:block>
+
+<fo:block keep-with-next="true" id="urban" text-align="start" font-size="18pt" text-indent="-3em" font-weight="bold" space-after="6pt" space-before.optimum="12pt">5. Urbán model<fotex:bookmark fotex-bookmark-level="0" fotex-bookmark-label="urban">5. Urbán model</fotex:bookmark></fo:block>
+
+<fo:block font-size="10pt" text-align="justified">The method for computing restricted energy losses with
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">δ</mi></fotex:inlinemath>-ray
+production above given threshold energy in <fo:inline-sequence font-family="Computer-Modern-Typewriter">GEANT</fo:inline-sequence> is a Monte Carlo method that
+can be used for thin layers. It is fast and it can be used for any thickness of a
+medium. Approaching the limit of the validity of Landau's theory, the loss
+distribution approaches smoothly the Landau form as shown in Figure <fo:inline-sequence color="green"><fo:simple-link internal-destination="fg:phys332-2">2</fo:simple-link></fo:inline-sequence>.
+</fo:block>
+<fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt"><fo:float id="fg:phys332-2"><fo:block text-align-last="centered"><fo:display-graphic href="phys332-2"/></fo:block><fo:block text-align-last="centered">Figure 2. Energy loss distribution for a 3 GeV electron in Argon as given by
+standard GEANT. The width of the layers is given in centimeters.</fo:block></fo:float></fo:block>
+<fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">It is assumed that the atoms have only two energy levels with binding energy
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>1</mn></mrow></msub></fotex:inlinemath> and
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>2</mn></mrow></msub></fotex:inlinemath>.
+The particle--atom interaction will then be an excitation with energy loss
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>1</mn></mrow></msub></fotex:inlinemath> or
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>2</mn></mrow></msub></fotex:inlinemath>, or
+an ionisation with an energy loss distributed according to a function
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">g</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">∼</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>2</mn></mrow></msup></fotex:inlinemath>:
+<fotex:equation xmlns:m="http://www.w3.org/1998/Math/MathML">
+ <mi xmlns="http://www.w3.org/1998/Math/MathML">g</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mo>(</mo><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi><mo>)</mo></mrow><mi>I</mi></mrow><mrow><msub><mi>E</mi><mi>max</mi></msub></mrow></mfrac>
+<mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn></mrow><mrow><msup><mi>E</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac>
+</fotex:equation></fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">The
+macroscopic cross-section for excitations (<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">i</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mo xmlns="http://www.w3.org/1998/Math/MathML">,</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">2</mn></fotex:inlinemath>)
+is <fotex:equation id="eq:sigex" xmlns:m="http://www.w3.org/1998/Math/MathML">
+ <msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>Σ</mi><mrow><mi>i</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">C</mi> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>f</mi><mrow><mi>i</mi></mrow></msub></mrow><mrow><msub><mi>E</mi><mrow><mi>i</mi></mrow></msub></mrow></mfrac> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>ln</mo><mrow><mo>(</mo><mn>2</mn><mi>m</mi><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><msup><mi>γ</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><msub><mi>E</mi><mrow><mi>i</mi></mrow></msub><mo>)</mo></mrow><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup></mrow><mrow><mo>ln</mo><mrow><mo>(</mo><mn>2</mn><mi>m</mi><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup><msup><mi>γ</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><mi>I</mi><mo>)</mo></mrow><mo>-</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac> <mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>1</mn><mo>-</mo><mi>r</mi><mo>)</mo></mrow> </fotex:equation>and
+the macroscopic cross-section for ionisation is
+<fotex:equation id="eq:sigion" xmlns:m="http://www.w3.org/1998/Math/MathML">
+ <msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>Σ</mi><mrow><mn>3</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">C</mi> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>E</mi><mi>max</mi></msub></mrow><mrow><mi>I</mi><mrow><mo>(</mo><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi><mo>)</mo></mrow><mo>ln</mo><mrow><mo>(</mo><mfrac><mrow><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi></mrow><mrow><mi>I</mi></mrow></mfrac> <mo>)</mo></mrow></mrow></mfrac><mi xmlns="http://www.w3.org/1998/Math/MathML">r</mi> </fotex:equation>
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>max</mi></msub></fotex:inlinemath>
+is the <fo:inline-sequence font-family="Computer-Modern-Typewriter">GEANT</fo:inline-sequence> cut for <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">δ</mi></fotex:inlinemath>-production,
+or the maximum energy transfer minus mean ionisation energy, if it is smaller than
+this cut-off value. The following notation is used:
+</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt"><fo:inline-included-container><fo:table id="N4332"><fo:table-body><fo:table-row><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">r</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">,</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">C</mi></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>parameters of the model</fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mi>i</mi></mrow></msub></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>atomic energy levels </fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">I</mi></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>mean ionisation energy </fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mrow><mi>i</mi></mrow></msub></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>oscillator strengths </fo:inline-sequence></fo:table-cell></fo:table-row></fo:table-body></fo:table></fo:inline-included-container>
+</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">The model has the parameters <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mrow><mi>i</mi></mrow></msub></fotex:inlinemath>,
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mi>i</mi></mrow></msub></fotex:inlinemath>,
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">C</mi></fotex:inlinemath> and
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">r</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>0</mn><mo>≤</mo><mi>r</mi><mo>≤</mo><mn>1</mn><mo>)</mo></mrow></fotex:inlinemath>. The oscillator
+strengths <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mrow><mi>i</mi></mrow></msub></fotex:inlinemath> and the
+atomic level energies <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mi>i</mi></mrow></msub></fotex:inlinemath>
+should satisfy the constraints
+ <fotex:eqnarray><fotex:subeqn id="eq:fisum" xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mrow><mn>1</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">+</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mrow><mn>2</mn></mrow></msub> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn>
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML">
+ </fotex:subeqn><fotex:subeqn id="eq:flnsum" xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mrow><mn>1</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">ln</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>1</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">+</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mrow><mn>2</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">ln</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>2</mn></mrow></msub> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mo xmlns="http://www.w3.org/1998/Math/MathML">ln</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">I</mi>
+</fotex:subeqn></fotex:eqnarray>
+The parameter <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">C</mi></fotex:inlinemath>
+can be defined with the help of the mean energy loss
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi></fotex:inlinemath> in the following way: The
+numbers of collisions (<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mi>i</mi></mrow></msub></fotex:inlinemath>,
+i = 1,2 for the excitation and 3 for the ionisation) follow the Poisson distribution with a mean
+number <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>&lt;</mo><msub><mi>n</mi><mrow><mi>i</mi></mrow></msub><mo>&gt;;</mo></mrow></fotex:inlinemath>. In a step
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi></fotex:inlinemath> the mean number
+of collisions is <fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML">
+ <mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>&lt;</mo><msub><mi>n</mi><mrow><mi>i</mi></mrow></msub><mo>&gt;;</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>Σ</mi><mrow><mi>i</mi></mrow></msub><mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi>
+</fotex:displaymath>The
+mean energy loss <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi></fotex:inlinemath>
+in a step is the sum of the excitation and ionisation contributions
+<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML">
+ <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>d</mi><mi>E</mi></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac> <mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mfenced open="[" close="]" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>Σ</mi><mrow><mn>1</mn></mrow></msub><msub><mi>E</mi><mrow><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>Σ</mi><mrow><mn>2</mn></mrow></msub><msub><mi>E</mi><mrow><mn>2</mn></mrow></msub><mo>+</mo><msub><mi>Σ</mi><mrow><mn>3</mn></mrow></msub><msubsup><mo>∫</mo>
+ <mrow><mi>I</mi></mrow><mrow><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi></mrow></msubsup><mi>E</mi><mi>g</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mi>d</mi><mi>E</mi></mfenced><mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi>
+</fotex:displaymath>From
+this, using the equations (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:sigex">2</fo:simple-link></fo:inline-sequence>), (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:sigion">3</fo:simple-link></fo:inline-sequence>), (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:fisum">1</fo:simple-link></fo:inline-sequence>) and (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:flnsum">1</fo:simple-link></fo:inline-sequence>), one can define the parameter
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">C</mi></fotex:inlinemath>
+<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML">
+ <mi xmlns="http://www.w3.org/1998/Math/MathML">C</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>d</mi><mi>E</mi></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac>
+</fotex:displaymath>
+</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">The following values have been chosen in <fo:inline-sequence font-family="Computer-Modern-Typewriter">GEANT</fo:inline-sequence> for the other parameters:
+<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML">
+ <mtable equalrows="false" equalcolumns="false"><mtr><mtd><msub><mi>f</mi><mrow><mn>2</mn></mrow></msub><mo>=</mo><mfenced open="{"><mtable equalrows="false" equalcolumns="false"><mtr><mtd><mn>0</mn> </mtd><mtd><mi>if</mi><mi>Z</mi><mo>≤</mo><mn>2</mn></mtd>
+</mtr><mtr><mtd><mn>2</mn><mo>/</mo><mi>Z</mi></mtd><mtd><mi>if</mi><mi>Z</mi><mo>&gt;</mo><mn>2</mn></mtd>
+</mtr><mtr><mtd> </mtd></mtr></mtable> </mfenced></mtd><mtd><mo>⇒</mo></mtd><mtd><msub><mi>f</mi><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>1</mn><mo>-</mo><msub><mi>f</mi><mrow><mn>2</mn></mrow></msub> </mtd>
+ </mtr><mtr><mtd><msub><mi>E</mi><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>1</mn><mn>0</mn><msup><mi>Z</mi><mrow><mn>2</mn></mrow></msup><mi>eV </mi> </mtd><mtd><mo>⇒</mo></mtd><mtd><msub><mi>E</mi><mrow><mn>1</mn></mrow></msub><mo>=</mo><msup><mfenced open="(" close=")"> <mfrac><mrow><mi>I</mi></mrow><mrow><msubsup><mi>E</mi><mrow><mn>2</mn></mrow><mrow><msub><mi>f</mi><mrow><mn>2</mn></mrow></msub></mrow></msubsup></mrow></mfrac> </mfenced><mrow> <mfrac><mrow><mn>1</mn></mrow><mrow><msub><mi>f</mi><mrow><mn>1</mn></mrow></msub></mrow></mfrac> </mrow></msup></mtd>
+ </mtr><mtr><mtd><mi>r</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>4</mn> </mtd><mtd> </mtd><mtd> </mtd>
+ </mtr><mtr><mtd> </mtd></mtr></mtable>
+</mrow></fotex:displaymath> With these values
+the atomic level <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>2</mn></mrow></msub></fotex:inlinemath>
+corresponds approximately the K-shell energy of the atoms and
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">Z</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mrow><mn>2</mn></mrow></msub></fotex:inlinemath> the number of
+K-shell electrons. <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">r</mi></fotex:inlinemath>
+is the only variable which can be tuned freely. It determines the relative contribution
+of ionisation and excitation to the energy loss.
+</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">The energy loss is computed with the assumption that the step length (or the relative
+energy loss) is small, and---in consequence---the cross-section can be considered
+constant along the path length. The energy loss due to the excitation is
+<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML">
+ <mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mi>e</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>1</mn></mrow></msub><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>1</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">+</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>2</mn></mrow></msub><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>2</mn></mrow></msub>
+</fotex:displaymath>where
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>1</mn></mrow></msub></fotex:inlinemath> and
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>2</mn></mrow></msub></fotex:inlinemath>
+are sampled from Poisson distribution as discussed above. The
+loss due to the ionisation can be generated from the distribution
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">g</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>E</mi><mo>)</mo></mrow></fotex:inlinemath> by
+the inverse transformation method:
+ <fotex:eqnarray><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">u</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">F</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>E</mi><mo>)</mo></mrow> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msubsup xmlns="http://www.w3.org/1998/Math/MathML"> <mo>∫</mo>
+ <mrow><mi>I</mi></mrow><mrow><mi>E</mi></mrow></msubsup><mi xmlns="http://www.w3.org/1998/Math/MathML">g</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">x</mi> <mtext xmlns="http://www.w3.org/1998/Math/MathML"/>
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML">
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>u</mi><mo>)</mo></mrow> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>I</mi></mrow><mrow><mn>1</mn><mo>-</mo><mi>u</mi> <mfrac><mrow><msub><mi>E</mi><mi>max</mi></msub></mrow><mrow><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi></mrow></mfrac> </mrow></mfrac>
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML">
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML">
+</fotex:subeqn></fotex:eqnarray>
+where <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">u</mi></fotex:inlinemath> is a uniform random
+number between <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">F</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>I</mi><mo>)</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn></fotex:inlinemath> and
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">F</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi><mo>)</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn></fotex:inlinemath>. The contribution from the
+ionisations will be <fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML">
+ <mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mi>i</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msubsup xmlns="http://www.w3.org/1998/Math/MathML"><mo>∑</mo>
+ <mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub></mrow></msubsup> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>I</mi></mrow><mrow><mn>1</mn><mo>-</mo><msub><mi>u</mi><mrow><mi>j</mi></mrow></msub> <mfrac><mrow><msub><mi>E</mi><mi>max</mi></msub></mrow><mrow><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi></mrow></mfrac> </mrow></mfrac>
+</fotex:displaymath>where
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub></fotex:inlinemath> is the
+number of ionisation (sampled from Poisson distribution). The energy loss in a step will
+then be <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mi>e</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">+</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mi>i</mi></mrow></msub></fotex:inlinemath>.
+</fo:block>
+<fo:block keep-with-next="true" id="N5956" text-align="start" font-size="14pt" text-indent="-3em" font-weight="bold" space-after="3pt" space-before.optimum="9pt">5.1. Fast simulation for <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">≥</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">6</mn></fotex:inlinemath><fotex:bookmark fotex-bookmark-level="1" fotex-bookmark-label="N5956">5.1. Fast simulation for n3≥16</fotex:bookmark></fo:block>
+
+<fo:block font-size="10pt" text-align="justified">If the number of ionisation <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub></fotex:inlinemath>
+is bigger than 16, a faster sampling method can be used. The possible energy loss
+interval is divided in two parts: one in which the number of collisions is large and the
+sampling can be done from a Gaussian distribution and the other in which
+the energy loss is sampled for each collision. Let us call the former interval
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>[</mo><mi>I</mi><mo>,</mo><mi>α</mi><mi>I</mi><mo>]</mo></mrow></fotex:inlinemath> the interval A,
+and the latter <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>[</mo><mi>α</mi><mi>I</mi><mo>,</mo><msub><mi>E</mi><mi>max</mi></msub><mo>]</mo></mrow></fotex:inlinemath> the
+interval B. <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">α</mi></fotex:inlinemath> lies
+between 1 and <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>max</mi></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">/</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">I</mi></fotex:inlinemath>.
+A collision with a loss in the interval A happens with the probability
+<fotex:displaymath id="eq:phys332-5" xmlns:m="http://www.w3.org/1998/Math/MathML">
+ <mi xmlns="http://www.w3.org/1998/Math/MathML">P</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>α</mi><mo>)</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msubsup xmlns="http://www.w3.org/1998/Math/MathML"><mo>∫</mo>
+ <mrow><mi>I</mi></mrow><mrow><mi>α</mi><mi>I</mi></mrow></msubsup><mi xmlns="http://www.w3.org/1998/Math/MathML">g</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mo>(</mo><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>α</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><msub><mi>E</mi><mi>max</mi></msub><mi>α</mi></mrow></mfrac>
+</fotex:displaymath>The
+mean energy loss and the standard deviation for this type of collision are
+<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML">
+ <mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>&lt;</mo><mi>Δ</mi><mi>E</mi><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow><mo>&gt;;</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn></mrow><mrow><mi>P</mi><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow></mrow></mfrac><msubsup xmlns="http://www.w3.org/1998/Math/MathML"><mo>∫</mo>
+ <mrow><mi>I</mi></mrow><mrow><mi>α</mi><mi>I</mi></mrow></msubsup><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">g</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>I</mi><mi>α</mi><mo>ln</mo><mi>α</mi></mrow><mrow><mi>α</mi><mo>-</mo><mn>1</mn></mrow></mfrac>
+</fotex:displaymath>and <fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mrow><mn>2</mn></mrow></msup><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>α</mi><mo>)</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn></mrow><mrow><mi>P</mi><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow></mrow></mfrac><msubsup xmlns="http://www.w3.org/1998/Math/MathML"><mo>∫</mo>
+ <mrow><mi>I</mi></mrow><mrow><mi>α</mi><mi>I</mi></mrow></msubsup><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>2</mn></mrow></msup><mi xmlns="http://www.w3.org/1998/Math/MathML">g</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mi xmlns="http://www.w3.org/1998/Math/MathML">d</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mrow><mn>2</mn></mrow></msup><mi xmlns="http://www.w3.org/1998/Math/MathML">α</mi><mfenced open="(" close=")" xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>-</mo> <mfrac><mrow><mi>α</mi><msup><mo>ln</mo><mrow><mn>2</mn></mrow></msup><mi>α</mi></mrow><mrow><msup><mrow><mo>(</mo><mi>α</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mfenced>
+</fotex:displaymath>If the
+collision number is high, we assume that the number of the type A collisions can be
+calculated from a Gaussian distribution with the following mean value and standard
+deviation:
+ <fotex:eqnarray><fotex:subeqn id="eq:phys332-1" xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>&lt;</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><mo>&gt;;</mo></mrow> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub><mi xmlns="http://www.w3.org/1998/Math/MathML">P</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>α</mi><mo>)</mo></mrow>
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML">
+ </fotex:subeqn><fotex:subeqn id="eq:phys332-2" xmlns:m="http://www.w3.org/1998/Math/MathML"><msubsup xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msubsup> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub><mi xmlns="http://www.w3.org/1998/Math/MathML">P</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>α</mi><mo>)</mo></mrow><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>1</mn><mo>-</mo><mi>P</mi><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow><mo>)</mo></mrow>
+</fotex:subeqn></fotex:eqnarray>
+It is further assumed that the energy loss in these collisions has a Gaussian
+distribution with
+ <fotex:eqnarray><fotex:subeqn id="eq:phys332-3" xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>&lt;</mo><mi>Δ</mi><msub><mi>E</mi><mrow><mi>A</mi></mrow></msub><mo>&gt;;</mo></mrow> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mi>A</mi></mrow></msub><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>&lt;</mo><mi>Δ</mi><mi>E</mi><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow><mo>&gt;;</mo></mrow>
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML">
+ </fotex:subeqn><fotex:subeqn id="eq:phys332-4" xmlns:m="http://www.w3.org/1998/Math/MathML"><msubsup xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mrow><mi>E</mi><mo>,</mo><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msubsup> <mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mi>A</mi></mrow></msub><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mrow><mn>2</mn></mrow></msup><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>α</mi><mo>)</mo></mrow>
+</fotex:subeqn></fotex:eqnarray>
+The energy loss of these collision can then be sampled from the Gaussian
+distribution.
+</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">The collisions where the energy loss is in the interval B are sampled directly from
+<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML">
+ <mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mi>B</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msubsup xmlns="http://www.w3.org/1998/Math/MathML"><mo>∑</mo>
+ <mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>-</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub></mrow></msubsup> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>α</mi><mi>I</mi></mrow><mrow><mn>1</mn><mo>-</mo><msub><mi>u</mi><mrow><mi>i</mi></mrow></msub> <mfrac><mrow><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi><mo>-</mo><mi>α</mi><mi>I</mi></mrow><mrow><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi></mrow></mfrac> </mrow></mfrac>
+</fotex:displaymath>The
+total energy loss is the sum of these two types of collisions:
+<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML">
+ <mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mi>A</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">+</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mi>B</mi></mrow></msub>
+</fotex:displaymath></fo:block>
+<fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">The approximation of equations (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-1">1</fo:simple-link></fo:inline-sequence>), (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-2">1</fo:simple-link></fo:inline-sequence>), (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-3">1</fo:simple-link></fo:inline-sequence>) and (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-4">1</fo:simple-link></fo:inline-sequence>) can be used under the following
+conditions:
+ <fotex:eqnarray><fotex:subeqn id="eq:phys332-6" xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>&lt;</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><mo>&gt;;</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">-</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">c</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mrow><mi>A</mi></mrow></msub> <mo xmlns="http://www.w3.org/1998/Math/MathML">≥</mo> <mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn>
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML">
+ </fotex:subeqn><fotex:subeqn id="eq:phys332-7" xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>&lt;</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><mo>&gt;;</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">+</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">c</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mrow><mi>A</mi></mrow></msub> <mo xmlns="http://www.w3.org/1998/Math/MathML">≤</mo> <msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub>
+ </fotex:subeqn><fotex:subeqn xmlns:m="http://www.w3.org/1998/Math/MathML">
+ </fotex:subeqn><fotex:subeqn id="eq:phys332-8" xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>&lt;</mo><mi>Δ</mi><msub><mi>E</mi><mrow><mi>A</mi></mrow></msub><mo>&gt;;</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">-</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">c</mi><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mrow><mi>E</mi><mo>,</mo><mi>A</mi></mrow></msub> <mo xmlns="http://www.w3.org/1998/Math/MathML">≥</mo> <mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn>
+</fotex:subeqn></fotex:eqnarray>
+where <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">c</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">≥</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">4</mn></fotex:inlinemath>. From
+the equations (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-5">6</fo:simple-link></fo:inline-sequence>), (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-1">1</fo:simple-link></fo:inline-sequence>) and (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-3">1</fo:simple-link></fo:inline-sequence>) and from the conditions (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-6">1</fo:simple-link></fo:inline-sequence>) and (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-7">1</fo:simple-link></fo:inline-sequence>) the following limits can be
+<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi><mrow><mi>min</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mo>(</mo><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>+</mo><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mo>(</mo><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi><mo>)</mo></mrow></mrow><mrow><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mrow><mo>(</mo><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi><mo>)</mo></mrow><mo>+</mo><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup><mi>I</mi></mrow></mfrac> <mo xmlns="http://www.w3.org/1998/Math/MathML">≤</mo><mi xmlns="http://www.w3.org/1998/Math/MathML">α</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">≤</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi><mrow><mtext>max</mtext></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mo>(</mo><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>+</mo><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mo>(</mo><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi><mo>)</mo></mrow></mrow><mrow><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><mi>I</mi><mo>)</mo></mrow><mo>+</mo><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mi>I</mi></mrow></mfrac>
+</fotex:displaymath>This
+conditions gives a lower limit to number of the ionisations
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub></fotex:inlinemath> for which the fast
+<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">≥</mo><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mrow><mn>2</mn></mrow></msup> </fotex:displaymath>As
+in the conditions (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-6">1</fo:simple-link></fo:inline-sequence>), (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-7">1</fo:simple-link></fo:inline-sequence>) and (<fo:inline-sequence color="green"><fo:simple-link internal-destination="eq:phys332-8">1</fo:simple-link></fo:inline-sequence>) the value of
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">c</mi></fotex:inlinemath> is as minimum
+4, one gets <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">≥</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">6</mn></fotex:inlinemath>.
