%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % STANDARD FORMAT FOR SCIENCE CASES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Should you have any questions please contact either % Alvio Renzini (arenzini@eso.org) or % Bruno Leibundgut (bleibundgut@eso.org) % % Documentation on the planned instrumentation for the VLT can be % obtained from ESO (ask your friendly coordinator or one of the above). % %!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! % % Look for a group of exclamation marks ('!!!!') for places to be % filled in this template form % %!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! % SCIENCE CASES documents should inclide the following: % % % 1) A Scientific Rationale, up to two TEX pages. % The discussion should also address the possible impact of current research % before the VLT will start operating. % % The above is needed for ... % % 2) A Description of the proposed observations. Including an estimate of % the total observing time required to achieve the scientific goal. % Possible La Silla observations that may be needed to prepare for the VLT % observations could also me mentioned and quantified. % % The above is needed for .... % % 3) List the technical requirements to accomplish the scientific goal. % (e.g., pointing, tracking, image quality, troughput, etc.). % Identify and quantitatively discuss the critical performances of the VLT % and the instruments that are required to achieve the science goal. % % 4) A list of calibration requirements. % % 5) Identify the limits of first generation instruments for the specific % science case, all the way from simple items (e.g., the filter list) % to the whole instrumentation plan ... (No more than half a page). % % 6) No target list required at this stage. % % 7) Deadline: April 30, 1996, please indicate by January 20 your % intent to supply a test case % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % LaTeX perliminaries % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \documentstyle[11pt]{article} \oddsidemargin -8pt \evensidemargin -8pt \marginparsep 0pt \topmargin -53pt \topskip 0pt \headheight 0pt \headsep -1pt \footheight 0pt \footskip 0pt \textheight 800pt \textwidth 500pt \columnsep 10pt \columnseprule 0pt \parindent 0pt \pagestyle{empty} \flushbottom %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Here we start the document % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % First we have to define some commands to ease the handling of % the form % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % definition of casetitle % \newcommand{\casetitle}[1]{ \large \fbox{\bf Title:} \par \vspace*{6pt} {\sc #1 } \vspace*{24pt} \normalsize\par } % % definition of name % \newcommand{\name}[1]{ \parbox[t]{250pt}{ \fbox{\bf Name:}\par \vspace*{6pt} #1 \par} } % % definition of address % \newcommand{\address}[1]{ \ \ \parbox[t]{250pt}{ \fbox{\bf Address:}\par \vspace*{6pt} #1 \par} } % % definition of phone % \newcommand{\phone}[1]{ %\vspace*{12pt} \parbox[t]{250pt}{ \fbox{\bf Phone:}\par \vspace*{6pt} #1 \par} } % % definition of email % \newcommand{\email}[1]{ \ \ \parbox[t]{250pt}{ \fbox{\bf E-mail:}\par \vspace*{6pt} #1 }\par } % % definition of collaborators % \newcommand{\collaborators}[1]{ \vspace*{24pt} \fbox{\bf Collaborators:}\par \vspace*{6pt} #1 \par} % % definition of coordinator % \newcommand{\coordinator}[1]{ \vspace*{24pt} \fbox{\bf ESO Coordinator:}\par \vspace*{6pt} #1 \par} % % definition of rationale % \newcommand{\rationale}[1]{ \vspace*{12pt} \fbox{\bf Scientific Rationale:} \par \scriptsize \parbox[t]{480pt}{ Up to two pages.