+In order to speed the simulation, the maximum value is used for
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">α</mi></fotex:inlinemath>.
+</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt">The number of collisions with energy loss in the interval B (the number of interactions
+which has to be simulated directly) increases slowly with the total number of collisions
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub></fotex:inlinemath>.
+The maximum number of these collisions can be estimated as
+<fotex:equation xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mi>B</mi><mo>,</mo><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">-</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mi>A</mi><mo>,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">≈</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mrow><mo>&lt;</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><mo>&gt;;</mo></mrow><mo>-</mo><msub><mi>σ</mi><mrow><mi>A</mi></mrow></msub><mo>)</mo></mrow>
+</fotex:equation>From the previous
+expressions for <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>&lt;</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><mo>&gt;;</mo></mrow></fotex:inlinemath> and
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mrow><mi>A</mi></mrow></msub></fotex:inlinemath> one can derive the
+<fotex:equation xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mi>B</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">≤</mo><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mi>B</mi><mo>,</mo><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>2</mn><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup></mrow><mrow><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>+</mo><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac>
+</fotex:equation>The following
+values are obtained with <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">c</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">4</mn></fotex:inlinemath>:
+</fo:block><fo:block font-size="10pt" text-align="justified" text-indent="1em" space-before="0pt"><fo:inline-included-container><fo:table id="N7981"><fo:table-body><fo:table-row><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mi>B</mi><mo>,</mo><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence/></fo:table-cell><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mn>3</mn></mrow></msub></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mrow><mi>B</mi><mo>,</mo><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></fotex:inlinemath></fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence>16 </fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>16 </fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence/></fo:table-cell><fo:table-cell><fo:inline-sequence> 200</fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence> 29.63</fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence>20 </fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>17.78 </fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence/></fo:table-cell><fo:table-cell><fo:inline-sequence> 500</fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence> 31.01</fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence>50 </fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>24.24 </fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence/></fo:table-cell><fo:table-cell><fo:inline-sequence> 1000</fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence> 31.50</fo:inline-sequence></fo:table-cell></fo:table-row><fo:table-row><fo:table-cell><fo:inline-sequence>100 </fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence>27.59 </fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence/></fo:table-cell><fo:table-cell><fo:inline-sequence><fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">∞</mi></fotex:inlinemath></fo:inline-sequence></fo:table-cell><fo:table-cell><fo:inline-sequence> 32.00</fo:inline-sequence></fo:table-cell></fo:table-row></fo:table-body></fo:table></fo:inline-included-container>
+</fo:block>
+
+<fo:block keep-with-next="true" id="N8234" text-align="start" font-size="14pt" text-indent="-3em" font-weight="bold" space-after="3pt" space-before.optimum="9pt">5.2. Special sampling for lower part of the spectrum<fotex:bookmark fotex-bookmark-level="1" fotex-bookmark-label="N8234">5.2. Special sampling for lower part of the spectrum</fotex:bookmark></fo:block>
+
+<fo:block font-size="10pt" text-align="justified">If the step length is very small (<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mo xmlns="http://www.w3.org/1998/Math/MathML">≤</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">5</mn></fotex:inlinemath>
+mm in gases, <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mo xmlns="http://www.w3.org/1998/Math/MathML">≤</mo></fotex:inlinemath>
+2-3 <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">μ</mi></fotex:inlinemath>m in solids)
+the model gives 0 energy loss for some events. To avoid this, the probability of 0 energy loss is
+<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">P</mi><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>Δ</mi><mi>E</mi><mo>=</mo><mn>0</mn><mo>)</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msup xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mrow><mo>-</mo><mrow><mo>(</mo><mrow><mo>&lt;</mo><msub><mi>n</mi><mrow><mn>1</mn></mrow></msub><mo>&gt;</mo></mrow><mo>+</mo><mrow><mo>&lt;</mo><msub><mi>n</mi><mrow><mn>2</mn></mrow></msub><mo>&gt;</mo></mrow><mo>+</mo><mrow><mo>&lt;</mo><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>&gt;</mo></mrow><mo>)</mo></mrow></mrow></msup>
+</fotex:displaymath>If the
+probability is bigger than 0.01 a special sampling is done, taking into account the fact that in
+these cases the projectile interacts only with the outer electrons of the atom. An energy level
+<fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><msub xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mrow><mn>0</mn></mrow></msub><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><mn xmlns="http://www.w3.org/1998/Math/MathML">1</mn><mn xmlns="http://www.w3.org/1998/Math/MathML">0</mn></fotex:inlinemath> eV is chosen
+to correspond to the outer electrons. The mean number of collisions can be calculated from
+<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><mrow xmlns="http://www.w3.org/1998/Math/MathML"><mo>&lt;</mo><mi>n</mi><mo>&gt;</mo></mrow><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo> <mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn></mrow><mrow><msub><mi>E</mi><mrow><mn>0</mn></mrow></msub></mrow></mfrac>
+</fotex:displaymath>The number
+of collisions <fotex:inlinemath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">n</mi></fotex:inlinemath>
+is sampled from Poisson distribution. In the case of the thin layers, all the
+collisions are considered as ionisations and the energy loss is computed as
+<fotex:displaymath xmlns:m="http://www.w3.org/1998/Math/MathML"><mi xmlns="http://www.w3.org/1998/Math/MathML">Δ</mi><mi xmlns="http://www.w3.org/1998/Math/MathML">E</mi><mo xmlns="http://www.w3.org/1998/Math/MathML">=</mo><msubsup xmlns="http://www.w3.org/1998/Math/MathML"><mo>∑</mo>
+ <mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup>
+<mfrac xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>E</mi><mrow><mn>0</mn></mrow></msub></mrow><mrow><mn>1</mn><mo>-</mo>
+<mfrac><mrow><msub><mi>E</mi><mi>max</mi></msub></mrow>
+<mrow><msub><mi>E</mi><mi>max</mi></msub><mo>+</mo><msub><mi>E</mi><mrow><mn>0</mn></mrow></msub></mrow></mfrac>
+<msub><mi>u</mi><mrow><mi>i</mi></mrow></msub></mrow></mfrac>
+</fotex:displaymath>
+</fo:block> <fo:block keep-with-next="true" id="N8570" text-align="start" font-size="18pt" text-indent="-3em" font-weight="bold" space-after="6pt" space-before.optimum="12pt">6. References<fotex:bookmark fotex-bookmark-level="0" fotex-bookmark-label="N8570">6. References</fotex:bookmark></fo:block> <fo:list-block font-size="10pt" margin-right="10pt" space-before.optimum="10pt" space-after.optimum="10pt" margin-left="15pt"><fo:list-item><fo:list-item-label id="bib-LAND"><fo:block margin-right="2.5pt" text-align="end"> [1]</fo:block></fo:list-item-label><fo:list-item-body><fo:block font-weight="normal"> <fo:block font-size="10pt" text-align="justified">L.Landau. On the Energy Loss of Fast Particles by
+Ionisation. Originally published in <fo:inline-sequence font-style="italic">J. Phys.</fo:inline-sequence>, 8:201,
+1944. Reprinted in D.ter Haar, Editor, <fo:inline-sequence font-style="italic">L.D.Landau, Collected
+papers</fo:inline-sequence>, page 417. Pergamon Press, Oxford, 1965.
+</fo:block></fo:block></fo:list-item-body></fo:list-item><fo:list-item><fo:list-item-label id="bib-SCH1"><fo:block margin-right="2.5pt" text-align="end"> [2]</fo:block></fo:list-item-label><fo:list-item-body><fo:block font-weight="normal"> <fo:block font-size="10pt" text-align="justified">B.Schorr. Programs for
+the Landau and the Vavilov distributions and the corresponding random
+numbers. <fo:inline-sequence font-style="italic">Comp. Phys. Comm.</fo:inline-sequence>, 7:216, 1974.
+</fo:block></fo:block></fo:list-item-body></fo:list-item><fo:list-item><fo:list-item-label id="bib-SELT"><fo:block margin-right="2.5pt" text-align="end"> [3]</fo:block></fo:list-item-label><fo:list-item-body><fo:block font-weight="normal"> <fo:block font-size="10pt" text-align="justified">S.M.Seltzer and
+M.J.Berger. Energy loss straggling of protons and mesons. In
+<fo:inline-sequence font-style="italic">Studies in Penetration of Charged Particles in Matter</fo:inline-sequence>,
+Nuclear Science Series 39, Nat. Academy of Sciences, Washington DC,
+1964. </fo:block></fo:block></fo:list-item-body></fo:list-item><fo:list-item><fo:list-item-label id="bib-TALM"><fo:block margin-right="2.5pt" text-align="end"> [4]</fo:block></fo:list-item-label><fo:list-item-body><fo:block font-weight="normal"> <fo:block font-size="10pt" text-align="justified">R.Talman. On the
+statistics of particle identification using ionization. <fo:inline-sequence font-style="italic">Nucl.
+Inst. Meth.</fo:inline-sequence>, 159:189, 1979. </fo:block></fo:block></fo:list-item-body></fo:list-item><fo:list-item><fo:list-item-label id="bib-VAVI"><fo:block margin-right="2.5pt" text-align="end"> [5]</fo:block></fo:list-item-label><fo:list-item-body><fo:block font-weight="normal"> <fo:block font-size="10pt" text-align="justified">P.V.Vavilov. Ionisation losses of high energy
+heavy particles. <fo:inline-sequence font-style="italic">Soviet Physics JETP</fo:inline-sequence>, 5:749,
+1957.</fo:block></fo:block></fo:list-item-body></fo:list-item></fo:list-block>
+ </fo:flow></fo:page-sequence></fo:root> \ No newline at end of file
diff --git a/Master/texmf-dist/doc/xmltex/passivetex/latextei.tex b/Master/texmf-dist/doc/xmltex/passivetex/latextei.tex
new file mode 100644
index 00000000000..40e379d8aa4
--- /dev/null
+++ b/Master/texmf-dist/doc/xmltex/passivetex/latextei.tex
@@ -0,0 +1,4 @@
+\def\xmlfile{latextei.xml}
+\input xmltex
+
+
diff --git a/Master/texmf-dist/doc/xmltex/passivetex/latextei.xml b/Master/texmf-dist/doc/xmltex/passivetex/latextei.xml
new file mode 100644
index 00000000000..af9fbb686c4
--- /dev/null
+++ b/Master/texmf-dist/doc/xmltex/passivetex/latextei.xml
@@ -0,0 +1,972 @@
+<?xml version="1.0"?>
+<!DOCTYPE TEI.2 SYSTEM "http://www.oucs.ox.ac.uk/dtds/tei-oucs.dtd" [
+<!ENTITY aacute "&#x00E1;">
+<!ENTITY ap "&#x2248;">
+<!ENTITY alpha "&#x03B1;">
+<!ENTITY barwed "&#x22BC;">
+<!ENTITY beta "&#x03B2;">
+<!ENTITY commaspace " ">
+<!ENTITY gamma "&#x03B3;">
+<!ENTITY delta "&#x03B4;">
+<!ENTITY Delta "&#x0394;">
+<!ENTITY dots "&#x2026;">
+<!ENTITY epsi "&#x03B5;">
+<!ENTITY gg "&#x22D9;">
+<!ENTITY Gt "&#x226B;">
+<!ENTITY geq "&#x2265;">
+<!ENTITY infin "&#x221E;">
+<!ENTITY infty "&#x221E;">
+<!ENTITY int "&#x222B;">
+<!ENTITY kappa "&#x03BA;">
+<!ENTITY lambda "&#x03BB;">
+<!ENTITY langle "&#x2329;">
+<!ENTITY leq "&#x2264;">
+<!ENTITY mu "&#x03BC;">
+<!ENTITY nbsp "&#x00A0;">
+<!ENTITY phi "&#x03C6;">
+<!ENTITY pi "&#x3C0;">
+<!ENTITY psi "&#x3C8;">
+<!ENTITY rangle "&#x232A;">
+<!ENTITY rho "&#x3C1;">
+<!ENTITY sigma "&#x3C3;">
+<!ENTITY Sigma "&#x03A3;">
+<!ENTITY sim "&#x223C;">
+<!ENTITY thinspace "&#x2009;">
+<!ENTITY thickspace "&#x2005;">
+<!ENTITY xi "&#x03BE;">
+<!ENTITY prime "&#x2032;">
+<!ENTITY isinv "&#x2208;">
+<!ENTITY macr "&#x0304;">
+<!ENTITY Emax "<msub><mi>E</mi><mi>max</mi></msub>">
+<!ENTITY exp "E<mtext>exp</mtext>">
+<!ENTITY ln "E<mtext>ln</mtext>">
+<!ENTITY Rarr "&#x21D2;">
+<!ENTITY rarr "&#x2192;">
+<!ENTITY GEANT "GEANT">
+<!ENTITY sum "&#x2211;">
+]>
+<TEI.2>
+ <teiHeader>
+ <fileDesc>
+ <titleStmt>
+ <title>A sample article</title>
+ </titleStmt>
+ <publicationStmt>
+ <availability><p>Converted from LaTeX by Sebastian Rahtz</p> </availability>
+ </publicationStmt>
+ <sourceDesc>
+ <p></p>
+ </sourceDesc>
+ </fileDesc>
+ <revisionDesc>
+ <list>
+ <item>
+ <date>23 Oct 1999</date> SR converted from LaTeX</item>
+ </list>
+ </revisionDesc>
+ </teiHeader>
+ <text>
+ <front>
+ <docTitle>
+ <titlePart type="main">Simulation of Energy Loss Straggling</titlePart>
+ </docTitle>
+ <docAuthor>Maria Physicist</docAuthor>
+ <docDate>January 17, 1999</docDate>
+ </front>
+ <body> <div id="intro"> <head>Introduction</head> <p>Due to
+the statistical nature of ionisation energy loss, large fluctuations
+can occur in the amount of energy deposited by a particle traversing
+an absorber element. Continuous processes such as multiple scattering
+and energy loss play a relevant role in the longitudinal and lateral
+development of electromagnetic and hadronic showers, and in the case
+of sampling calorimeters the measured resolution can be significantly
+affected by such fluctuations in their active layers. The description
+of ionisation fluctuations is characterised by the significance
+parameter <formula><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&kappa;</mi></math></formula>, which is
+proportional to the ratio of mean energy loss to the maximum allowed
+energy transfer in a single collision with an atomic electron
+ <formula
+type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow> <mi>&kappa;</mi><mo>=</mo>
+<mfrac>
+ <mrow><mi>&xi;</mi></mrow>
+ <mrow>
+ &Emax;
+ </mrow>
+</mfrac>
+</mrow>
+</math></formula>
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+>&Emax;</math></formula> is the
+maximum transferable energy in a single collision with an atomic electron.
+<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mrow>
+ &Emax;<mo>=</mo> <mfrac><mrow><mn>2</mn><msub><mi>m</mi><mrow><mi>e</mi></mrow></msub><msup><mi>&beta;</mi><mrow><mn>2</mn></mrow></msup><msup><mi>&gamma;</mi><mrow><mn>2</mn></mrow></msup></mrow><!--____________
+--><mrow><mn>1</mn><mo>+</mo><mn>2</mn><mi>&gamma;</mi><msub><mi>m</mi><mrow><mi>e</mi></mrow></msub><mo>/</mo><msub><mi>m</mi><mrow><mi>x</mi></mrow></msub><mo>+</mo><msup><mfenced
+open='(' close=')'><msub><mi>m</mi><mrow><mi>e</mi></mrow></msub><mo>/</mo><msub><mi>m</mi><mrow><mi>x</mi></mrow></msub> </mfenced><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo>,</mo>
+</mrow></math></formula> where
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&gamma;</mi><mo>=</mo><mi>E</mi><mo>/</mo><msub><mi>m</mi><mrow><mi>x</mi></mrow></msub></math></formula>,
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>E</mi></math></formula> is energy and
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>m</mi><mrow><mi>x</mi></mrow></msub></math></formula> the mass of the
+incident particle, <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msup><mi>&beta;</mi><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>1</mn><mo>-</mo><mn>1</mn><mo>/</mo><msup><mi>&gamma;</mi><mrow><mn>2</mn></mrow></msup></math></formula>
+and <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>m</mi><mrow><mi>e</mi></mrow></msub></math></formula> is the
+electron mass. <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&xi;</mi></math></formula>
+comes from the Rutherford scattering crosss section and is defined as:
+ <table rend="inline"><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&xi;</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi>&pi;</mi><msup><mi>z</mi><mrow><mn>2</mn></mrow></msup><msup><mi>e</mi><mrow><mn>4</mn></mrow></msup><msub><mi>N</mi><mrow><mi>A</mi><mi>v</mi></mrow></msub><mi>Z</mi><mi>&rho;</mi><mi>&delta;</mi><mi>x</mi></mrow><!--
+ --><mrow><msub><mi>m</mi><mrow><mi>e</mi></mrow></msub><msup><mi>&beta;</mi><mrow><mn>2</mn></mrow></msup><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup><mi>A</mi></mrow></mfrac> <mo>=</mo><mn>1</mn><mn>5</mn><mn>3</mn><mo>.</mo><mn>4</mn> <mfrac><mrow><msup><mi>z</mi><mrow><mn>2</mn></mrow></msup></mrow><!--
+--><mrow><msup><mi>&beta;</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac> <mfrac><mrow><mi>Z</mi></mrow><!--
+--><mrow><mi>A</mi></mrow></mfrac><mi>&rho;</mi><mi>&delta;</mi><mi>x</mi><mspace width='12pt'/><mi>keV </mi><mo>,</mo> <mtext></mtext>
+</math></formula></cell></row></table>
+where
+</p><p><table rend="inline"><row><cell
+><formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>z</mi></math></formula></cell><cell
+>charge of the incident particle </cell>
+</row><row><cell
+><formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>N</mi><mrow><mi>A</mi><mi>v</mi></mrow></msub></math></formula></cell><cell
+>Avogadro's number </cell>
+</row><row><cell
+><formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>Z</mi></math></formula></cell><cell
+>atomic number of the material</cell>
+</row><row><cell
+><formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>A</mi></math></formula></cell><cell
+>atomic weight of the material </cell>
+</row><row><cell
+><formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&rho;</mi></math></formula></cell><cell
+>density </cell>
+</row><row><cell
+><formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&delta;</mi><mi>x</mi></math></formula></cell><cell
+>thickness of the material </cell>
+</row><row><cell
+> </cell>
+</row></table>
+</p><p><formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&kappa;</mi></math></formula>
+measures the contribution of the collisions with energy transfer close to
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+>&Emax;</math></formula>. For a given absorber,
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&kappa;</mi></math></formula> tends towards large
+values if <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&delta;</mi><mi>x</mi></math></formula> is large
+and/or if <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&beta;</mi></math></formula> is small.
+Likewise, <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&kappa;</mi></math></formula> tends
+towards zero if <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&delta;</mi><mi>x</mi></math></formula> is
+small and/or if <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&beta;</mi></math></formula>
+approaches 1.
+</p><p>The value of <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&kappa;</mi></math></formula>
+distinguishes two regimes which occur in the description of ionisation fluctuations
+:
+</p><list type="enumerate">
+<item>
+<p>A
+large
+number
+of
+collisions
+involving
+the
+loss
+of
+all
+or
+most
+of
+the
+incident
+particle
+energy
+during
+the
+traversal
+of
+an
+absorber.
+</p><p>As
+the
+total
+energy
+transfer
+is
+composed
+of
+a
+multitude
+of
+small
+energy
+losses,
+we
+can
+apply
+the
+central
+limit
+theorem
+and
+describe
+the
+fluctuations
+by
+a
+Gaussian
+distribution.
+This
+case
+is
+applicable
+to
+non-relativistic
+particles
+and
+is
+described
+by
+the
+inequality
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&kappa;</mi><mo>&gt;</mo><mn>1</mn><mn>0</mn></math></formula>
+(i.e.
+when
+the
+mean
+energy
+loss
+in
+the
+absorber
+is
+greater
+than
+the
+maximum
+energy
+transfer
+in
+a
+single
+collision).
+</p></item>
+<item>
+<p>Particles
+traversing
+thin
+counters
+and
+incident
+electrons
+under
+any
+conditions.
+</p><p>The
+relevant
+inequalities
+and
+distributions
+are
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mn>0</mn><mo>.</mo><mn>0</mn><mn>1</mn><mo>&lt;</mo><mi>&kappa;</mi><mo>&lt;</mo><mn>1</mn><mn>0</mn></math></formula>,
+Vavilov
+distribution,
+and
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&kappa;</mi><mo>&lt;</mo><mn>0</mn><mo>.</mo><mn>0</mn><mn>1</mn></math></formula>,
+Landau
+distribution.</p></item></list>
+<p>An additional regime is defined by the contribution of the collisions
+with low energy transfer which can be estimated with the relation
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&xi;</mi><mo>/</mo><msub><mi>I</mi><mrow><mn>0</mn></mrow></msub></math></formula>,
+where <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>I</mi><mrow><mn>0</mn></mrow></msub></math></formula>
+is the mean ionisation potential of the atom. Landau theory assumes that
+the number of these collisions is high, and consequently, it has a restriction
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&xi;</mi><mo>/</mo><msub><mi>I</mi><mrow><mn>0</mn></mrow></msub><mo>&Gt;</mo><mn>1</mn></math></formula>. In <code>GEANT</code> (see
+URL <xptr url="http://wwwinfo.cern.ch/asdoc/geant/geantall.html"/>), the limit of Landau theory has
+been set at <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&xi;</mi><mo>/</mo><msub><mi>I</mi><mrow><mn>0</mn></mrow></msub><mo>=</mo><mn>5</mn><mn>0</mn></math></formula>.
+Below this limit special models taking into account the atomic structure of the material are
+used. This is important in thin layers and gaseous materials. Figure <ptr target="fg:phys332-1"/> shows the behaviour
+of <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&xi;</mi><mo>/</mo><msub><mi>I</mi><mrow><mn>0</mn></mrow></msub></math></formula> as
+a function of the layer thickness for an electron of 100 keV and 1 GeV of kinetic
+energy in Argon, Silicon and Uranium.
+</p>
+<p><figure file="phys332-1" id="fg:phys332-1">
+<head>The variable <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&xi;</mi><mo>/</mo><msub><mi>I</mi><mrow><mn>0</mn></mrow></msub></math></formula>
+can be used to measure the validity range of the Landau
+theory. It depends on the type and energy of the particle,
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>Z</mi></math></formula>,
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>A</mi></math></formula>
+and the ionisation potential of the material and the layer thickness. </head>
+</figure></p>
+<p>In the following sections, the different theories and models for the energy loss
+fluctuation are described. First, the Landau theory and its limitations are discussed,
+and then, the Vavilov and Gaussian straggling functions and the methods in the thin
+layers and gaseous materials are presented.
+</p>
+</div>
+<div id="sec:phys332-1">
+<head>Landau theory</head>
+<p>For a particle of mass <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>m</mi><mrow><mi>x</mi></mrow></msub></math></formula> traversing
+a thickness of material <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&delta;</mi><mi>x</mi></math></formula>,
+the Landau probability distribution may be written in terms of the universal Landau
+function <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&phi;</mi><mrow><mo>(</mo><mi>&lambda;</mi><mo>)</mo></mrow></math></formula>
+as<ptr target="bib-LAND"/>:
+ <table rend="inline"><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mrow><mo>(</mo><mi>&epsi;</mi><mo>,</mo><mi>&delta;</mi><mi>x</mi><mo>)</mo></mrow> <mo>=</mo> <mfrac><mrow><mn>1</mn></mrow><!--
+--><mrow><mi>&xi;</mi></mrow></mfrac><mi>&phi;</mi><mrow><mo>(</mo><mi>&lambda;</mi><mo>)</mo></mrow> <mtext></mtext>
+</math></formula></cell></row></table>
+where
+ <table rend="inline"><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&phi;</mi><mrow><mo>(</mo><mi>&lambda;</mi><mo>)</mo></mrow> <mo>=</mo> <mfrac><mrow><mn>1</mn></mrow><!--_
+--><mrow><mn>2</mn><mi>&pi;</mi><mi>i</mi></mrow></mfrac><msubsup><mo>&int;</mo>
+ <mrow><mi>c</mi><mo>+</mo><mi>i</mi><mi>&infin;</mi></mrow><mrow><mi>c</mi><mo>-</mo><mi>i</mi><mi>&infin;</mi></mrow></msubsup><mo>exp</mo><mfenced
+open='(' close=')'><mi>u</mi><mo>ln</mo><mi>u</mi><mo>+</mo><mi>&lambda;</mi><mi>u</mi></mfenced><mi>d</mi><mi>u</mi><mspace width='2cm'/><mi>c</mi><mo>&geq;</mo><mn>0</mn> <mtext></mtext>
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&lambda;</mi> <mo>=</mo> <mfrac><mrow><mi>&epsi;</mi><mo>-</mo><munderover accent='true'><mo>&macr;</mo><mi>&epsi;</mi><mrow></mrow></munderover></mrow><!--
+ --><mrow><mi>&xi;</mi></mrow></mfrac> <mo>-</mo><mi>&gamma;</mi><mi>&prime;</mi><mo>-</mo><msup><mi>&beta;</mi><mrow><mn>2</mn></mrow></msup><mo>-</mo><mo>ln</mo> <mfrac><mrow><mi>&xi;</mi></mrow><!-- ___
+--><mrow>&Emax;</mrow></mfrac> <mtext></mtext>
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&gamma;</mi><mi>&prime;</mi> <mo>=</mo> <mn>0</mn><mo>.</mo><mn>4</mn><mn>2</mn><mn>2</mn><mn>7</mn><mn>8</mn><mn>4</mn><mo>.</mo><mo>.</mo><mo>.</mo><mo>=</mo><mn>1</mn><mo>-</mo><mi>&gamma;</mi> <mtext></mtext>
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&gamma;</mi> <mo>=</mo> <mn>0</mn><mo>.</mo><mn>5</mn><mn>7</mn><mn>7</mn><mn>2</mn><mn>1</mn><mn>5</mn><mo>.</mo><mo>.</mo><mo>.</mo><mtext>(Eulers constant)</mtext> <mtext></mtext>
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><munderover accent='true'><mo>&macr;</mo><mi>&epsi;</mi><mrow></mrow></munderover> <mo>=</mo> <mtext>average energy loss</mtext> <mtext></mtext>
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&epsi;</mi> <mo>=</mo> <mtext>actual energy loss</mtext> <mtext></mtext>
+</math></formula></cell></row></table>
+</p>
+<div >
+<head>Restrictions</head>
+<p>The Landau formalism makes two restrictive assumptions :
+</p><list type="enumerate">
+<item>
+<p>The
+typical
+energy
+loss
+is
+small
+compared
+to
+the
+maximum
+energy
+loss
+in
+a
+single
+collision.
+This
+restriction
+is
+removed
+in
+the
+Vavilov
+theory
+(see
+section
+<ptr target="vavref"/>).
+</p></item>
+<item>
+<p>The
+typical
+energy
+loss
+in
+the
+absorber
+should
+be
+large
+compared
+to
+the
+binding
+energy
+of
+the
+most
+tightly
+bound
+electron.
+For
+gaseous
+detectors,
+typical
+energy
+losses
+are
+a
+few
+keV
+which
+is
+comparable
+to
+the
+binding
+energies
+of
+the
+inner
+electrons.
+In
+such
+cases
+a
+more
+sophisticated
+approach
+which
+accounts
+for
+atomic
+energy
+levels<ptr target="bib-TALM"/>
+is
+necessary
+to
+accurately
+simulate
+data
+distributions.
+In
+<code>GEANT</code>,
+a
+parameterised
+model
+by
+L.
+Urb&aacute;n
+is
+used
+(see
+section
+<ptr target="urban"/>).</p></item></list>
+<p>In addition, the average value of the Landau distribution is infinite.
+Summing the Landau fluctuation obtained to the average energy from the
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>d</mi><mi>E</mi><mo>/</mo><mi>d</mi><mi>x</mi></math></formula>
+tables, we obtain a value which is larger than the one coming from the table. The
+probability to sample a large value is small, so it takes a large number of steps
+(extractions) for the average fluctuation to be significantly larger than zero. This
+introduces a dependence of the energy loss on the step size which can affect
+calculations.
+</p><p>A solution to this has been to introduce a limit on the value of the
+variable sampled by the Landau distribution in order to keep the average
+fluctuation to 0. The value obtained from the <code>GLANDO</code> routine is:
+<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mrow>
+ <mi>&delta;</mi><mi>d</mi><mi>E</mi><mo>/</mo><mi>d</mi><mi>x</mi><mo>=</mo><mi>&epsi;</mi><mo>-</mo><munderover accent='true'><mo>&macr;</mo><mi>&epsi;</mi><mrow></mrow></munderover><mo>=</mo><mi>&xi;</mi><mrow><mo>(</mo><mi>&lambda;</mi><mo>-</mo><mi>&gamma;</mi><mi>&prime;</mi><mo>+</mo><msup><mi>&beta;</mi><mrow><mn>2</mn></mrow></msup><mo>+</mo><mo>ln</mo> <mfrac><mrow><mi>&xi;</mi></mrow><!-- ___
+--><mrow>&Emax;</mrow></mfrac> <mo>)</mo></mrow>
+</mrow></math></formula>
+In order for this to have average 0, we must impose that:
+<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mrow>
+ <munderover accent='true'><mo>&macr;</mo><mi>&lambda;</mi><mrow></mrow></munderover><mo>=</mo><mo>-</mo><mi>&gamma;</mi><mi>&prime;</mi><mo>-</mo><msup><mi>&beta;</mi><mrow><mn>2</mn></mrow></msup><mo>-</mo><mo>ln</mo> <mfrac><mrow><mi>&xi;</mi></mrow><!-- ___
+--><mrow>&Emax;</mrow></mfrac>
+</mrow></math></formula>
+</p><p>This is realised introducing a <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>&lambda;</mi><mrow><mtext>max</mtext></mrow></msub><mrow><mo>(</mo><munderover accent='true'><mo>&macr;</mo><mi>&lambda;</mi><mrow></mrow></munderover><mo>)</mo></mrow></math></formula>
+such that if only values of <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&lambda;</mi><mo>&leq;</mo><msub><mi>&lambda;</mi><mrow><mtext>max</mtext></mrow></msub></math></formula>
+are accepted, the average value of the distribution is
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><munderover accent='true'><mo>&macr;</mo><mi>&lambda;</mi><mrow></mrow></munderover></math></formula>.
+</p><p>A parametric fit to the universal Landau distribution has been performed, with following result:
+<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mrow>
+ <msub><mi>&lambda;</mi><mrow><mtext>max</mtext></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>6</mn><mn>0</mn><mn>7</mn><mn>1</mn><mn>5</mn><mo>+</mo><mn>1</mn><mo>.</mo><mn>1</mn><mn>9</mn><mn>3</mn><mn>4</mn><munderover accent='true'><mo>&macr;</mo><mi>&lambda;</mi><mrow></mrow></munderover><mo>+</mo><mrow><mo>(</mo><mn>0</mn><mo>.</mo><mn>6</mn><mn>7</mn><mn>7</mn><mn>9</mn><mn>4</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>0</mn><mn>5</mn><mn>2</mn><mn>3</mn><mn>8</mn><mn>2</mn><munderover accent='true'><mi>&lambda;</mi><mrow></mrow><mo>&macr;</mo></munderover><mo>)</mo></mrow><mo>exp</mo><mrow><mo>(</mo><mn>0</mn><mo>.</mo><mn>9</mn><mn>4</mn><mn>7</mn><mn>5</mn><mn>3</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>7</mn><mn>4</mn><mn>4</mn><mn>4</mn><mn>2</mn><munderover accent='true'><mi>&lambda;</mi><mrow></mrow><mo>&macr;</mo></munderover><mo>)</mo></mrow>
+</mrow></math></formula> only values
+smaller than <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>&lambda;</mi><mrow><mtext>max</mtext></mrow></msub></math></formula>
+are accepted, otherwise the distribution is resampled.
+</p>
+</div>
+</div>
+<div id="vavref">
+<head>Vavilov theory</head>
+<p>Vavilov<ptr target="bib-VAVI"/> derived a more accurate straggling distribution by introducing the kinematic
+limit on the maximum transferable energy in a single collision, rather than using
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+>&Emax;<mo>=</mo><mi>&infin;</mi></math></formula>. Now
+we can write<ptr target="bib-SCH1"/>:
+ <table rend="inline"><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi> <mfenced
+open='(' close=')'><mi>&epsi;</mi><mo>,</mo><mi>&delta;</mi><mi>s</mi></mfenced> <mo>=</mo> <mfrac><mrow><mn>1</mn></mrow><!--
+--><mrow><mi>&xi;</mi></mrow></mfrac><msub><mi>&phi;</mi><mrow><mi>v</mi></mrow></msub> <mfenced
+open='(' close=')'><msub><mi>&lambda;</mi><mrow><mi>v</mi></mrow></msub><mo>,</mo><mi>&kappa;</mi><mo>,</mo><msup><mi>&beta;</mi><mrow><mn>2</mn></mrow></msup></mfenced> <mtext></mtext>
+</math></formula></cell></row></table>
+where
+ <table rend="inline"><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>&phi;</mi><mrow><mi>v</mi></mrow></msub> <mfenced
+open='(' close=')'><msub><mi>&lambda;</mi><mrow><mi>v</mi></mrow></msub><mo>,</mo><mi>&kappa;</mi><mo>,</mo><msup><mi>&beta;</mi><mrow><mn>2</mn></mrow></msup></mfenced> <mo>=</mo> <mfrac><mrow><mn>1</mn></mrow><!--_
+--><mrow><mn>2</mn><mi>&pi;</mi><mi>i</mi></mrow></mfrac><msubsup><mo>&int;</mo>
+ <mrow><mi>c</mi><mo>+</mo><mi>i</mi><mi>&infin;</mi></mrow><mrow><mi>c</mi><mo>-</mo><mi>i</mi><mi>&infin;</mi></mrow></msubsup><mi>&phi;</mi><mfenced
+open='(' close=')'><mi>s</mi></mfenced><msup><mi>e</mi><mrow><mi>&lambda;</mi><mi>s</mi></mrow></msup><mi>d</mi><mi>s</mi><mspace width='2cm'/><mi>c</mi><mo>&geq;</mo><mn>0</mn> <mtext></mtext>
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&phi;</mi><mfenced
+open='(' close=')'><mi>s</mi></mfenced> <mo>=</mo> <mo>exp</mo><mfenced
+open='[' close=']'><mi>&kappa;</mi><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msup><mi>&beta;</mi><mrow><mn>2</mn></mrow></msup><mi>&gamma;</mi><mo>)</mo></mrow></mfenced><mo>exp</mo><mfenced
+open='[' close=']'><mi>&psi;</mi> <mfenced
+open='(' close=')'><mi>s</mi></mfenced></mfenced><mo>,</mo> <mtext></mtext>
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&psi;</mi> <mfenced
+open='(' close=')'><mi>s</mi></mfenced> <mo>=</mo> <mi>s</mi><mo>ln</mo><mi>&kappa;</mi><mo>+</mo><mrow><mo>(</mo><mi>s</mi><mo>+</mo><msup><mi>&beta;</mi><mrow><mn>2</mn></mrow></msup><mi>&kappa;</mi><mo>)</mo></mrow><mfenced
+open='[' close=']'><mo>ln</mo><mrow><mo>(</mo><mi>s</mi><mo>/</mo><mi>&kappa;</mi><mo>)</mo></mrow><mo>+</mo><msub><mi>E</mi><mrow>
+<mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>s</mi><mo>/</mo><mi>&kappa;</mi><mo>)</mo></mrow></mfenced><mo>-</mo><mi>&kappa;</mi><msup><mi>e</mi><mrow><mo>-</mo><mi>s</mi><mo>/</mo><mi>&kappa;</mi></mrow></msup><mo>,</mo> <mtext></mtext>
+</math></formula></cell></row></table>
+and
+ <table rend="inline"><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow> <mo>=</mo><msubsup> <mo>&int;</mo>
+ <mrow><mi>&infin;</mi></mrow><mrow><mi>z</mi></mrow></msubsup><msup><mi>t</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><msup><mi>e</mi><mrow><mo>-</mo><mi>t</mi></mrow></msup><mi>d</mi><mi>t</mi><mspace width='1cm'/><mtext>(the exponential integral)</mtext> <mtext></mtext>
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>&lambda;</mi><mrow><mi>v</mi></mrow></msub> <mo>=</mo> <mi>&kappa;</mi><mfenced
+open='[' close=']'><mfrac><mrow><mi>&epsi;</mi><mo>-</mo><munderover accent='true'><mo>&macr;</mo><mi>&epsi;</mi><mrow></mrow></munderover></mrow><!--
+ --><mrow><mi>&xi;</mi></mrow></mfrac> <mo>-</mo><mi>&gamma;</mi><mi>&prime;</mi><mo>-</mo><msup><mi>&beta;</mi><mrow><mn>2</mn></mrow></msup></mfenced> <mtext></mtext>
+</math></formula></cell></row></table>
+</p><p>The Vavilov parameters are simply related to the Landau parameter by
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>&lambda;</mi><mrow><mi>L</mi></mrow></msub><mo>=</mo><msub><mi>&lambda;</mi><mrow><mi>v</mi></mrow></msub><mo>/</mo><mi>&kappa;</mi><mo>-</mo><mo>ln</mo><mi>&kappa;</mi></math></formula>. It can be shown that
+as <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&kappa;</mi><mo>&rarr;</mo><mn>0</mn></math></formula>, the distribution of
+the variable <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>&lambda;</mi><mrow><mi>L</mi></mrow></msub></math></formula> approaches
+that of Landau. For <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&kappa;</mi><mo>&leq;</mo><mn>0</mn><mo>.</mo><mn>0</mn><mn>1</mn></math></formula>
+the two distributions are already practically identical. Contrary to what many textbooks
+report, the Vavilov distribution <emph>does not</emph> approximate the Landau distribution for small
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&kappa;</mi></math></formula>, but rather the
+distribution of <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>&lambda;</mi><mrow><mi>L</mi></mrow></msub></math></formula>
+defined above tends to the distribution of the true
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&lambda;</mi></math></formula> from
+the Landau density function. Thus the routine <code>GVAVIV</code> samples the variable
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>&lambda;</mi><mrow><mi>L</mi></mrow></msub></math></formula> rather
+than <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>&lambda;</mi><mrow><mi>v</mi></mrow></msub></math></formula>.
+For <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&kappa;</mi><mo>&geq;</mo><mn>1</mn><mn>0</mn></math></formula>
+the Vavilov distribution tends to a Gaussian distribution (see next section).