\par\noindent The possible impact of current research before the VLT will start operating should also be addressed. VLT Science Cases will have to evolve so as to remain competitive in their field of research. The above is needed to scientifically justify the requirements below.} \normalsize \par \vspace{4pt} #1 } % % definition of observations % \newcommand{\observations}[1]{ \vspace*{12pt} \hspace*{6pt} {\bf Proposed Observations:}\par\noindent \scriptsize \hspace*{6pt} \parbox{480pt}{ Describe the proposed observations. Indicate the instrument and instrument modes, filters, gratings, etc. Include an estimate of the total observing time required to achieve the scientific goal. Possible La Silla observations that may be needed to prepare for the VLT observations could also me mentioned and quantified. The above is needed to provide facts to orient ESO policy (e.g. the OPC) about the expected needs for small, medium, and large projects. } \normalsize \par \vspace*{-52pt} \unitlength 1pt \begin{picture}(500,380)(0,0) \put(0,0){\framebox(500,380)[tl]{ \parbox[b]{1pt}{\vspace*{62pt} \hfill } \\ \parbox[t]{480pt}{ #1 }}} \end{picture}\par } % % definition of techniques % \newcommand{\techniques}[1]{ \vspace*{12pt} \hspace*{6pt} {\bf Technical Description of the Observations:}\par\noindent \scriptsize \hspace*{6pt} \parbox{480pt}{ List the technical requirements to accomplish the scientific goal. (e.g., pointing, tracking, image quality, troughput, etc.). Identify and quantitatively discuss the critical performances of the VLT, its instruments, and its operations that are required to achieve the science goal. } \normalsize \par \vspace*{-42pt} \unitlength 1pt \begin{picture}(500,380)(0,0) \put(0,0){\framebox(500,380)[tl]{ \parbox[b]{1pt}{\vspace*{52pt} \hfill } \\ \parbox[t]{480pt}{ #1 }}} \end{picture}\par } % % definition of calibration % \newcommand{\calibration}[1]{ \vspace*{12pt} \hspace*{8pt} {\bf Calibration Needs:}\par\noindent \scriptsize \hspace*{8pt} \parbox{480pt}{ Describe the required calibrations (type, accuracy, etc.) to achieve the science goal. } \normalsize \par \vspace*{-28pt} \unitlength 1pt \begin{picture}(500,380)(0,0) \put(0,0){\framebox(500,380)[tl]{ \parbox[b]{1pt}{\vspace*{38pt} \hfill } \\ \parbox[t]{480pt}{ #1 }}} \end{picture}\par } % % definition of limitations % \newcommand{\limitations}[1]{ \vspace*{12pt} \hspace*{8pt} {\bf Limitation of Instrumentation and Program Extensions:}\par\noindent \scriptsize \hspace*{8pt} \parbox{480pt}{ Identify the limits of first generation instruments for the specific science case, all the way from simple items (e.g., missing filters) to the whole instrumentation plan. If appropriate, discuss to which extent the planned VLT instrumentation will be competitive to that of other 8m class telescopes. } \normalsize \par \vspace*{-42pt} \unitlength 1pt \begin{picture}(500,380)(0,0) \put(0,0){\framebox(500,380)[tl]{ \parbox[b]{1pt}{\vspace*{52pt} \hfill } \\ \parbox[t]{480pt}{ #1 }}} \end{picture}\par } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % End of command definitions % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Print form header % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % ESO header % \setlength{\unitlength}{1mm} \begin{picture}(185,53.5) \put(32,42){{\fontfamily{cmr}\fontseries{m}\fontshape{n}\fontsize{17}{22pt}\selectfont\hbox to 147mm{E\hfil U\hfil R\hfil O\hfil P\hfil E\hfil A\hfil N\hfil \ \hfil S\hfil O\hfil U\hfil T\hfil H\hfil