+</p>
+</div>
+<div >
+<head>Gaussian Theory</head>
+<p>Various conflicting forms have been proposed for Gaussian straggling functions, but most
+of these appear to have little theoretical or experimental basis. However, it has been shown<ptr target="bib-SELT"/>
+that for <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&kappa;</mi><mo>&geq;</mo><mn>1</mn><mn>0</mn></math></formula>
+the Vavilov distribution can be replaced by a Gaussian of the form:
+ <table rend="inline"><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mrow><mo>(</mo><mi>&epsi;</mi><mo>,</mo><mi>&delta;</mi><mi>s</mi><mo>)</mo></mrow><mo>&ap;</mo> <mfrac><mrow><mn>1</mn></mrow><!--________
+--><mrow><mi>&xi;</mi><msqrt><!--<mi>&radical;</mi>
+ ______________--><mfrac><mrow><mn>2</mn><mi>&pi;</mi></mrow><!--
+ --><mrow><mi>&kappa;</mi></mrow></mfrac> <mfenced
+open='(' close=')'><mn>1</mn><mo>-</mo><msup><mi>&beta;</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><mn>2</mn></mfenced></msqrt></mrow></mfrac><mo>exp</mo><mfenced
+open='[' close=']'><mfrac><mrow><msup><mrow><mo>(</mo><mi>&epsi;</mi><mo>-</mo><munderover accent='true'><mo>&macr;</mo><mi>&epsi;</mi><mrow></mrow></munderover><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow><!--
+ --><mrow><mn>2</mn></mrow></mfrac> <mfrac><mrow><mi>&kappa;</mi></mrow><!-- _______
+--><mrow><msup><mi>&xi;</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mn>1</mn><mo>-</mo><msup><mi>&beta;</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><mn>2</mn><mo>)</mo></mrow></mrow></mfrac></mfenced> <mtext></mtext>
+</math></formula></cell></row></table>
+thus implying
+ <table rend="inline"><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mean</mi> <mo>=</mo> <munderover accent='true'><mo>&macr;</mo><mi>&epsi;</mi><mrow></mrow></munderover> <mtext></mtext>
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>&sigma;</mi><mrow><mn>2</mn></mrow></msup> <mo>=</mo> <mfrac><mrow><msup><mi>&xi;</mi><mrow><mn>2</mn></mrow></msup></mrow><!--
+ --><mrow><mi>&kappa;</mi></mrow></mfrac> <mrow><mo>(</mo><mn>1</mn><mo>-</mo><msup><mi>&beta;</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><mn>2</mn><mo>)</mo></mrow><mo>=</mo><mi>&xi;</mi><msub><mi>E</mi><mrow><mi>
+max</mi></mrow></msub><mrow><mo>(</mo><mn>1</mn><mo>-</mo><msup><mi>&beta;</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><mn>2</mn><mo>)</mo></mrow> <mtext></mtext>
+</math></formula></cell></row></table>
+</p>
+</div>
+<div id="urban">
+<head>Urb&aacute;n model</head>
+<p>The method for computing restricted energy losses with
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&delta;</mi></math></formula>-ray
+production above given threshold energy in <code>GEANT</code> is a Monte Carlo method that
+can be used for thin layers. It is fast and it can be used for any thickness of a
+medium. Approaching the limit of the validity of Landau's theory, the loss
+distribution approaches smoothly the Landau form as shown in Figure <ptr target="fg:phys332-2"/>.
+</p>
+<p><figure file="phys332-2" id="fg:phys332-2">
+<head>Energy loss distribution for a 3 GeV electron in Argon as given by
+standard GEANT. The width of the layers is given in centimeters.</head>
+</figure></p>
+<p>It is assumed that the atoms have only two energy levels with binding energy
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>E</mi><mrow><mn>1</mn></mrow></msub></math></formula> and
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>E</mi><mrow><mn>2</mn></mrow></msub></math></formula>.
+The particle--atom interaction will then be an excitation with energy loss
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>E</mi><mrow><mn>1</mn></mrow></msub></math></formula> or
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>E</mi><mrow><mn>2</mn></mrow></msub></math></formula>, or
+an ionisation with an energy loss distributed according to a function
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>g</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mo>&sim;</mo><mn>1</mn><mo>/</mo><msup><mi>E</mi><mrow><mn>2</mn></mrow></msup></math></formula>:
+<formula type="equation"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ <mi>g</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mrow><mo>(</mo>&Emax;<mo>+</mo><mi>I</mi><mo>)</mo></mrow><mi>I</mi></mrow><!--
+ --><mrow>&Emax;</mrow></mfrac>
+<mfrac><mrow><mn>1</mn></mrow><!-- _
+--><mrow><msup><mi>E</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac>
+</math></formula></p><p>The
+macroscopic cross-section for excitations (<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></math></formula>)
+is <formula id="eq:sigex" type="equation"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ <msub><mi>&Sigma;</mi><mrow><mi>i</mi></mrow></msub><mo>=</mo><mi>C</mi> <mfrac><mrow><msub><mi>f</mi><mrow><mi>i</mi></mrow></msub></mrow><!--
+--><mrow><msub><mi>E</mi><mrow><mi>i</mi></mrow></msub></mrow></mfrac> <mfrac><mrow><mo>ln</mo><mrow><mo>(</mo><mn>2</mn><mi>m</mi><msup><mi>&beta;</mi><mrow><mn>2</mn></mrow></msup><msup><mi>&gamma;</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><msub><mi>E</mi><mrow><mi>i</mi></mrow></msub><mo>)</mo></mrow><mo>-</mo><msup><mi>&beta;</mi><mrow><mn>2</mn></mrow></msup></mrow><!--
+ --><mrow><mo>ln</mo><mrow><mo>(</mo><mn>2</mn><mi>m</mi><msup><mi>&beta;</mi><mrow><mn>2</mn></mrow></msup><msup><mi>&gamma;</mi><mrow><mn>2</mn></mrow></msup><mo>/</mo><mi>I</mi><mo>)</mo></mrow><mo>-</mo><msup><mi>&beta;</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac> <mrow><mo>(</mo><mn>1</mn><mo>-</mo><mi>r</mi><mo>)</mo></mrow> </math></formula>and
+the macroscopic cross-section for ionisation is
+<formula id="eq:sigion" type="equation"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ <msub><mi>&Sigma;</mi><mrow><mn>3</mn></mrow></msub><mo>=</mo><mi>C</mi> <mfrac><mrow>&Emax;</mrow><!-- ________________
+--><mrow><mi>I</mi><mrow><mo>(</mo>&Emax;<mo>+</mo><mi>I</mi><mo>)</mo></mrow><mo>ln</mo><mrow><mo>(</mo><mfrac><mrow>&Emax;<mo>+</mo><mi>I</mi></mrow><!--
+ --><mrow><mi>I</mi></mrow></mfrac> <mo>)</mo></mrow></mrow></mfrac><mi>r</mi> </math></formula>
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML">&Emax;</math></formula>
+is the <code>GEANT</code> cut for <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&delta;</mi></math></formula>-production,
+or the maximum energy transfer minus mean ionisation energy, if it is smaller than
+this cut-off value. The following notation is used:
+</p><p><table rend="inline"><row><cell
+><formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>r</mi><mo>,</mo><mi>C</mi></math></formula></cell><cell
+>parameters of the model</cell>
+</row><row><cell
+><formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>E</mi><mrow><mi>i</mi></mrow></msub></math></formula></cell><cell
+>atomic energy levels </cell>
+</row><row><cell
+><formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>I</mi></math></formula></cell><cell
+>mean ionisation energy </cell>
+</row><row><cell
+><formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>f</mi><mrow><mi>i</mi></mrow></msub></math></formula></cell><cell
+>oscillator strengths </cell>
+</row></table>
+</p><p>The model has the parameters <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>f</mi><mrow><mi>i</mi></mrow></msub></math></formula>,
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>E</mi><mrow><mi>i</mi></mrow></msub></math></formula>,
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>C</mi></math></formula> and
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>r</mi><mrow><mo>(</mo><mn>0</mn><mo>&leq;</mo><mi>r</mi><mo>&leq;</mo><mn>1</mn><mo>)</mo></mrow></math></formula>. The oscillator
+strengths <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>f</mi><mrow><mi>i</mi></mrow></msub></math></formula> and the
+atomic level energies <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>E</mi><mrow><mi>i</mi></mrow></msub></math></formula>
+should satisfy the constraints
+ <table rend="inline"><row><cell><formula type="subeqn" id="eq:fisum"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mrow><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>f</mi><mrow><mn>2</mn></mrow></msub> <mo>=</mo> <mn>1</mn>
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ </math></formula></cell></row><row><cell><formula type="subeqn" id="eq:flnsum"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mrow><mn>1</mn></mrow></msub><mo>ln</mo><msub><mi>E</mi><mrow><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>f</mi><mrow><mn>2</mn></mrow></msub><mo>ln</mo><msub><mi>E</mi><mrow><mn>2</mn></mrow></msub> <mo>=</mo> <mo>ln</mo><mi>I</mi>
+</math></formula></cell></row></table>
+The parameter <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>C</mi></math></formula>
+can be defined with the help of the mean energy loss
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>d</mi><mi>E</mi><mo>/</mo><mi>d</mi><mi>x</mi></math></formula> in the following way: The
+numbers of collisions (<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>n</mi><mrow><mi>i</mi></mrow></msub></math></formula>,
+i = 1,2 for the excitation and 3 for the ionisation) follow the Poisson distribution with a mean
+number <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mrow><mo>&lt;</mo><msub><mi>n</mi><mrow><mi>i</mi></mrow></msub><mo>>;</mo></mrow></math></formula>. In a step
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&Delta;</mi><mi>x</mi></math></formula> the mean number
+of collisions is <formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ <mrow><mo>&lt;</mo><msub><mi>n</mi><mrow><mi>i</mi></mrow></msub><mo>>;</mo></mrow><mo>=</mo><msub><mi>&Sigma;</mi><mrow><mi>i</mi></mrow></msub><mi>&Delta;</mi><mi>x</mi>
+</math></formula>The
+mean energy loss <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>d</mi><mi>E</mi><mo>/</mo><mi>d</mi><mi>x</mi></math></formula>
+in a step is the sum of the excitation and ionisation contributions
+<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ <mfrac><mrow><mi>d</mi><mi>E</mi></mrow><!--
+--><mrow><mi>d</mi><mi>x</mi></mrow></mfrac> <mi>&Delta;</mi><mi>x</mi><mo>=</mo><mfenced
+open='[' close=']'><msub><mi>&Sigma;</mi><mrow><mn>1</mn></mrow></msub><msub><mi>E</mi><mrow><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>&Sigma;</mi><mrow><mn>2</mn></mrow></msub><msub><mi>E</mi><mrow><mn>2</mn></mrow></msub><mo>+</mo><msub><mi>&Sigma;</mi><mrow><mn>3</mn></mrow></msub><msubsup><mo>&int;</mo>
+ <mrow><mi>I</mi></mrow><mrow>&Emax;<mo>+</mo><mi>I</mi></mrow></msubsup><mi>E</mi><mi>g</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mi>d</mi><mi>E</mi></mfenced><mi>&Delta;</mi><mi>x</mi>
+</math></formula>From
+this, using the equations (<ptr target="eq:sigex"/>), (<ptr target="eq:sigion"/>), (<ptr target="eq:fisum"/>) and (<ptr target="eq:flnsum"/>), one can define the parameter
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>C</mi></math></formula>
+<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ <mi>C</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mi>E</mi></mrow><!--
+--><mrow><mi>d</mi><mi>x</mi></mrow></mfrac>
+</math></formula>
+</p><p>The following values have been chosen in <code>GEANT</code> for the other parameters:
+<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mrow>
+ <mtable equalrows='false' equalcolumns='false'><mtr><mtd><msub><mi>f</mi><mrow><mn>2</mn></mrow></msub><mo>=</mo><mfenced
+open='{' ><mtable equalrows='false' equalcolumns='false'><mtr><mtd><mn>0</mn> </mtd><mtd><mi>if</mi><mi>Z</mi><mo>&leq;</mo><mn>2</mn></mtd>
+</mtr><mtr><mtd><mn>2</mn><mo>/</mo><mi>Z</mi></mtd><mtd><mi>if</mi><mi>Z</mi><mo>&gt;</mo><mn>2</mn></mtd>
+</mtr><mtr><mtd> </mtd></mtr></mtable> </mfenced></mtd><mtd><mo>&Rarr;</mo></mtd><mtd><msub><mi>f</mi><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>1</mn><mo>-</mo><msub><mi>f</mi><mrow><mn>2</mn></mrow></msub> </mtd>
+ </mtr><mtr><mtd><msub><mi>E</mi><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>1</mn><mn>0</mn><msup><mi>Z</mi><mrow><mn>2</mn></mrow></msup><mi>eV </mi> </mtd><mtd><mo>&Rarr;</mo></mtd><mtd><msub><mi>E</mi><mrow><mn>1</mn></mrow></msub><mo>=</mo><msup><mfenced
+open='(' close=')'> <mfrac><mrow><mi>I</mi></mrow><!--___
+--><mrow><msubsup><mi>E</mi><mrow><mn>2</mn></mrow><mrow><msub><mi>f</mi><mrow><mn>2</mn></mrow></msub></mrow></msubsup></mrow></mfrac> </mfenced><mrow> <mfrac><mrow><mn>1</mn></mrow><!-- _
+--><mrow><msub><mi>f</mi><mrow><mn>1</mn></mrow></msub></mrow></mfrac> </mrow></msup></mtd>
+ </mtr><mtr><mtd><mi>r</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>4</mn> </mtd><mtd> </mtd><mtd> </mtd>
+ </mtr><mtr><mtd> </mtd></mtr></mtable>
+</mrow></math></formula> With these values
+the atomic level <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>E</mi><mrow><mn>2</mn></mrow></msub></math></formula>
+corresponds approximately the K-shell energy of the atoms and
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>Z</mi><msub><mi>f</mi><mrow><mn>2</mn></mrow></msub></math></formula> the number of
+K-shell electrons. <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>r</mi></math></formula>
+is the only variable which can be tuned freely. It determines the relative contribution
+of ionisation and excitation to the energy loss.
+</p><p>The energy loss is computed with the assumption that the step length (or the relative
+energy loss) is small, and---in consequence---the cross-section can be considered
+constant along the path length. The energy loss due to the excitation is
+<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ <mi>&Delta;</mi><msub><mi>E</mi><mrow><mi>e</mi></mrow></msub><mo>=</mo><msub><mi>n</mi><mrow><mn>1</mn></mrow></msub><msub><mi>E</mi><mrow><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>n</mi><mrow><mn>2</mn></mrow></msub><msub><mi>E</mi><mrow><mn>2</mn></mrow></msub>
+</math></formula>where
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>n</mi><mrow><mn>1</mn></mrow></msub></math></formula> and
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>n</mi><mrow><mn>2</mn></mrow></msub></math></formula>
+are sampled from Poisson distribution as discussed above. The
+loss due to the ionisation can be generated from the distribution
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>g</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow></math></formula> by
+the inverse transformation method:
+ <table rend="inline"><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mi>F</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow> <mo>=</mo><msubsup> <mo>&int;</mo>
+ <mrow><mi>I</mi></mrow><mrow><mi>E</mi></mrow></msubsup><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>d</mi><mi>x</mi> <mtext></mtext>
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><msup><mi>F</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow> <mo>=</mo> <mfrac><mrow><mi>I</mi></mrow><!--____
+--><mrow><mn>1</mn><mo>-</mo><mi>u</mi> <mfrac><mrow>&Emax;</mrow><!-- ___
+--><mrow>&Emax;<mo>+</mo><mi>I</mi></mrow></mfrac> </mrow></mfrac>
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML">
+</math></formula></cell></row></table>
+where <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>u</mi></math></formula> is a uniform random
+number between <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>F</mi><mrow><mo>(</mo><mi>I</mi><mo>)</mo></mrow><mo>=</mo><mn>0</mn></math></formula> and
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>F</mi><mrow><mo>(</mo>&Emax;<mo>+</mo><mi>I</mi><mo>)</mo></mrow><mo>=</mo><mn>1</mn></math></formula>. The contribution from the
+ionisations will be <formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ <mi>&Delta;</mi><msub><mi>E</mi><mrow><mi>i</mi></mrow></msub><mo>=</mo><msubsup><mo>&sum;</mo>
+ <mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub></mrow></msubsup> <mfrac><mrow><mi>I</mi></mrow><!--________
+--><mrow><mn>1</mn><mo>-</mo><msub><mi>u</mi><mrow><mi>j</mi></mrow></msub> <mfrac><mrow>&Emax;</mrow><!-- ___
+--><mrow>&Emax;<mo>+</mo><mi>I</mi></mrow></mfrac> </mrow></mfrac>
+</math></formula>where
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub></math></formula> is the
+number of ionisation (sampled from Poisson distribution). The energy loss in a step will
+then be <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&Delta;</mi><mi>E</mi><mo>=</mo><mi>&Delta;</mi><msub><mi>E</mi><mrow><mi>e</mi></mrow></msub><mo>+</mo><mi>&Delta;</mi><msub><mi>E</mi><mrow><mi>i</mi></mrow></msub></math></formula>.
+</p>
+<div >
+<head>Fast simulation for <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>&geq;</mo><mn>1</mn><mn>6</mn></math></formula></head>
+<p>If the number of ionisation <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub></math></formula>
+is bigger than 16, a faster sampling method can be used. The possible energy loss
+interval is divided in two parts: one in which the number of collisions is large and the
+sampling can be done from a Gaussian distribution and the other in which
+the energy loss is sampled for each collision. Let us call the former interval
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mrow><mo>[</mo><mi>I</mi><mo>,</mo><mi>&alpha;</mi><mi>I</mi><mo>]</mo></mrow></math></formula> the interval A,
+and the latter <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mrow><mo>[</mo><mi>&alpha;</mi><mi>I</mi><mo>,</mo>&Emax;<mo>]</mo></mrow></math></formula> the
+interval B. <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&alpha;</mi></math></formula> lies
+between 1 and <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+>&Emax;<mo>/</mo><mi>I</mi></math></formula>.
+A collision with a loss in the interval A happens with the probability
+<formula type="display" id="eq:phys332-5"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ <mi>P</mi><mrow><mo>(</mo><mi>&alpha;</mi><mo>)</mo></mrow><mo>=</mo><msubsup><mo>&int;</mo>
+ <mrow><mi>I</mi></mrow><mrow><mi>&alpha;</mi><mi>I</mi></mrow></msubsup><mi>g</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mi>d</mi><mi>E</mi><mo>=</mo><mfrac><mrow><mrow><mo>(</mo>&Emax;<mo>+</mo><mi>I</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>&alpha;</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><!--
+ --><mrow>&Emax;<mi>&alpha;</mi></mrow></mfrac>
+</math></formula>The
+mean energy loss and the standard deviation for this type of collision are
+<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ <mrow><mo>&lt;</mo><mi>&Delta;</mi><mi>E</mi><mrow><mo>(</mo><mi>&alpha;</mi><mo>)</mo></mrow><mo>>;</mo></mrow><mo>=</mo> <mfrac><mrow><mn>1</mn></mrow><!--___
+--><mrow><mi>P</mi><mrow><mo>(</mo><mi>&alpha;</mi><mo>)</mo></mrow></mrow></mfrac><msubsup><mo>&int;</mo>
+ <mrow><mi>I</mi></mrow><mrow><mi>&alpha;</mi><mi>I</mi></mrow></msubsup><mi>E</mi><mi>g</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mi>d</mi><mi>E</mi><mo>=</mo><mfrac><mrow><mi>I</mi><mi>&alpha;</mi><mo>ln</mo><mi>&alpha;</mi></mrow><!--
+ --><mrow><mi>&alpha;</mi><mo>-</mo><mn>1</mn></mrow></mfrac>
+</math></formula>and <formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>&sigma;</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>&alpha;</mi><mo>)</mo></mrow><mo>=</mo> <mfrac><mrow><mn>1</mn></mrow><!--___
+--><mrow><mi>P</mi><mrow><mo>(</mo><mi>&alpha;</mi><mo>)</mo></mrow></mrow></mfrac><msubsup><mo>&int;</mo>
+ <mrow><mi>I</mi></mrow><mrow><mi>&alpha;</mi><mi>I</mi></mrow></msubsup><msup><mi>E</mi><mrow><mn>2</mn></mrow></msup><mi>g</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mi>d</mi><mi>E</mi><mo>=</mo><msup><mi>I</mi><mrow><mn>2</mn></mrow></msup><mi>&alpha;</mi><mfenced
+open='(' close=')'><mn>1</mn><mo>-</mo> <mfrac><mrow><mi>&alpha;</mi><msup><mo>ln</mo><mrow><mn>2</mn></mrow></msup><mi>&alpha;</mi></mrow><!--_
+--><mrow><msup><mrow><mo>(</mo><mi>&alpha;</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></mfenced>
+</math></formula>If the
+collision number is high, we assume that the number of the type A collisions can be
+calculated from a Gaussian distribution with the following mean value and standard
+deviation:
+ <table rend="inline"><row><cell><formula type="subeqn" id="eq:phys332-1"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>&lt;</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><mo>>;</mo></mrow> <mo>=</mo> <msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mi>P</mi><mrow><mo>(</mo><mi>&alpha;</mi><mo>)</mo></mrow>
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ </math></formula></cell></row><row><cell><formula type="subeqn" id="eq:phys332-2"><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>&sigma;</mi><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msubsup> <mo>=</mo> <msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mi>P</mi><mrow><mo>(</mo><mi>&alpha;</mi><mo>)</mo></mrow><mrow><mo>(</mo><mn>1</mn><mo>-</mo><mi>P</mi><mrow><mo>(</mo><mi>&alpha;</mi><mo>)</mo></mrow><mo>)</mo></mrow>
+</math></formula></cell></row></table>
+It is further assumed that the energy loss in these collisions has a Gaussian
+distribution with
+ <table rend="inline"><row><cell><formula type="subeqn" id="eq:phys332-3"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>&lt;</mo><mi>&Delta;</mi><msub><mi>E</mi><mrow><mi>A</mi></mrow></msub><mo>>;</mo></mrow> <mo>=</mo> <msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><mrow><mo>&lt;</mo><mi>&Delta;</mi><mi>E</mi><mrow><mo>(</mo><mi>&alpha;</mi><mo>)</mo></mrow><mo>>;</mo></mrow>
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ </math></formula></cell></row><row><cell><formula type="subeqn" id="eq:phys332-4"><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>&sigma;</mi><mrow><mi>E</mi><mo>,</mo><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msubsup> <mo>=</mo> <msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><msup><mi>&sigma;</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>&alpha;</mi><mo>)</mo></mrow>
+</math></formula></cell></row></table>
+The energy loss of these collision can then be sampled from the Gaussian
+distribution.
+</p><p>The collisions where the energy loss is in the interval B are sampled directly from
+<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ <mi>&Delta;</mi><msub><mi>E</mi><mrow><mi>B</mi></mrow></msub><mo>=</mo><msubsup><mo>&sum;</mo>
+ <mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>-</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub></mrow></msubsup> <mfrac><mrow><mi>&alpha;</mi><mi>I</mi></mrow><!--_________
+--><mrow><mn>1</mn><mo>-</mo><msub><mi>u</mi><mrow><mi>i</mi></mrow></msub> <mfrac><mrow>&Emax;<mo>+</mo><mi>I</mi><mo>-</mo><mi>&alpha;</mi><mi>I</mi></mrow><!--
+ --><mrow>&Emax;<mo>+</mo><mi>I</mi></mrow></mfrac> </mrow></mfrac>
+</math></formula>The
+total energy loss is the sum of these two types of collisions:
+<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ <mi>&Delta;</mi><mi>E</mi><mo>=</mo><mi>&Delta;</mi><msub><mi>E</mi><mrow><mi>A</mi></mrow></msub><mo>+</mo><mi>&Delta;</mi><msub><mi>E</mi><mrow><mi>B</mi></mrow></msub>
+</math></formula></p>
+<p>The approximation of equations (<ptr target="eq:phys332-1"/>), (<ptr target="eq:phys332-2"/>), (<ptr target="eq:phys332-3"/>) and (<ptr target="eq:phys332-4"/>) can be used under the following
+conditions:
+ <table rend="inline"><row><cell><formula type="subeqn" id="eq:phys332-6"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>&lt;</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><mo>>;</mo></mrow><mo>-</mo><mi>c</mi><msub><mi>&sigma;</mi><mrow><mi>A</mi></mrow></msub> <mo>&geq;</mo> <mn>0</mn>
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ </math></formula></cell></row><row><cell><formula type="subeqn" id="eq:phys332-7"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>&lt;</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><mo>>;</mo></mrow><mo>+</mo><mi>c</mi><msub><mi>&sigma;</mi><mrow><mi>A</mi></mrow></msub> <mo>&leq;</mo> <msub><mi>n</mi><mrow><mn>3</mn></mrow></msub>
+ </math></formula></cell></row><row><cell><formula type="subeqn"><math xmlns="http://www.w3.org/1998/Math/MathML">
+ </math></formula></cell></row><row><cell><formula type="subeqn" id="eq:phys332-8"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>&lt;</mo><mi>&Delta;</mi><msub><mi>E</mi><mrow><mi>A</mi></mrow></msub><mo>>;</mo></mrow><mo>-</mo><mi>c</mi><msub><mi>&sigma;</mi><mrow><mi>E</mi><mo>,</mo><mi>A</mi></mrow></msub> <mo>&geq;</mo> <mn>0</mn>
+</math></formula></cell></row></table>
+where <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>c</mi><mo>&geq;</mo><mn>4</mn></math></formula>. From
+the equations (<ptr target="eq:phys332-5"/>), (<ptr target="eq:phys332-1"/>) and (<ptr target="eq:phys332-3"/>) and from the conditions (<ptr target="eq:phys332-6"/>) and (<ptr target="eq:phys332-7"/>) the following limits can be
+<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>&alpha;</mi><mrow><mi>min</mi></mrow></msub><mo>=</mo><mfrac><mrow><mrow><mo>(</mo><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>+</mo><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mo>(</mo>&Emax;<mo>+</mo><mi>I</mi><mo>)</mo></mrow></mrow><!--
+--><mrow><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mrow><mo>(</mo>&Emax;<mo>+</mo><mi>I</mi><mo>)</mo></mrow><mo>+</mo><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup><mi>I</mi></mrow></mfrac> <mo>&leq;</mo><mi>&alpha;</mi><mo>&leq;</mo><msub><mi>&alpha;</mi><mrow><mtext>max</mtext></mrow></msub><mo>=</mo><mfrac><mrow><mrow><mo>(</mo><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>+</mo><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mo>(</mo>&Emax;<mo>+</mo><mi>I</mi><mo>)</mo></mrow></mrow><!--
+--><mrow><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo>&Emax;<mo>+</mo><mi>I</mi><mo>)</mo></mrow><mo>+</mo><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mi>I</mi></mrow></mfrac>
+</math></formula>This
+conditions gives a lower limit to number of the ionisations
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub></math></formula> for which the fast
+<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>&geq;</mo><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup> </math></formula>As
+in the conditions (<ptr target="eq:phys332-6"/>), (<ptr target="eq:phys332-7"/>) and (<ptr target="eq:phys332-8"/>) the value of
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>c</mi></math></formula> is as minimum
+4, one gets <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>&geq;</mo><mn>1</mn><mn>6</mn></math></formula>.
+In order to speed the simulation, the maximum value is used for
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&alpha;</mi></math></formula>.
+</p><p>The number of collisions with energy loss in the interval B (the number of interactions
+which has to be simulated directly) increases slowly with the total number of collisions
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub></math></formula>.
+The maximum number of these collisions can be estimated as
+<formula type="equation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mrow><mi>B</mi><mo>,</mo><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo>=</mo><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>-</mo><msub><mi>n</mi><mrow><mi>A</mi><mo>,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo>&ap;</mo><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mrow><mo>(</mo><mrow><mo>&lt;</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><mo>>;</mo></mrow><mo>-</mo><msub><mi>&sigma;</mi><mrow><mi>A</mi></mrow></msub><mo>)</mo></mrow>
+</math></formula>From the previous
+expressions for <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mrow><mo>&lt;</mo><msub><mi>n</mi><mrow><mi>A</mi></mrow></msub><mo>>;</mo></mrow></math></formula> and
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>&sigma;</mi><mrow><mi>A</mi></mrow></msub></math></formula> one can derive the
+<formula type="equation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mrow><mi>B</mi></mrow></msub><mo>&leq;</mo><msub><mi>n</mi><mrow><mi>B</mi><mo>,</mo><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo>=</mo> <mfrac><mrow><mn>2</mn><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup></mrow><!--_
+--><mrow><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>+</mo><msup><mi>c</mi><mrow><mn>2</mn></mrow></msup></mrow></mfrac>
+</math></formula>The following
+values are obtained with <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>c</mi><mo>=</mo><mn>4</mn></math></formula>:
+</p><p><table rend="inline"><row><cell
+><formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub></math></formula></cell><cell
+><formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>n</mi><mrow><mi>B</mi><mo>,</mo><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></math></formula></cell><cell
+></cell><cell
+><formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub></math></formula></cell><cell
+><formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>n</mi><mrow><mi>B</mi><mo>,</mo><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub></math></formula></cell>
+</row><row><cell
+>16 </cell><cell
+>16 </cell><cell
+></cell><cell
+> 200</cell><cell
+> 29.63</cell>
+</row><row><cell
+>20 </cell><cell
+>17.78 </cell><cell
+></cell><cell
+> 500</cell><cell
+> 31.01</cell>
+</row><row><cell
+>50 </cell><cell
+>24.24 </cell><cell
+></cell><cell
+> 1000</cell><cell
+> 31.50</cell>
+</row><row><cell
+>100 </cell><cell
+>27.59 </cell><cell
+></cell><cell
+><formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&infin;</mi></math></formula></cell><cell
+> 32.00</cell>
+</row></table>
+</p>
+</div>
+<div >
+<head>Special sampling for lower part of the spectrum</head>
+<p>If the step length is very small (<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mo>&leq;</mo><mn>5</mn></math></formula>
+mm in gases, <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mo>&leq;</mo></math></formula>
+2-3 <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>&mu;</mi></math></formula>m in solids)
+the model gives 0 energy loss for some events. To avoid this, the probability of 0 energy loss is
+<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mrow><mo>(</mo><mi>&Delta;</mi><mi>E</mi><mo>=</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><msup><mi>e</mi><mrow><mo>-</mo><mrow><mo>(</mo><mrow><mo>&lt;</mo><msub><mi>n</mi><mrow><mn>1</mn></mrow></msub><mo>></mo></mrow><mo>+</mo><mrow><mo>&lt;</mo><msub><mi>n</mi><mrow><mn>2</mn></mrow></msub><mo>></mo></mrow><mo>+</mo><mrow><mo>&lt;</mo><msub><mi>n</mi><mrow><mn>3</mn></mrow></msub><mo>></mo></mrow><mo>)</mo></mrow></mrow></msup>
+</math></formula>If the
+probability is bigger than 0.01 a special sampling is done, taking into account the fact that in
+these cases the projectile interacts only with the outer electrons of the atom. An energy level
+<formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><msub><mi>E</mi><mrow><mn>0</mn></mrow></msub><mo>=</mo><mn>1</mn><mn>0</mn></math></formula> eV is chosen
+to correspond to the outer electrons. The mean number of collisions can be calculated from
+<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>&lt;</mo><mi>n</mi><mo>></mo></mrow><mo>=</mo> <mfrac><mrow><mn>1</mn></mrow><mrow><msub><mi>E</mi><mrow><mn>0</mn></mrow></msub></mrow></mfrac>
+</math></formula>The number
+of collisions <formula><math xmlns="http://www.w3.org/1998/Math/MathML"
+><mi>n</mi></math></formula>
+is sampled from Poisson distribution. In the case of the thin layers, all the
+collisions are considered as ionisations and the energy loss is computed as
+<formula type="display"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&Delta;</mi><mi>E</mi><mo>=</mo><msubsup><mo>&sum;</mo>
+ <mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup>
+<mfrac><mrow><msub><mi>E</mi><mrow><mn>0</mn></mrow></msub></mrow><mrow><mn>1</mn><mo>-</mo>
+<mfrac><mrow>&Emax;</mrow>
+<mrow>&Emax;<mo>+</mo><msub><mi>E</mi><mrow><mn>0</mn></mrow></msub></mrow></mfrac>
+<msub><mi>u</mi><mrow><mi>i</mi></mrow></msub></mrow></mfrac>
+</math></formula>
+</p> </div> </div> <div
+type="star"> <head>References</head> <list type="bibliography"> <item
+id="bib-LAND"> <p>L.Landau. On the Energy Loss of Fast Particles by
+Ionisation. Originally published in <emph>J. Phys.</emph>, 8:201,
+1944. Reprinted in D.ter Haar, Editor, <emph>L.D.Landau, Collected
+papers</emph>, page 417. Pergamon Press, Oxford, 1965.
+</p></item> <item id="bib-SCH1"> <p>B.Schorr. Programs for
+the Landau and the Vavilov distributions and the corresponding random
+numbers. <emph>Comp. Phys. Comm.</emph>, 7:216, 1974.
+</p></item> <item id="bib-SELT"> <p>S.M.Seltzer and
+M.J.Berger. Energy loss straggling of protons and mesons. In
+<emph>Studies in Penetration of Charged Particles in Matter</emph>,
+Nuclear Science Series 39, Nat. Academy of Sciences, Washington DC,
+1964. </p></item> <item id="bib-TALM"> <p>R.Talman. On the
+statistics of particle identification using ionization. <emph>Nucl.
+Inst. Meth.</emph>, 159:189, 1979. </p></item> <item
+id="bib-VAVI"> <p>P.V.Vavilov. Ionisation losses of high energy
+heavy particles. <emph>Soviet Physics JETP</emph>, 5:749,
+1957.</p></item></list> </div>
+ </body> </text> </TEI.2>
+
+
diff --git a/Master/texmf-dist/doc/xmltex/passivetex/passivetex.xml b/Master/texmf-dist/doc/xmltex/passivetex/passivetex.xml
new file mode 100644
index 00000000000..87ddc55816f
--- /dev/null
+++ b/Master/texmf-dist/doc/xmltex/passivetex/passivetex.xml
@@ -0,0 +1,388 @@
+<?xml version="1.0"?>
+<!DOCTYPE TEI.2 SYSTEM "http://www.oucs.ox.ac.uk/dtds/tei-oucs.dtd" [
+ <!ENTITY properties SYSTEM "properties.xml">
+]>
+<TEI.2>
+ <teiHeader>
+ <fileDesc>
+ <titleStmt>
+ <title>PassiveTeX</title>
+ </titleStmt>
+ <publicationStmt>
+ <p> </p>
+ </publicationStmt>
+ <sourceDesc>
+ <p></p>
+ </sourceDesc>
+ </fileDesc>
+ <revisionDesc>
+ <list>
+ <item><date>2000/12/11</date>version 1.4 </item>
+ <item><date>2000/11/23</date>version 1.3 </item>
+ <item><date>2000/10/04</date>version 1.1 </item>
+ <item><date>2000/09/13</date>A couple of changes to property list</item>
+ <item><date>2000/09/12</date>Notes on memory sizes</item>
+ <item><date>2000/06/24</date>Checking links</item>
+ <item><date>2000/05/30</date>Added conformance and dependency notes</item>
+ <item><date>2000/02/07</date>Second version</item>
+ <item><date>1999/08/08</date>First version, authored in TEI XML</item>
+ </list>
+ </revisionDesc>
+ </teiHeader>
+ <text>
+<front>
+<titlePage>
+<docTitle>
+ <titlePart type="main">PassiveTeX</titlePart>
+</docTitle>
+<docAuthor>Sebastian Rahtz</docAuthor>
+<docDate>November 2000</docDate>
+</titlePage>
+</front>
+<body>
+<div>
+<head>Summary</head>
+<list type="unordered">
+<item>
+PassiveTeX is a library of TeX macros which can be used to process an XML
+document which results from an XSL transformation to formatting objects.
+</item>
+<item>
+PassiveTeX provides a rapid development environment for experimenting
+with XSL FO, using a reliable pre-existing formatter
+</item>
+<item>
+Running PassiveTeX with the pdfTeX variant of TeX generates high-quality
+PDF files in a single operation.
+</item>
+<item>
+PassiveTeX shows how TeX can remain the formatter of choice for XML, while
+hiding the details of its operation from the user.
+</item>
+</list>
+<p>
+Available from <xptr
+ url="http://users.ox.ac.uk/~rahtz/passivetex/"/>.
+ The current version is 1.4, 2000/12/11.
+</p>
+</div>
+<div><head>How does it work?</head>
+<p>
+PassiveTeX relies heavily on work by David Carlisle
+(his namespace-aware XML parser written in
+TeX, <code>xmltex</code>), and was developed from my
+<xref url="http://www.tug.org/applications/jadetex/">JadeTeX</xref>
+macros for processing DSSSL via Jade.
+</p>
+<p>
+Taking the XML version of the TEI Lite guidelines
+(<xref url="test/teiu5.xml">teiu5.xml</xref>, with DTD
+<xref url="test/teixlite.dtd">teixlite.dtd</xref>), we apply an XSL stylesheet
+(see my page of <xref url="http://users.ox.ac.uk/~rahtz/tei">TEI style sheets</xref>),
+and run it through James Clark's XT XSL processor:
+<eg>
+ java com.jclark.xsl.sax.Driver teiu5.xml tei.xsl teiu5.fo
+</eg>
+(assuming you have <code>xt.jar</code>, <code>xp.jar</code> and <code>sax.jar</code>
+on your CLASSPATH ). This creates the new XML file
+<xref url="test/teiu5.fo">teiu5.fo</xref>. We now run XMLTeX on this
+<eg>
+ pdfxmltex teiu5.fo
+</eg>
+which creates <xref url="test/teiu5.pdf">teiu5.pdf</xref>. Voila!
+Actually, we need to do
+<eg>
+ pdfxmltex teiu5.fo
+</eg>
+again, to resolve page-number references in the table of contents. For a comparison
+with an HTML rendering of the same document (using XSL again),
+see <xref url="http://users.ox.ac.uk/~rahtz/tei/teiu5.html">teiu5.html</xref>
+on my TEI page. </p>
+</div>
+<div>
+<head>Installation</head>
+<p>
+The PassiveTeX macros should be downloaded (as a ZIP file,
+<xptr url="passivetex.zip"/>), unpacked, and installed in a TeX system (eg in
+<code>texmf/tex/latex/passivetex</code>) in the normal place where you put
+macros. Consult your local documentation or local expert if you do not know
+how to install a new package; on a web2c-based system, don't forget to
+ run <code>mktexlsr</code> when you have the files in place,
+ to update the file lookup table.
+</p>
+<p>
+What about that <code>pdfxmltex</code> command we saw in the last section?
+You don't have it on your system? You need to download
+<xref url="ftp://ftp.tex.ac.uk/tex-archive/macros/xmltex/base.zip">xmltex</xref>
+(that link gives you a ZIP archive of the system) and install it in the your TeX system.
+It too is just a set of TeX macro packages.
+Then you can use it on a file called (eg) <code>teiu5.fo</code> in one of two ways:
+<list type="ordered">
+<item>Build an <code>xmltex</code> format file for pdfTeX with
+<eg>
+pdftex -ini "&amp;pdflatex" pdfxmltex.ini
+</eg>
+and process your file with
+<eg>
+pdflatex "&amp;pdfxmltex" teiu5.fo
+</eg>
+Or,
+</item>
+<item>
+Make a wrapper file called (eg) <code>teiu5.tex</code> looking like this:
+<eg>
+\def\xmlfile{teiu5.fo}
+\input xmltex
+</eg>
+and run pdfTeX on it as normal with
+<eg>
+pdflatex teiu5.tex
+</eg>
+</item>
+</list>
+Do not worry, <code>xmltex</code> knows how to find the PassiveTeX macros as
+it needs them. You will likely need to increase TeX memory
+values (in the file <code>texmf.cnf</code> if you use a Web2c-based TeX);
+I use:
+<eg>
+main_memory = 2500000
+param_size = 1500
+stack_size = 1500
+hash_extra = 50000
+string_vacancies = 45000
+pool_free = 47500
+nest_size = 500
+save_size = 10000
+pool_size = 500000
+max_strings = 55000
+</eg>
+</p>
+<p>
+For reference, the PassiveTeX package consists of the following files:
+<list>
+<item>The core xmltex `style' files for XSL FO XML:
+<eg>
+ fotex.xmt
+ fotex.sty
+</eg>
+</item>
+<item>
+Support for direct formatting of TEI XML with xmltex
+<eg>
+ tei.xmt
+ teixml.sty
+</eg>
+</item>
+<item>
+Some support files, shared with JadeTeX:
+<eg>
+ unicode.sty
+ ucharacters.sty
+ mlnames.sty
+ dummyels.sty
+</eg>
+</item>
+</list>
+</p>
+<p>
+NOTE: TeX has a limit
+on the length of line it can read,
+and some .fo files you generate may cause
+TeX to die with an message about increasing buf_size.
+If you get that, edit your
+<code>texmf.cnf</code> file, increase the size of <code>buf_size</code> (mine is
+200000), and remake any format files.
+</p>
+<div><head>LaTeX package dependencies</head>
+<p>This setup assumes you have a decent modern TeX setup. The TeX Live 5 CD-ROM
+is what I use, and it is up to date
+(see <xptr url="http://www.tug.org/texlive/"/>).
+</p>
+<p> Here is a
+ list of the packages loaded in a typical run of
+ PassiveTeX, with their version numbers where known:
+<table rend="rules">
+<row><cell> amsbsy.sty </cell><cell> 1999/11/29 v1.2d</cell></row>
+<row><cell>amsfonts.sty </cell><cell> 1997/09/17 v2.2e</cell></row>
+<row><cell> amsgen.sty </cell><cell> 1999/11/30 v2.0</cell></row>
+<row><cell> amsmath.sty </cell><cell> 2000/03/29 v2.08 AMS math features</cell></row>
+<row><cell> amsopn.sty </cell><cell> 1999/12/14 v2.01 operator names</cell></row>
+<row><cell> amssymb.sty </cell><cell> 1996/11/03 v2.2b</cell></row>
+<row><cell> amstext.sty </cell><cell> 1999/11/15 v2.0</cell></row>
+<row><cell> array.sty </cell><cell> 1998/05/13 v2.3m Tabular extension package (FMi)</cell></row>
+<row><cell> article.cls </cell><cell> 1999/09/10 v1.4a Standard LaTeX document class</cell></row>
+<row><cell> bm.sty </cell><cell> 1999/07/05 v1.0g Bold Symbol Support (DPC/FMi)</cell></row>
+<row><cell> color.sty </cell><cell> 1999/02/16 v1.0i Standard LaTeX Color (DPC)</cell></row>
+<row><cell> fontenc.sty </cell><cell> (version not available)</cell></row>
+<row><cell>graphics.sty </cell><cell> 1999/02/16 v1.0l Standard LaTeX Graphics (DPC,SPQR)</cell></row>
+<row><cell>graphicx.sty </cell><cell> 1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR)</cell></row>
+<row><cell> hpdftex.def </cell><cell> 2000/05/08 v6.70f Hyperref driver for pdfTeX</cell></row>
+<row><cell>hyperref.sty </cell><cell> 2000/05/08 v6.70f Hypertext links for LaTeX</cell></row>
+<row><cell> ifthen.sty </cell><cell> 1999/09/10 v1.1b Standard LaTeX ifthen package (DPC)</cell></row>
+<row><cell> keyval.sty </cell><cell> 1999/03/16 v1.13 key=value parser (DPC)</cell></row>
+<row><cell>longtable.sty </cell><cell> 1998/05/13 v4.09 Multi-page Table package (DPC)</cell></row>
+<row><cell>multicol.sty </cell><cell> 1999/10/21 v1.5w multicolumn formatting (FMi)</cell></row>
+<row><cell> nameref.sty </cell><cell> 2000/05/08 v2.18 Cross-referencing by name of section</cell></row>
+<row><cell> ot1phv.fd </cell><cell> 2000/01/12 PSNFSS-v8.1 scalable font definitions for OT1/phv.</cell></row>
+<row><cell> pd1enc.def </cell><cell> 2000/05/08 v6.70f Hyperref: PDFDocEncoding definition (HO)</cell></row>
+<row><cell> pifont.sty </cell><cell> 2000/01/12 PSNFSS-v8.1 Pi font support (SPQR) </cell></row>
+<row><cell>rotating.sty </cell><cell> 1997/09/26, v2.13 Rotation package</cell></row>
+<row><cell> size10.clo </cell><cell> 1999/09/10 v1.4a Standard LaTeX file (size option)</cell></row>
+<row><cell>stmaryrd.sty </cell><cell> 1994/03/03 St Mary's Road symbol package</cell></row>
+<row><cell> t1enc.def </cell><cell> 1999/12/08 v1.9x Standard LaTeX file</cell></row>
+<row><cell> t1phv.fd </cell><cell> 2000/01/12 PSNFSS-v8.1 scalable font definitions for T1/phv.</cell></row>
+<row><cell> t1ptm.fd </cell><cell> 2000/01/12 PSNFSS-v8.1 font definitions for T1/ptm.</cell></row>
+<row><cell> t2acmr.fd </cell><cell> 1999/01/07 v1.0 Computer Modern Cyrillic font definitions</cell></row>
+<row><cell> t2aenc.def </cell><cell> 1999/11/29 v1.0c Cyrillic encoding definition file</cell></row>
+<row><cell> t3enc.def </cell><cell> (version not available)</cell></row>
+<row><cell>textcomp.sty </cell><cell> 1999/12/08 v1.9x Standard LaTeX package</cell></row>
+<row><cell> times.sty </cell><cell> 2000/01/12 PSNFSS-v8.1 Times font as default roman (SPQR) </cell></row>
+<row><cell> tipa.sty </cell><cell> 1996/06/10 TIPA version 1.0</cell></row>
+<row><cell> trig.sty </cell><cell> 1999/03/16 v1.09 sin cos tan (DPC)</cell></row>
+<row><cell> ts1cmr.fd </cell><cell> 1999/05/25 v2.5h Standard LaTeX font definitions</cell></row>
+<row><cell> ts1enc.def </cell><cell> 1998/06/12 v3.0d (jk/car/fm) Standard LaTeX file</cell></row>
+<row><cell> ts1ptm.fd </cell><cell> 2000/01/12 PSNFSS-v8.1 font definitions for TS1/ptm.</cell></row>
+<row><cell> ulem.sty </cell><cell> 1997/04/21</cell></row>
+<row><cell> umsa.fd </cell><cell> 1995/01/05 v2.2e AMS font definitions</cell></row>
+<row><cell> umsb.fd </cell><cell> 1995/01/05 v2.2e AMS font definitions</cell></row>
+<row><cell> upsy.fd </cell><cell> 2000/01/12 PSNFSS-v8.1 font definitions for U/psy.</cell></row>
+<row><cell> upzd.fd </cell><cell> 2000/01/12 PSNFSS-v8.1 font definitions for U/pzd.</cell></row>
+<row><cell> url.sty </cell><cell> 1999/03/28 ver 1.5x Verb mode for urls, etc.</cell></row>
+<row><cell> Ustmry.fd </cell><cell> (version not available)</cell></row>
+<row><cell> uwasy.fd </cell><cell> 1999/05/13 v1.0iWasy-2 symbol font definitions</cell></row>
+<row><cell> wasysym.sty </cell><cell> 1999/05/13 v1.0i Wasy-2 symbol support package</cell></row>
+</table>
+</p>
+</div>
+</div>
+
+
+<div>
+<head>Extensions</head>
+<p>
+PassiveTeX interprets MathML natively (elements must use the MathML namespace).
+I also support a <code>bookmark</code> element in the
+<code>fotex</code> namespace, used to make PDF bookmarks. Usage is like this:
+<eg>
+&lt;xsl:template match="div2">
+ &lt;xsl:apply-templates select="head"/>
+ &lt;fotex:bookmark
+ xmlns:fotex="http://www.tug.org/fotex"
+ fotex-bookmark-level="2"
+ fotex-bookmark-label="{@id}">
+ &lt;xsl:value-of select="head"/>
+ &lt;/fotex:bookmark>
+ &lt;/fo:block>
+&lt;/xsl:template>
+</eg>
+</p>
+</div>
+
+
+<div>
+<head>Notes on conformance to the XSL draft specification of November 2000</head>
+&properties;
+</div>
+
+<div>
+<head>Sample files</head>
+<p>
+<list>
+<item> The TEI Lite description (<xref
+url="test/teiu5.xml">teiu5.xml</xref>) converted PDF as <xref
+url="test/teiu5.pdf">teiu5.pdf</xref></item>
+<item> A TEI test file (<xref
+url="test/exercise.xml">exercise.xml</xref>)
+converted to PDF as <xref
+url="test/exercise.pdf">exercise.pdf</xref></item>
+<item> A physics paper (<xref url="test/latextei.xml">latextei.xml</xref>) containing a fair
+ amount of MathML markup, originally
+ translated from LaTeX into XML.
+ It is used extensively as an example in the
+ <xref url="http://cseng.awl.com/bookpage.taf?ISBN=0-201-43311-7&amp;ptype=0&amp;catid=&amp;navmin=&amp;ctype=author&amp;catpage=&amp;seriesid=">LaTeX Web Companion</xref>.
+Here we see it
+ converted to <xref url="test/latextei.pdf">latextei.pdf</xref> using
+ <xref url="test/latextei.xsl">test/latextei.xsl</xref></item>
+<item> James Tauber prepared a simple XSL spec (<xref
+url="test/darkness.xsl">darkness.xsl</xref>) for Joseph Conrad's
+<xref url="test/darkness.xml"><emph>Heart of
+Darkness</emph></xref>, which I ran to PDF as <xref
+url="test/darkness.pdf">darkness.pdf</xref></item>
+</list>
+</p>
+</div>
+
+<div>
+<head>Concerns and problems</head>
+<p>
+Some points to bear in mind
+<list type="ordered">
+ <item> Obviously, the XSL FO spec is still a draft.
+ And this system is not conforming
+ precisely to the current draft. </item>
+ <item> This is an experiment system to check whether the
+ idea works. Expect something more polished eventually.</item>
+ <item> You need a modern TeX setup (like
+ <xref url="http://www.tug.org/teTeX/">teTeX</xref> or
+ <xref url="http://www.tug.org/texlive/">TeX Live</xref>)
+to get to grips with it.</item>
+ <item> Quite a few flow objects and characteristics are not dealt with yet.
+ I will add support for more things as needed or requested.</item>
+ <item> I do not have any objective check that what I think XSL FOs are
+ supposed to do is actually right :-}</item>
+ <item> I have only worked so far with the TEI Lite (XML version) and
+ Docbook DTDs, and probably misinterpreted half of what they say.</item>
+</list>
+</p>
+</div>
+
+<div>
+<head>Things for LaTeX users to remember</head>
+<p>
+<list type="unordered">
+<item> No use is made of LaTeX high-level constructs. No sections,
+ no lists, no cross-refs, no bibliographies; on the other hand,
+ some extensions in the <code>fotex:</code> namespace are supported
+(eg to get Acrobat bookmarks)
+</item>
+<item> XSL FO's underlying character set is Unicode; by default,
+ entities are mapped to their Unicode position;
+</item>
+<item> All vertical and horizontal space is explicit in the
+ specification
+</item>
+<item> Page and line breaking is left to TeX: the rest is up to you.
+</item>
+</list>
+</p>
+</div>
+
+<div>
+<head>Future directions</head>
+<p>
+<list type="unordered">
+<item>Complete the MathML handling</item>
+<item>Handle more variety in property values (eg colors, fonts) </item>
+<item>Deal with more complex tables</item>
+<item>Support SVG. How?
+ <list type="unordered">
+ <item>By direct intepretation and mapping to raw PDF</item>
+ <item>By translation to MetaPost, and spawning a MetaPost process</item>
+ <item>By pre-processing to existing TeX graphics languages</item>
+ </list>
+In any case, SVG fragments need to be recognized directly to perform in-line
+graphical functions (setting text at an angle?)
+</item>
+<item>Use Unicode-based TeX variant (Omega) to handle non-Latin material
+more naturally</item>
+</list>
+</p>
+<p>
+I will be very glad to discuss details with anyone. Contact me (Sebastian Rahtz) as
+<xref url="mailto:sebastian.rahtz@oucs.ox.ac.uk">sebastian.rahtz@oucs.ox.ac.uk</xref>
+</p>
+</div>
+</body>
+</text>
+</TEI.2>
+
diff --git a/Master/texmf-dist/doc/xmltex/passivetex/properties.xml b/Master/texmf-dist/doc/xmltex/passivetex/properties.xml
new file mode 100644
index 00000000000..85cd904b3c0
--- /dev/null
+++ b/Master/texmf-dist/doc/xmltex/passivetex/properties.xml
@@ -0,0 +1,592 @@
+<!--
+0. done
+1. more or less OK
+2. not done, but pending when for when I need it
+3. not done, cannot see how to do it
+4. N/A
+-->
+<p>
+The following general limitations apply to most of the PassiveTeX
+ implementation of XSL FO:
+<list type="ordered">
+<item>The `px' unit is not recognised</item>
+<item>Absolute dimensions always work, but proportional ones
+are often not recognized </item>
+<item>The functions allowed in attribute values are usually not
+ recognized</item>
+<item>There is no error checking at all, and all properies are
+ recognized; do not assume that they do anything...</item>
+</list>
+</p>
+<p>
+Most of the formatting objects are implemented more or less; the
+following are not implemented at all:
+<list type="ordered">
+<item><code>fo:bidi-override</code></item>
+<item><code>fo:color-profile</code></item>
+<item><code>fo:declarations</code></item>
+<item><code>fo:initial-property-set</code></item>
+<item><code>fo:instream-foreign-object</code></item>
+<item><code>fo:multi-case</code></item>
+<item><code>fo:multi-properties</code></item>
+<item><code>fo:multi-property-set</code></item>
+<item><code>fo:multi-switch</code></item>
+<item><code>fo:multi-toggle</code></item>
+<item><code>fo:region-end</code></item>
+<item><code>fo:region-start</code></item>
+<item><code>fo:table-footer</code></item>
+</list>
+</p>
+<div><head>Properties needed for basic conformance</head>
+<p>
+<table rend="rules">
+<row><cell>alignment-adjust</cell><cell>auto | percentage | length | inherit</cell><cell>Basic</cell>
+<cell>2. should be possible </cell></row>
+
+<row><cell>azimuth</cell><cell>angle | [[ left-side | far-left | left | center-left | center | center-right | right | far-right | right-side
+] || behind ] | leftwards | rightwards | inherit</cell><cell>Basic</cell>
+<cell>4. N/A </cell></row>
+
+<row><cell>background-color</cell><cell>color | transparent | inherit</cell><cell>Basic</cell> <cell>3. does not really map in TeX </cell></row>
+
+<row><cell>baseline-identifier</cell><cell>baseline | before-edge | text-before-edge | middle | after-edge
+| text-after-edge | ideographic | alphabetic | hanging | mathematical
+| inherit</cell><cell>Basic</cell>
+<cell>3. not at all sure where to start </cell></row>
+
+<row><cell>baseline-shift</cell><cell>baseline | sub | super | percentage | length | inherit</cell><cell>Basic</cell>
+<cell>1. basically works </cell></row>
+
+<row><cell>block-progression-dimension</cell><cell>auto | length | percentage | length-range | inherit</cell><cell>Basic</cell>
+<cell>3. do not really understand it </cell></row>
+
+<row><cell>border-after-color</cell><cell>color | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row>
+
+<row><cell>border-after-style</cell><cell>border-style | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row>
+
+<row><cell>border-after-width</cell><cell>border-width | length-conditional | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row>
+
+<row><cell>border-before-color</cell><cell>color | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row>
+
+<row><cell>border-before-style</cell><cell>border-style | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row>
+
+<row><cell>border-before-width</cell><cell>border-width | length-conditional | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row>
+
+<row><cell>border-bottom-color</cell><cell>color | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row>
+
+<row><cell>border-bottom-style</cell><cell>border-style | inherit</cell><cell>Basic</cell> <cell>1. used in places </cell></row>
+
+<row><cell>border-bottom-width</cell><cell>border-width | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row>
+
+<row><cell>border-end-color</cell><cell>color | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row>
+
+<row><cell>border-end-style</cell><cell>border-style | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row>
+
+<row><cell>border-end-width</cell><cell>border-width | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row>
+
+<row><cell>border-left-color</cell><cell>color | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row>
+
+<row><cell>border-left-style</cell><cell>border-style | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row>
+
+<row><cell>border-left-width</cell><cell>border-width | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row>
+
+<row><cell>border-right-color</cell><cell>color | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row>
+
+<row><cell>border-right-style</cell><cell>border-style | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row>
+
+<row><cell>border-right-width</cell><cell>border-width | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row>
+
+<row><cell>border-start-color</cell><cell>color | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row>
+
+<row><cell>border-start-style</cell><cell>border-style | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row>
+
+<row><cell>border-start-width</cell><cell>border-width | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row>
+
+<row><cell>border-top-color</cell><cell>color | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row>
+
+<row><cell>border-top-style</cell><cell>border-style | inherit</cell><cell>Basic</cell> <cell>1. used in places </cell></row>
+
+<row><cell>border-top-width</cell><cell>border-width | inherit</cell><cell>Basic</cell> <cell>2. works for blocks (non-breaking) </cell></row>
+
+<row><cell>break-after</cell><cell>auto | column | page | even-page | odd-page | inherit</cell><cell>Basic</cell> <cell>0. should be working </cell></row>
+
+<row><cell>break-before</cell><cell>auto | column | page | even-page | odd-page | inherit</cell><cell>Basic</cell> <cell>0. should be working </cell></row>
+
+<row><cell>character</cell><cell>character</cell><cell>Basic</cell> <cell>0. should be working </cell></row>
+
+<row><cell>clip</cell><cell>shape | auto | inherit</cell><cell>Basic</cell> <cell>2. theoretically possible </cell></row>
+
+<row><cell>color</cell><cell>color | inherit</cell><cell>Basic</cell> <cell>1. more or less complete </cell></row>
+
+<row><cell>column-number</cell><cell>number</cell><cell>Basic</cell> <cell>0. OK </cell></row>
+
+<row><cell>column-width</cell><cell>length</cell><cell>Basic</cell> <cell>0. OK </cell></row>
+
+<row><cell>content-type</cell><cell>string | auto</cell><cell>Basic</cell> <cell>4. N/A, I think </cell></row>
+
+<row><cell>cue-after</cell><cell>uri | none | inherit </cell><cell>Basic</cell> <cell>4. N/A </cell></row>
+
+<row><cell>cue-before</cell><cell>uri | none | inherit </cell><cell>Basic</cell> <cell>4. N/A </cell></row>
+
+<row><cell>direction</cell><cell>ltr | rtl | inherit</cell><cell>Basic</cell> <cell>3. waiting for extended TeX </cell></row>
+
+<row><cell>display-align</cell><cell>auto | before | center | after | inherit</cell><cell>Basic</cell>
+<cell>0. working </cell></row>
+
+<row><cell>dominant-baseline</cell><cell>auto | autosense-script | no-change | reset-size | ideographic | alphabetic | hanging | mathematical
+| inherit</cell><cell>Basic</cell>
+<cell>3. dont know where to begin </cell></row>
+
+<row><cell>elevation</cell><cell>angle | below | level | above | higher | lower | inherit</cell><cell>Basic</cell>
+<cell>4. N/A </cell></row>
+
+<row><cell>end-indent</cell><cell>length | inherit</cell><cell>Basic</cell> <cell>0. working </cell></row>
+
+<row><cell>flow-name</cell><cell>name</cell><cell>Basic</cell> <cell>0. working </cell></row>
+
+<row><cell>font-family</cell><cell>[[ family-name | generic-family ],]* [family-name | generic-family] | inherit</cell><cell>Basic</cell>
+<cell>1. more or less OK </cell></row>
+
+<row><cell>font-size</cell><cell>absolute-size | relative-size | length | percentage | inherit</cell><cell>Basic</cell>
+<cell>1. more or less all implemented </cell></row>
+
+<row><cell>font-style</cell><cell>normal | italic | oblique | backslant | inherit</cell><cell>Basic</cell> <cell>1. no oblique or backslant </cell></row>
+
+<row><cell>font-variant</cell><cell>normal | small-caps | inherit</cell><cell>Basic</cell> <cell>0. done </cell></row>
+
+<row><cell>font-weight</cell><cell>normal | bold | bolder | lighter | 100 | 200 | 300 | 400 | 500 | 600 | 700 | 800 | 900 | inherit</cell><cell>Basic</cell>
+<cell>1. normal and bold only at present, others to follow</cell></row>
+
+<row><cell>format</cell><cell>string</cell><cell>Basic</cell> <cell>3. dont want to think about it </cell></row>
+
+<row><cell>grouping-separator</cell><cell>character</cell><cell>Basic</cell> <cell>3. dont want to think about it </cell></row>
+
+<row><cell>grouping-size</cell><cell>number</cell><cell>Basic</cell> <cell>3. dont want to think about it </cell></row>
+
+<row><cell>height</cell><cell>length | percentage | auto | inherit</cell><cell>Basic</cell> <cell>2. should be OK, waiting for a need </cell></row>
+
+<row><cell>id</cell><cell> id</cell><cell>Basic</cell> <cell>0. used </cell></row>
+
+<row><cell>initial-page-number</cell><cell>auto | auto-odd | auto-even | number | inherit</cell><cell>Basic</cell> <cell>0. done </cell></row>
+
+<row><cell>inline-progression-dimension</cell><cell>auto | length | percentage | length-range | inherit</cell><cell>Basic</cell>
+<cell>3. have not considered at all </cell></row>
+
+<row><cell>keep-with-next</cell><cell>keep | inherit</cell><cell>Basic</cell> <cell>1. done in theory, not working 100%</cell></row>
+
+<row><cell>keep-with-previous</cell><cell>keep | inherit</cell><cell>Basic</cell> <cell>1. done in theory, not working 100% </cell></row>
+
+<row><cell>leader-length</cell><cell>length-range | inherit</cell><cell>Basic</cell> <cell>2. waiting to do soon </cell></row>
+
+<row><cell>leader-pattern</cell><cell>space | rule | dots | use-content | inherit</cell><cell>Basic</cell> <cell>2. waiting to do soon </cell></row>
+
+<row><cell>letter-value</cell><cell>auto | alphabetic | traditional</cell><cell>Basic</cell> <cell>3. dont want to think about it </cell></row>
+
+<row><cell>line-height</cell><cell>normal | length | number | percentage | space | inherit</cell><cell>Basic</cell>
+<cell>1. largely done </cell></row>
+
+<row><cell>line-stacking-strategy</cell><cell>line-height | font-height | max-height | inherit</cell><cell>Basic</cell> <cell>3. untouched </cell></row>
+
+<row><cell>margin-bottom</cell><cell>margin-width | inherit</cell><cell>Basic</cell> <cell>1. done in places </cell></row>
+
+<row><cell>margin-left</cell><cell>margin-width | inherit</cell><cell>Basic</cell> <cell>1. done in places </cell></row>
+
+<row><cell>margin-right</cell><cell>margin-width | inherit</cell><cell>Basic</cell> <cell>1. done in places </cell></row>
+
+<row><cell>margin-top</cell><cell>margin-width | inherit</cell><cell>Basic</cell> <cell>1. done in places </cell></row>
+
+<row><cell>master-name</cell><cell>name</cell><cell>Basic</cell> <cell>0. ok </cell></row>
+
+<row><cell>max-height</cell><cell>length | percentage | none | inherit </cell><cell>Basic</cell> <cell>2. should be doable </cell></row>
+
+<row><cell>max-width</cell><cell>length | percentage | none | inherit</cell><cell>Basic</cell> <cell>2. should be doable </cell></row>
+
+<row><cell>min-height</cell><cell>length | percentage | inherit </cell><cell>Basic</cell> <cell>2. should be doable </cell></row>
+
+<row><cell>min-width</cell><cell>length | percentage | inherit</cell><cell>Basic</cell> <cell>2. should be doable </cell></row>
+
+<row><cell>number-columns-repeated</cell><cell>number</cell><cell>Basic</cell>
+ <cell>2. doable in theory </cell></row>
+
+<row><cell>number-columns-spanned</cell><cell>number</cell><cell>Basic</cell> <cell>2. doable in theory </cell></row>
+
+<row><cell>number-rows-spanned</cell><cell>number</cell><cell>Basic</cell> <cell>2. doable in theory </cell></row>
+
+<row><cell>orphans</cell><cell>integer | inherit</cell><cell>Basic</cell> <cell>2. should be doable </cell></row>
+
+<row><cell>overflow</cell><cell>visible | hidden | scroll | auto | inherit</cell><cell>Basic</cell> <cell>2. theoretically </cell></row>
+
+<row><cell>padding-after</cell><cell>padding-width | length-conditional | inherit</cell><cell>Basic</cell> <cell>1. implemented crudely </cell></row>
+
+<row><cell>padding-before</cell><cell>padding-width | length-conditional | inherit</cell><cell>Basic</cell> <cell>1. implemented crudely </cell></row>
+
+<row><cell>padding-bottom</cell><cell>padding-width | inherit</cell><cell>Basic</cell> <cell>1. implemented crudely </cell></row>
+
+<row><cell>padding-end</cell><cell>padding-width | inherit</cell><cell>Basic</cell> <cell>1. implemented crudely </cell></row>
+
+<row><cell>padding-left</cell><cell>padding-width | inherit</cell><cell>Basic</cell> <cell>1. implemented crudely </cell></row>
+
+<row><cell>padding-right</cell><cell>padding-width | inherit</cell><cell>Basic</cell> <cell>1. implemented crudely </cell></row>
+
+<row><cell>padding-start</cell><cell>padding-width | inherit</cell><cell>Basic</cell> <cell>1. implemented crudely </cell></row>
+
+<row><cell>padding-top</cell><cell>padding-width | inherit</cell><cell>Basic</cell> <cell>1. implemented crudely </cell></row>
+
+<row><cell>page-break-after</cell><cell>auto | always | avoid | left | right | inherit</cell><cell>Basic</cell> <cell>1. Mostly implemented </cell></row>
+
+<row><cell>page-break-before</cell><cell>auto | always | avoid | left | right | inherit</cell><cell>Basic</cell> <cell>1. Mostly implemented </cell></row>
+
+<row><cell>page-height</cell><cell>auto | indefinite | length | inherit</cell><cell>Basic</cell> <cell>1. not all possibilities</cell></row>
+
+<row><cell>page-width</cell><cell>auto | indefinite | length | inherit</cell><cell>Basic</cell> <cell>1. not all possibilities</cell></row>
+
+<row><cell>pause-after</cell><cell>time | percentage | inherit</cell><cell>Basic</cell> <cell>4. N/A </cell></row>
+
+<row><cell>pause-before</cell><cell>time | percentage | inherit</cell><cell>Basic</cell> <cell>4. N/A </cell></row>
+
+<row><cell>pitch</cell><cell>frequency | x-low | low | medium | high | x-high | inherit</cell><cell>Basic</cell>
+<cell>4. N/A </cell></row>
+
+<row><cell>pitch-range</cell><cell>number | inherit</cell><cell>Basic</cell> <cell>4. N/A </cell></row>
+
+<row><cell>play-during</cell><cell>uri mix? repeat? | auto | none | inherit </cell><cell>Basic</cell> <cell>4. N/A </cell></row>
+
+<row><cell>precedence</cell><cell>true | false | inherit</cell><cell>Basic</cell> <cell>3. do not know where to start </cell></row>
+
+<row><cell>provisional-distance-between-starts</cell><cell>length | inherit</cell><cell>Basic</cell> <cell>1. does something, probably wrong </cell></row>
+
+<row><cell>provisional-label-separation</cell><cell>length | inherit</cell><cell>Basic</cell> <cell>1. does something, probably wrong </cell></row>
+
+<row><cell>ref-id</cell><cell>idref | inherit</cell><cell>Basic</cell> <cell>0. used in pagenumber </cell></row>
+
+<row><cell>reference-orientation</cell><cell> 0 | 90 | 180 | 270 | -90 | -180 | -270 | inherit</cell><cell>Basic</cell> <cell>2. doable for most objects </cell></row>
+
+<row><cell>region-name</cell><cell>xsl-region-body | xsl-region-start | xsl-region-end | xsl-region-before | xsl-region-after | xsl-before-float-separator
+| xsl-footnote-separator | name</cell><cell>Basic</cell>
+<cell>0. done </cell></row>
+
+<row><cell>relative-align</cell><cell>before | baseline | inherit</cell><cell>Basic</cell>
+<cell>3. have not got to grips with this </cell></row>
+
+<row><cell>richness</cell><cell>number | inherit</cell><cell>Basic</cell> <cell>4. N/A </cell></row>
+
+<row><cell>role</cell><cell>string | none | inherit</cell><cell>Basic</cell> <cell>4. N/A what should I do with it?</cell></row>
+
+<row><cell>rule-style</cell><cell>none | dotted | dashed | solid | double | groove | ridge | inherit</cell><cell>Basic</cell>
+<cell>1. done as far as possible </cell></row>
+
+<row><cell>rule-thickness</cell><cell>length</cell><cell>Basic</cell> <cell>0. done </cell></row>
+
+<row><cell>source-document</cell><cell>uri+ | none | inherit</cell><cell>Basic</cell> <cell>4. N/A not sure what to do with it</cell></row>
+
+<row><cell>space-after</cell><cell>space | inherit</cell><cell>Basic</cell> <cell>1. working more or less </cell></row>
+
+<row><cell>space-before</cell><cell>space | inherit</cell><cell>Basic</cell> <cell>1. working more or less </cell></row>
+
+<row><cell>space-end</cell><cell>space | inherit</cell><cell>Basic</cell> <cell>1. working more or less </cell></row>
+
+<row><cell>space-start</cell><cell>space | inherit</cell><cell>Basic</cell> <cell>1. working more or less </cell></row>
+
+<row><cell>speak</cell><cell>normal | none | spell-out | inherit</cell><cell>Basic</cell> <cell>4. N/A </cell></row>
+
+<row><cell>speak-header</cell><cell>once | always | inherit</cell><cell>Basic</cell> <cell>4. N/A </cell></row>
+
+<row><cell>speak-numeral</cell><cell>digits | continuous | inherit</cell><cell>Basic</cell> <cell>4. N/A </cell></row>
+
+<row><cell>speak-punctuation</cell><cell>code | none | inherit</cell><cell>Basic</cell> <cell>4. N/A </cell></row>
+
+<row><cell>speech-rate</cell><cell>number | x-slow | slow | medium | fast | x-fast | faster | slower | inherit</cell><cell>Basic</cell>
+<cell>4. N/A </cell></row>
+
+<row><cell>src</cell><cell> uri | inherit</cell><cell>Basic</cell> <cell>0. implemented </cell></row>
+
+<row><cell>start-indent</cell><cell>length | inherit</cell><cell>Basic</cell> <cell>0. done </cell></row>
+
+<row><cell>stress</cell><cell>number | inherit</cell><cell>Basic</cell> <cell>4. N/A </cell></row>
+
+<row><cell>text-align</cell><cell>start | center | end | justify | inside | outside | left | right | string | inherit</cell><cell>Basic</cell>
+<cell>0. done </cell></row>
+
+<row><cell>text-indent</cell><cell>length | percentage | inherit</cell><cell>Basic</cell> <cell>0. done </cell></row>
+
+<row><cell>visibility</cell><cell>visible | hidden | collapse | inherit</cell><cell>Basic</cell> <cell>2. I think can do this </cell></row>
+
+<row><cell>voice-family</cell><cell>[[specific-voice | generic-voice ],]* [specific-voice | generic-voice ] | inherit</cell><cell>Basic</cell>
+<cell>4. N/A </cell></row>
+
+<row><cell>volume</cell><cell>number | percentage | silent | x-soft | soft | medium | loud | x-loud | inherit</cell><cell>Basic</cell>
+<cell>4. N/A </cell></row>
+
+<row><cell>widows</cell><cell>integer | inherit</cell><cell>Basic</cell> <cell>2. should be doable </cell></row>
+
+<row><cell>width</cell><cell>length | percentage | auto | inherit</cell><cell>Basic</cell> <cell>2. should be OK, waiting for a need </cell></row>
+
+<row><cell>wrap-option</cell><cell>no-wrap | wrap | inherit</cell><cell>Basic</cell> <cell>0. should be working </cell></row>
+
+<row><cell>writing-mode</cell><cell>lr-tb | rl-tb | tb-rl | lr | rl | tb | inherit</cell><cell>Basic</cell> <cell>3. will need an extended TeX </cell></row>
+
+<row><cell>z-index</cell><cell>auto | integer | inherit</cell><cell>Basic</cell> <cell>3. dont know where to start </cell></row>
+</table>
+</p>
+</div>
+
+
+<div><head>Properties needed for full conformance</head>
+<p>
+<table rend="rules">
+<row><cell>absolute-position</cell><cell>auto | absolute | fixed | inherit</cell><cell>Complete</cell> <cell>2. should be doable </cell></row>
+
+<row><cell>background</cell><cell>[background-color || background-image
+|| background-repeat || background-attachment || background-position
+| ]]inherit</cell><cell>Complete</cell>
+<cell>1. implemented but very fragile </cell></row>
+
+<row><cell>background-position</cell><cell>[ [percentage | length ]{1,2} | [ [top | center | bottom] || [left | center | right] ] ] | inherit</cell><cell>Complete</cell>
+<cell> </cell></row>
+
+<row><cell>border</cell><cell>[ border-width || border-style || color ] | inherit</cell><cell>Complete</cell>
+<cell> </cell></row>
+
+<row><cell>border-bottom</cell><cell>[ border-top-width || border-style || color ] | inherit</cell><cell>Complete</cell>
+<cell> </cell></row>
+
+<row><cell>border-color</cell><cell>color{1,4} | transparent | inherit</cell><cell>Complete</cell> <cell> </cell></row>
+
+<row><cell>border-left</cell><cell>[ border-top-width || border-style || color ] | inherit</cell><cell>Complete</cell>
+<cell> </cell></row>
+
+<row><cell>border-right</cell><cell>[ border-top-width || border-style || color ] | inherit</cell><cell>Complete</cell>
+<cell> </cell></row>
+
+<row><cell>border-spacing</cell><cell>length length? | inherit</cell><cell>Complete</cell> <cell> </cell></row>
+
+<row><cell>border-style</cell><cell>border-style{1,4} | inherit</cell><cell>Complete</cell> <cell> </cell></row>
+
+<row><cell>border-top</cell><cell>[ border-top-width || border-style || color ] | inherit</cell><cell>Complete</cell>
+<cell> </cell></row>
+
+<row><cell>border-width</cell><cell>border-width{1,4} | inherit</cell><cell>Complete</cell> <cell> </cell></row>
+
+<row><cell>caption-side</cell><cell>before | after | start | end | top | bottom | left | right | inherit</cell><cell>Complete</cell> <cell> </cell></row>
+
+<row><cell>cue</cell><cell>cue-before || cue-after | inherit</cell><cell>Complete</cell> <cell> </cell></row>
+
+<row><cell>font</cell><cell>[ [ font-style || font-variant || font-weight ]? font-size [ / line-height]? font-family
+] | caption | icon | menu | message-box | small-caption | status-bar
+| inherit</cell><cell>Complete</cell>
+<cell> </cell></row>
+
+<row><cell>margin</cell><cell>margin-width{1,4} | inherit </cell><cell>Complete</cell> <cell> </cell></row>
+
+<row><cell>padding</cell><cell>padding-width{1,4} | inherit</cell><cell>Complete</cell> <cell> </cell></row>
+
+<row><cell>page-break-inside</cell><cell>avoid | auto | inherit</cell><cell>Complete</cell> <cell> </cell></row>
+
+<row><cell>pause</cell><cell>[time | percentage]{1,2} | inherit</cell><cell>Complete</cell> <cell> </cell></row>
+
+<row><cell>position</cell><cell>static | relative | absolute | fixed | inherit</cell><cell>Complete</cell> <cell> </cell></row>
+
+<row><cell>size</cell><cell>length{1,2} | auto | landscape | portrait | inherit</cell><cell>Complete</cell>
+<cell> </cell></row>
+
+<row><cell>vertical-align</cell><cell>baseline | middle | sub | super | text-top | text-bottom | percentage | length | top | bottom | inherit</cell><cell>Complete</cell>
+<cell> </cell></row>
+
+<row><cell>white-space</cell><cell>normal | pre | nowrap | inherit</cell><cell>Complete</cell> <cell> </cell></row>
+
+<row><cell>xml:lang</cell><cell>country-language | inherit</cell><cell>Complete</cell> <cell>2. not done yet, but will be </cell></row>
+</table>
+</p>
+</div>
+
+<div><head>Properties needed for extended conformance</head>
+<p>
+<table rend="rules">
+<row><cell>table-layout</cell><cell>auto | fixed | inherit</cell><cell>Extended.Fallback: fixed</cell> <cell> </cell></row>
+
+<row><cell>background-attachment</cell><cell>scroll | fixed | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>2. I can see where I might start </cell></row>
+
+<row><cell>background-image</cell><cell>uri | none | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>2. I can see where I might start </cell></row>
+
+<row><cell>background-position-horizontal</cell><cell>percentage | length | left | center | right | inherit</cell><cell>Extended.Fallback: Initial value</cell>
+<cell>2. I can see where I might start </cell></row>
+
+<row><cell>background-position-vertical</cell><cell>percentage | length | top | center | bottom | inherit</cell><cell>Extended.Fallback: Initial value</cell>
+<cell>2. I can see where I might start </cell></row>
+
+<row><cell>border-collapse</cell><cell>collapse | separate | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row>
+
+<row><cell>border-separation</cell><cell>length-bp-ip-direction | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row>
+
+<row><cell>column-count</cell><cell>number | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>0. implemented </cell></row>
+
+<row><cell>content-height</cell><cell>auto | length | percentage | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>1. done for graphics </cell></row>
+
+<row><cell>content-width</cell><cell>auto | length | percentage | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>1. done for graphics </cell></row>
+
+<row><cell>country</cell><cell>none | country | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>2. waiting to find a use for it </cell></row>
+
+<row><cell>empty-cells</cell><cell>show | hide | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row>
+
+<row><cell>ends-row</cell><cell>yes | no</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row>
+
+<row><cell>font-height-override-after</cell><cell>use-font-metrics | length | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>3. need extended TeX </cell></row>
+
+<row><cell>font-height-override-before</cell><cell>use-font-metrics | length | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>3. need extended TeX </cell></row>
+
+<row><cell>font-size-adjust</cell><cell>number | none | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>2. doable, I think </cell></row>
+
+<row><cell>font-stretch</cell><cell>normal | wider | narrower | ultra-condensed | extra-condensed | condensed | semi-condensed | semi-expanded |
+expanded | extra-expanded | ultra-expanded |inherit</cell><cell>Extended.Fallback: Initial value</cell>
+<cell>0. should be OK </cell></row>
+
+<row><cell>glyph-orientation-horizontal</cell><cell>angle | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>3. need extended TeX </cell></row>
+
+<row><cell>glyph-orientation-vertical</cell><cell>auto | angle | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>3. need extended TeX </cell></row>
+
+<row><cell>hyphenate</cell><cell>false | true | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>0. done </cell></row>
+
+<row><cell>keep-together</cell><cell>keep | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row>
+
+<row><cell>language</cell><cell>none | language | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>0. done, if underlying TeX system OK </cell></row>
+
+<row><cell>last-line-end-indent</cell><cell>length | percentage | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row>
+
+<row><cell>leader-alignment</cell><cell>none | reference-area | page | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row>
+
+<row><cell>leader-pattern-width</cell><cell>use-font-metrics | length | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row>
+
+<row><cell>letter-spacing</cell><cell>normal | length | space | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>2. doable in limited circumstances </cell></row>
+
+<row><cell>line-height-shift-adjustment</cell><cell>consider-shifts | disregard-shifts | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row>
+
+<row><cell>linefeed-treatment</cell><cell>ignore | preserve | treat-as-space | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>2. doable, if tiresome </cell></row>
+
+<row><cell>relative-position</cell><cell>auto | static | relative | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row>
+
+<row><cell>scaling</cell><cell>uniform | non-uniform | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>0. ok </cell></row>
+
+<row><cell>scaling-method</cell><cell>auto | integer-pixels | resample-any-method | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>4. N/A, I think </cell></row>
+
+<row><cell>score-spaces</cell><cell>true | false | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>3. dont think I can do this </cell></row>
+
+<row><cell>space-treatment</cell><cell>ignore | preserve | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>0. seems to work </cell></row>
+
+<row><cell>span</cell><cell>none | all | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>3. proving hard </cell></row>
+
+<row><cell>starts-row</cell><cell>yes |
+ no</cell><cell>Extended.Fallback: Initial value</cell>
+ <cell>0. works</cell></row>
+
+<row><cell>suppress-at-line-break</cell><cell>auto | suppress | retain | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row>
+
+<row><cell>table-omit-footer-at-break</cell><cell>yes | no</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row>
+
+<row><cell>table-omit-header-at-break</cell><cell>yes | no</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row>
+
+<row><cell>text-align-last</cell><cell>relative | start | center | end | justify | inside | outside | left | right | string | inherit</cell><cell>Extended.Fallback: Initial value</cell>
+<cell>1. works, usually </cell></row>
+
+<row><cell>text-decoration</cell><cell>none | [ [ underline | no-underline] || [ overline | no-overline ] || [ line-through | no-line-through ] || [ blink | no-blink ] ]
+
+| inherit</cell><cell>Extended.Fallback: Initial value</cell>
+<cell>1. done for some possibilities, not all </cell></row>
+
+<row><cell>text-shadow</cell><cell>none | [color || length length length? ,]* [color || length length length?] | inherit</cell><cell>Extended.Fallback: Initial value</cell>
+<cell> </cell></row>
+
+<row><cell>text-transform</cell><cell>capitalize | uppercase | lowercase | none | </cell><cell>Extended.Fallback: Initial value</cell> <cell>2. doable </cell></row>
+
+<row><cell>treat-as-word-space</cell><cell>auto | yes | no | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row>
+
+<row><cell>white-space-collapse</cell><cell>false | true | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell>0. Done </cell></row>
+
+<row><cell>word-spacing</cell><cell>normal | length | space | inherit</cell><cell>Extended.Fallback: Initial value</cell> <cell> </cell></row>
+
+<row><cell>bottom</cell><cell>length | percentage | auto | inherit</cell><cell>Extended.Fallback: N/A due to fallback for absolute-position, relative-position</cell> <cell>2. doable, I think </cell></row>
+
+<row><cell>left</cell><cell>length | percentage | auto | inherit</cell><cell>Extended.Fallback: N/A due to fallback for absolute-position, relative-position</cell> <cell>2. doable, I think </cell></row>
+
+<row><cell>right</cell><cell>length | percentage | auto | inherit</cell><cell>Extended.Fallback: N/A due to fallback for absolute-position, relative-position</cell> <cell>2. doable, I think </cell></row>
+
+<row><cell>top</cell><cell>length | percentage | auto | inherit</cell><cell>Extended.Fallback: N/A due to fallback for absolute-position, relative-position</cell> <cell>2. doable, I think </cell></row>
+
+<row><cell>column-gap</cell><cell>length | percentage | inherit</cell><cell>Extended.Fallback: N/A due to fallback for column-count</cell> <cell>1. implemented (not for all value types) </cell></row>
+
+<row><cell>hyphenation-character</cell><cell>character | inherit</cell><cell>Extended.Fallback: N/A due to fallback for hyphenate</cell> <cell>3. need to think about how to do this </cell></row>
+
+<row><cell>hyphenation-keep</cell><cell>auto | column | page | inherit</cell><cell>Extended.Fallback: N/A due to fallback for hyphenate</cell> <cell>3. not sure how to do this </cell></row>
+
+<row><cell>hyphenation-ladder-count</cell><cell>no-limit | number | inherit</cell><cell>Extended.Fallback: N/A due to fallback for hyphenate</cell> <cell>3. I dont see how to do this </cell></row>
+
+<row><cell>hyphenation-push-character-count</cell><cell>number | inherit</cell><cell>Extended.Fallback: N/A due to fallback for hyphenate</cell> <cell>2. I think this maps in TeX </cell></row>
+
+<row><cell>hyphenation-remain-character-count</cell><cell>number | inherit</cell><cell>Extended.Fallback: N/A due to fallback for hyphenate</cell> <cell>2. I think this maps in TeX </cell></row>
+
+<row><cell>color-profile-name</cell><cell>name | inherit</cell><cell>Extended.Fallback: N/A use fallback for fo:color-profile</cell> <cell>3. would need a lot of thought </cell></row>
+
+<row><cell>rendering-intent</cell><cell>auto | perceptual | relative-colorimetric | saturation | absolute-colorimetric | inherit</cell><cell>Extended.Fallback: N/A use fallback for fo:color-profile</cell> <cell>3. not sure how to do this </cell></row>
+
+<row><cell>clear</cell><cell>start | end | left | right | both | none | inherit</cell><cell>Extended.Fallback: N/A use fallback for fo:float</cell> <cell> </cell></row>
+
+<row><cell>float</cell><cell>before | start | end | left | right | none | inherit</cell><cell>Extended.Fallback: N/A use fallback for fo:float</cell> <cell> </cell></row>
+
+<row><cell>marker-class-name</cell><cell>name</cell><cell>Extended.Fallback: N/A use fallback for fo:marker</cell> <cell> </cell></row>
+
+<row><cell>active-state</cell><cell>link | visited | active | hover | focus</cell><cell>Extended.Fallback: N/A use fallback for fo:multi-properties</cell> <cell> </cell></row>
+
+<row><cell>auto-restore</cell><cell>yes | no</cell><cell>Extended.Fallback: N/A use fallback for fo:multi-switch</cell> <cell> </cell></row>
+
+<row><cell>case-name</cell><cell>name</cell><cell>Extended.Fallback: N/A use fallback for fo:multi-switch</cell> <cell> </cell></row>
+
+<row><cell>case-title</cell><cell>string</cell><cell>Extended.Fallback: N/A use fallback for fo:multi-switch</cell> <cell> </cell></row>
+
+<row><cell>starting-state</cell><cell>show | hide</cell><cell>Extended.Fallback: N/A use fallback for fo:multi-switch</cell> <cell> </cell></row>
+
+<row><cell>switch-to</cell><cell>xsl-preceding | xsl-following | xsl-any | name[ name]*</cell><cell>Extended.Fallback: N/A use fallback for fo:multi-switch</cell> <cell> </cell></row>
+
+<row><cell>extent</cell><cell>length | percentage | inherit</cell><cell>Extended.Fallback: N/A use fallback for fo:region-before, fo:region-after, fo:region-start, and fo:region-end</cell> <cell> </cell></row>
+
+<row><cell>blank-or-not-blank</cell><cell>blank | not-blank | any | inherit</cell><cell>Extended.Fallback: N/A use fallback for fo:repeatable-page-master-alternatives</cell> <cell>3. dont want to think about it </cell></row>
+
+<row><cell>odd-or-even</cell><cell>odd | even | any | inherit</cell><cell>Extended.Fallback: N/A use fallback for fo:repeatable-page-master-alternatives</cell> <cell> </cell></row>
+
+<row><cell>page-position</cell><cell>first | last | rest | any | inherit</cell><cell>Extended.Fallback: N/A use fallback for fo:repeatable-page-master-alternatives</cell> <cell> </cell></row>
+
+<row><cell>maximum-repeats</cell><cell>number | no-limit | inherit</cell><cell>Extended.Fallback: N/A use fallback for fo:repeatable-page-master-reference and fo:repeatable-page-master-alternatives</cell> <cell> </cell></row>
+
+<row><cell>retrieve-boundary</cell><cell>page | page-sequence | document</cell><cell>Extended.Fallback: N/A use fallback for fo:retrieve-marker</cell> <cell> </cell></row>
+
+<row><cell>retrieve-class-name</cell><cell>name</cell><cell>Extended.Fallback:
+ N/A use fallback for fo:retrieve-marker</cell> <cell>1. works usually </cell></row>
+
+<row><cell>retrieve-position</cell><cell>first-starting-within-page | first-including-carryover | last-starting-within-page | last-ending-within-page</cell><cell>Extended.Fallback: N/A use fallback for fo:retrieve-marker</cell>
+<cell> </cell></row>
+
+<row><cell>destination-placement-offset</cell><cell>length</cell><cell>Extended.Fallback: N/A use fallback for fo:simple-link</cell> <cell> </cell></row>
+
+<row><cell>external-destination</cell><cell>uri-reference</cell><cell>Extended.Fallback:
+ N/A use fallback for fo:simple-link</cell> <cell>0. works ok </cell></row>
+
+<row><cell>indicate-destination</cell><cell>yes |
+ no</cell><cell>Extended.Fallback: N/A use fallback for
+ fo:simple-link</cell> <cell>1. should work </cell></row>
+
+<row><cell>internal-destination</cell><cell>null string |
+ idref</cell><cell>Extended.Fallback: N/A use fallback for
+ fo:simple-link</cell> <cell>0. works </cell></row>
+
+<row><cell>show-destination</cell><cell>replace | new</cell><cell>Extended.Fallback: N/A use fallback for fo:simple-link</cell> <cell> </cell></row>
+
+<row><cell>force-page-count</cell><cell>auto | even | odd | end-on-even | end-on-odd | no-force | inherit</cell><cell>Extended.Fallback: no-force</cell>
+<cell> </cell></row>
+
+<row><cell>background-repeat</cell><cell>repeat | repeat-x | repeat-y | no-repeat | inherit</cell><cell>Extended.Fallback: no-repeat</cell> <cell> </cell></row>
+
+<row><cell>script</cell><cell>none | auto | script | inherit</cell><cell>Extended.Fallback: none</cell> <cell>4. dont know what to do with it </cell></row>
+
+<row><cell>unicode-bidi</cell><cell>normal | embed | bidi-override | inherit</cell><cell>Extended.Fallback: See prose</cell> <cell> </cell>
+</row>
+</table>
+</p>
+</div>
diff --git a/Master/texmf-dist/doc/xmltex/passivetex/test.xml b/Master/texmf-dist/doc/xmltex/passivetex/test.xml
new file mode 100644
index 00000000000..321a22835d4
--- /dev/null
+++ b/Master/texmf-dist/doc/xmltex/passivetex/test.xml
@@ -0,0 +1,280 @@
+<?xml version="1.0"?>
+<!DOCTYPE TEI.2 SYSTEM "teixlite.dtd">
+<TEI.2>
+ <teiHeader>
+ <fileDesc>
+ <titleStmt>
+ <title>This and that</title>
+ </titleStmt>
+ <publicationStmt>
+ <p> </p>
+ </publicationStmt>
+ <sourceDesc>
+ <p></p>
+ </sourceDesc>
+ </fileDesc>
+ <revisionDesc>
+ <list>
+ <item><date>October 10th 1999</date>Initial version</item>
+ </list>
+ </revisionDesc>
+ </teiHeader>
+ <text>
+<front>
+ <docTitle>
+ <titlePart type="main">Texts for beginners</titlePart>
+ </docTitle>
+<docAuthor>A N Other</docAuthor>
+<docDate>October 10th 1999</docDate>
+</front>
+<body>
+
+<div><head>The table in section 1</head>
+<p>
+Over the whine of the electric mixer, Mara heard her name called, but she
+didn't bother to acknowledge it. Instead she added more sugar to the egg
+whites and continued to beat them until they formed stiff peaks. She was
+spooning the meringue on to the pie filling when she heard the hum of the
+wheelchair approaching the kitchen.
+</p><p>
+`Mara, the mailman just drove by.' The chair rolled to a stop inside the
+room. `I'm expecting some correspondence from Fitzgerald. Will you see if
+it's come?'
+</p><p>
+Mara didn't turn around. I'm busy at the moment, Adam.' She continued to
+spread the meringue thickly over the pie, ignoring the instant of tense
+silence.
+</p>
+<div><head>The table in section 1</head>
+<q rend="display">
+<table cols="3" rend="inline">
+<row><cell cols="3">AT&amp;T Common Stock</cell></row>
+<row><cell>Year </cell><cell> Price</cell><cell>Dividend</cell></row>
+<row><cell>1971</cell><cell>41--54</cell><cell>$2.60</cell></row>
+<row><cell> 2</cell><cell>41--54</cell><cell>2.70</cell></row>
+<row><cell> 3</cell><cell>46--55</cell><cell>2.87</cell></row>
+<row><cell> 4</cell><cell>40--53</cell><cell>3.24</cell></row>
+<row><cell> 5</cell><cell>45--52</cell><cell>3.40</cell></row>
+<row><cell> 6</cell><cell>51--59</cell><cell>.95*</cell></row>
+<row><cell cols="3">(* first quarter only)</cell></row>
+</table>
+</q>
+
+<eg>
+<![CDATA[
+<xsl:template match="eg">
+ <fo:block font-family="{$typewriterFont}"
+ white-space-collapse="false"
+ wrap-option="no-wrap"
+ text-indent="0em"
+ start-indent="{$exampleMargin}"
+ text-align="start"
+ font-size="{$exampleSize}"
+ background="red"
+ color="white"
+ space-before.optimum="4pt"
+ space-after.optimum="4pt"
+ >
+ <xsl:value-of select="translate(.,' ','&#160;')"/>
+ </fo:block>
+</xsl:template>
+]]>
+</eg>
+</div>
+</div>
+<div><head>LOOMINGS</head>
+
+<p>Call me Ishmael. Some years ago&#8212;never mind how long
+precisely &#8212;having little or no money in my purse, and nothing
+particular to interest me on shore, I thought I would sail about a
+little and see the watery part of the world. It is a way I have of
+driving off the spleen, and regulating the circulation. Whenever I
+find myself growing grim about the mouth; whenever it is a damp,
+drizzly November in my soul; whenever I find myself involuntarily
+pausing before coffin warehouses, and bringing up the rear of every
+funeral I meet; and especially whenever my hypos get such an upper
+hand of me, that it requires a strong moral principle to prevent me
+from deliberately stepping into the street, and methodically knocking
+people's hats off&#8212;then, I account it high time to get to sea as
+soon as I can. This is my substitute for pistol and ball. With a
+philosophical flourish Cato throws himself upon his sword; I quietly
+take to the ship. There is nothing surprising in this. If they but
+knew it, almost all men in their degree, some time or other, cherish
+very nearly the same feelings towards the ocean with me. There now is
+your insular city of the Manhattoes, belted round by wharves as Indian
+isles by coral reefs&#8212;commerce surrounds it with her surf. Right
+and left, the streets take you waterward. Its extreme down-town is
+the battery, where that noble mole is washed by waves, and cooled by
+breezes, which a few hours previous were out of sight of land. Look
+at the crowds of water-gazers there. Circumambulate the city of a
+dreamy Sabbath afternoon. Go from Corlears Hook to Coenties Slip, and
+from thence, by Whitehall northward. What do you see?&#8212;Posted
+like silent sentinels all around the town, stand thousands upon
+thousands of mortal men fixed in ocean reveries. Some leaning against
+the spiles; some seated upon the pier-heads; some looking over the
+bulwarks glasses! of ships from China; some high aloft in the
+rigging, as if striving to get a still better seaward peep. But these
+are all landsmen; of week days pent up in lath and plaster&#8212;tied
+to counters, nailed to benches, clinched to desks. How then is this?
+Are the green fields gone? What do they here? But look! here come
+more crowds, pacing straight for the water, and seemingly bound for a
+dive. Strange! Nothing will content them but the extremest limit of
+the land; loitering under the shady lee of yonder warehouses will not
+suffice. No. They must get just as nigh the water as they possibly
+can without falling in. And there they stand&#8212;miles of
+them&#8212;leagues. </p>
+
+<p> Inlanders all, they come from lanes and alleys, streets and
+avenues, &#8212;north, east, south, and west. Yet here they all
+unite. Tell me, does the magnetic virtue of the needles of the
+compasses of all those ships attract them thither? Once more. Say,
+you are in the country; in some high land of lakes. Take almost any
+path you please, and ten to one it carries you down in a dale, and
+leaves you there by a pool in the stream. There is magic in it. Let
+the most absent-minded of men be plunged in his deepest
+reveries&#8212;stand that man on his legs, set his feet a-going, and
+he will infallibly lead you to water, if water there be in all that
+region. Should you ever be athirst in the great American desert, try
+this experiment, if your caravan happen to be supplied with a
+metaphysical professor. Yes, as every one knows, meditation and water
+are wedded for ever.
+ But here is an artist. He desires to paint you the dreamiest,
+shadiest, quietest, most enchanting bit of romantic landscape in all
+the valley of the Saco. What is the chief element he employs? There
+stand his trees, each with a hollow trunk, as if a hermit and a
+crucifix were within; and here sleeps his meadow, and there sleep his
+cattle; and up from yonder cottage goes a sleepy smoke. Deep into
+distant woodlands winds a mazy way, reaching to overlapping spurs of
+mountains bathed in their hill-side blue. But though the picture lies
+thus tranced, and though this pine-tree shakes down its sighs like
+leaves upon this shepherd's head, yet all were vain, unless the
+shepherd's eye were fixed upon the magic stream before him. Go visit
+the Prairies in June, when for scores on scores of miles you wade
+knee-deep among Tiger-lilies&#8212;what is the one charm wanting?
+&#8212;Water &#8212;there is not a drop of water there! Were Niagara
+but a cataract of sand, would you travel your thousand miles to see
+it? Why did the poor poet of Tennessee, upon suddenly receiving two
+handfuls of silver, deliberate whether to buy him a coat, which he
+sadly needed, or invest his money in a pedestrian trip to Rockaway
+Beach? Why is almost every robust healthy boy with a robust healthy
+soul in him, at some time or other crazy to go to sea? Why upon your
+first voyage as a passenger, did you yourself feel such a mystical
+vibration, when first told that you and your ship were now out of
+sight of land? Why did the old Persians hold the sea holy? Why did
+the Greeks give it a separate deity, and own brother of Jove? Surely
+all this is not without meaning. And still deeper the meaning of that
+story of Narcissus, who because he could not grasp the tormenting,
+mild image he saw in the fountain, plunged into it and was drowned.
+But that same image, we ourselves see in all rivers and oceans. It is
+the image of the ungraspable phantom of life; and this is the key to
+it all. Now, when I say that I am in the habit of going to sea
+whenever I begin to grow hazy about the eyes, and begin to be over
+conscious of my lungs, I do not mean to have it inferred that I ever
+go to sea as a passenger. For to go as a passenger you must needs
+have a purse, and a purse is but a rag unless you have something in
+it. Besides, passengers get sea-sick &#8212;grow quarrelsome
+&#8212;don't sleep of nights &#8212;do not enjoy themselves much, as a
+general thing; &#8212;no, I never go as a passenger; nor, though I am
+something of a salt, do I ever go to sea as a Commodore, or a Captain,
+or a Cook. I abandon the glory and distinction of such offices to
+those who like them. For my part, I abominate all honorable
+respectable toils, trials, and tribulations of every kind whatsoever.
+It is quite as much as I can do to take care of myself, without taking
+care of ships, barques, brigs, schooners, and what not. And as for
+going as cook, &#8212; though I confess there is considerable glory in
+that, a cook being a sort of officer on ship-board &#8212;yet,
+somehow, I never fancied broiling fowls; &#8212;though once broiled,
+judiciously buttered, and judgmatically salted and peppered, there is
+no one who will speak more respectfully, not to say reverentially, of
+a broiled fowl than I will. It is out of the idolatrous dotings of
+the old Egyptians upon broiled ibis and roasted river horse, that you
+see the mummies of those creatures in their huge bake-houses the
+pyramids. No, when I go to sea, I go as a simple sailor, right before
+the mast, plumb down into the forecastle, aloft there to the royal
+mast-head. True, they rather order me about some, and make me jump
+from spar to spar, like a grasshopper in a May meadow. And at first,
+this sort of thing is unpleasant enough. It touches one's sense of
+honor, particularly if you come of an old established family in the
+land, the van Rensselaers, or Randolphs, or Hardicanutes. And more
+than all, if just previous to putting your hand into the tar-pot, you
+have been lording it as a country schoolmaster, making the tallest
+boys stand in awe of you. The transition is a keen one, I assure you,
+from the schoolmaster to a sailor, and requires a strong decoction of
+Seneca and the Stoics to enable you to grin and bear it. But even
+this wears off in time. What of it, if some old hunks of a
+sea-captain orders me to get a broom and sweep down the decks? What
+does that indignity amount to, weighed, I mean, in the scales of the
+New Testament? Do you think the archangel Gabriel thinks anything the
+less of me,
+ because I promptly and respectfully obey that old hunks in that
+particular instance? Who aint a slave? Tell me that. Well, then,
+however the old sea-captains may order me about&#8212;however they may
+thump and punch me about, I have the satisfaction of knowing that it
+is all right; that everybody else is one way or other served in much
+the same way &#8212; either in a physical or metaphysical point of
+view, that is; and so the universal thump is passed round, and all
+hands should rub each other's shoulder-blades, and be content. Again,
+I always go to sea as a sailor, because they make a point of paying me
+for my trouble, whereas they never pay passengers a single penny that
+I ever heard of. On the contrary, passengers themselves must pay.
+And there is all the difference in the world between paying and being
+paid. The act of paying is perhaps the most uncomfortable infliction
+that the two orchard thieves entailed upon us. But being paid,
+&#8212;what will compare with it? The urbane activity with which a
+man receives money is really marvellous, considering that we so
+earnestly believe money to be the root of all earthly ills, and that
+on no account can a monied man enter heaven. Ah! how cheerfully we
+consign ourselves to perdition! Finally, I always go to sea as a
+sailor, because of the wholesome exercise and pure air of the
+forecastle deck. For as in this world, head winds are far more
+prevalent than winds from astern (that is, if you never violate the
+Pythagorean maxim), so for the most part the Commodore on the
+quarter-deck gets his atmosphere at second hand from the sailors on
+the forecastle. He thinks he breathes it first; but not so. In much
+the same way do the commonalty lead their leaders in many other
+things, at the same time that the leaders little suspect it. But
+wherefore it was that after having repeatedly smelt the sea as a
+merchant sailor, I should now take it into my head to go on a whaling
+voyage; this the invisible police officer of the Fates, who has the
+constant surveillance of me, and secretly dogs me, and influences me
+in some unaccountable way &#8212;he can better answer than any one
+else. And, doubtless, my going on this whaling
+ voyage, formed part of the grand programme of Providence that was drawn up a
+long time ago. It came in as a sort of brief interlude and solo between more
+extensive performances. I take it that this part of the bill must have run
+something like this:
+<list>
+<item>Grand Contested Election for the Presidency of the
+United States. </item>
+<item>Whaling Voyage by one Ishmael. </item>
+<item>Bloody Battle in Affghanistan.</item>
+</list>Though I cannot tell why it was exactly that those stage
+managers, the Fates, put me down for this shabby part of a whaling voyage,
+when others were set down for magnificent parts in high tragedies, and short
+and easy parts in genteel comedies, and jolly parts in farces &#8212;though I
+cannot tell why this was exactly; yet, now that I recall all the
+circumstances, I think I can see a little into the springs and motives which
+being cunningly presented to me under various disguises, induced me to set
+about
+performing the part I did, besides cajoling me into the delusion that it was
+a choice resulting from my own unbiased freewill and discriminating judgment.
+chief among these motives was the overwhelming idea of the great whale
+himself. Such a portentous and mysterious monster roused all my curiosity.
+Then the wild and distant seas where he rolled his island bulk; the
+undeliverable, nameless perils of the whale; these, with all the attending
+marvels of a thousand Patagonian sights and sounds, helped to sway me to my
+wish. With other men, perhaps, such things would not have been inducements;
+but as for me, I am tormented with an everlasting itch for things remote. I
+love to sail forbidden seas, and land on barbarous coasts. Not ignoring what
+is good, I am quick to perceive a horror, and could still be social with
+it&#8212;would they let me &#8212;since it is but well to be on friendly terms with all
+the inmates of the place one lodges in. By reason of these things, then, the
+whaling voyage was welcome; the great flood-gates of the wonder-world swung
+open, and in the wild conceits that swayed me to my purpose, two and two
+there floated into my inmost soul, endless processions of the whale, and, mid
+most of them all, one grand hooded phantom, like a snow hill in the air.
+</p>
+</div>
+</body>
+</text>
+</TEI.2>
diff --git a/Master/texmf-dist/doc/xmltex/passivetex/xsa.xml b/Master/texmf-dist/doc/xmltex/passivetex/xsa.xml
new file mode 100644
index 00000000000..df46cbc7896
--- /dev/null
+++ b/Master/texmf-dist/doc/xmltex/passivetex/xsa.xml
@@ -0,0 +1,14 @@
+<xsa version="1.0">
+ <vendor>
+ <name>Sebastian Rahtz</name>
+ <email>sebastian.rahtz@oucs.ox.ac.uk</email>
+ </vendor>
+ <product id="fotex">
+ <name>Passive TeX</name>
+ <version>1.3, 10th December 2000</version>
+ <last-release>20001210</last-release>
+ <info-url>http://users.ox.ac.uk/~rahtz/passivetex/</info-url>
+ </product>
+</xsa>
+
+