E\hfil R\hfil N\hfil \ \hfil O\hfil B\hfil S\hfil E\hfil R\hfil V\hfil A\hfil T\hfil O\hfil R\hfil Y}}} \put(32,33){{\fontfamily{cmr}\fontseries{m}\fontshape{n}\fontsize{11}{13.6pt}\selectfont\hbox to 147mm{Organisation\hfil Europ\'eenne\hfil pour\hfil des\hfil Recherches\hfil Astronomiques\hfil dans\hfil l'H\'emisph\`ere\hfil Austral}}} \put(32,27){{\fontfamily{cmr}\fontseries{m}\fontshape{n}\fontsize{11}{13.6pt}\selectfont\hbox to 147mm{Europ\"{a}ische\hfil Organisation\hfil f\"{u}r\hfil astronomische\hfil Forschung\hfil in\hfil der\hfil s\"{u}dlichen\hfil Hemisph\"{a}re}}} %\def\@{\kern-0.048387mm} %\put(-3,16.5){{\sixrm E\@ S\@ O\@\,--\@\,\@ %S\@ E\@ C\@ T\@ I\@ O\@ N\@\ \@ V\@ I\@ S\@ %I\@ T\@ I\@ N\@ G\@\ \@ A\@ S\@ T\@ R\@ O\@ %N\@ O\@ M\@ E\@ R\@ S}} %\def\@{\kern-0.15432mm} %\put(-3,13.5){{\sixrm K\@ a\@ r\@ l\@-\@ S\@ %c\@ h\@ w\@ a\@ r\@ z\@ s\@ c\@ h\@ i\@ l\@ %d\@-\@ S\@ t\@ r\@ a\@\ss\@ e\@\ \@2\@\ \@$\cdot$ %\@ D\@-\@8\@5\@7\@4\@8\@\ \@ G\@ a\@ r\@ c\@ %h\@ i\@ n\@ g\@\ \@ b\@ e\@ i\@\ \@ M\@\"{u}\@ %n\@ c\@ h\@ e\@ n\@\ \@$\cdot$\@\ \@ T\@ e\@ %l\@.\@\,\@:\@\ \@(\@0\@8\@9\@)\@\ \@3\@2 %\@\ \@0\@0\@\ \@6\@2\@\ \@2\@3}} %%%%%%%%%%%%%%%%%% Definition of ESO logo %%%%%%%%%%%%%%%%%%%% \put(-3,20){\framebox(24.1,32.1){\ }} \put(4,37){{\Huge E}} \put(10,38){{\Huge S}} \put(6.5,28){{\Huge O}} \put(7,21.5){{\LARGE $\ast$}} \put(-2,37){{\Large $\ast$}} \put(17,40.5){{\large $\ast$}} \put(9.5,49){{\normalsize $\ast$}} \end{picture} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Headline for the test case form % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \Large \framebox[510pt]{\bf \centerline{Form for VLT Science Test Cases}} \par \vspace*{15mm} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Indicate a title for your proposal % !!!! \casetitle{High redshift radio galaxies: a) their stellar content and surrounding clusters } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Give name and address below % !!!! \name{G Miley, S di Serego Alighieri } % % Enter your address on the next line (end lines with \\) % !!!! \address{c/- ST-ECF\\ Karl Schwarzschild Str 2\\ D-85748 Garching bei M\"unchen } % % Please indicate your phone number and e-mail address % Phone-Nr.: % !!!! \phone{+49 89 320 06 235 } % e-mail: % !!!! \email{miley@strw.leidenuniv.nl, sperello@arcetri.astro.it } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Please indicate any collaborators and their institutions (no % addresses) for this project on the next lines (end lines with \\) % !!!! \collaborators{ rottgeri@strw.leidenuniv.nl (Huub R\"ottgering, Leiden)\\ {\bf miley@strw.leidenuniv.nl (George Miley. Leiden)}\\ {\bf sperello@arcetri.astro.it (Sperello di Serego Alighieri, Arcetri)}\\ C.Tadhunter@sheffield.ac.uk (Clive Tadhunter, Sheffield)\\ rfosbury@eso.org (Bob Fosbury, ST-ECF, coordinator)\\ cimatti@arcetri.astro.it (Andrea Cimatti, Florence)\\ amoorwoo@eso.org (Alan Moorwood, ESO)\\ pquinn@eso.org (Peter Quinn, ESO)\\ nb. lead author(s) for this sub-proposal in {\bf bf type} } % % The following line should contain the name of the ESO science % performance group coordinator % !!!! \coordinator{R A E Fosbury } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Rest of page 1 (footnotes) % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \vfill \rule{100mm}{0.1mm} \scriptsize \newcounter{notes} \begin{list}{\arabic{notes}.}% {\usecounter{notes} \setlength{\itemsep 0pt} \setlength{\parsep 0pt} % \setlength{\topsep 0pt} \setlength{\parskip 0pt} % \setlength{\leftmargin 15pt} \setlength{\labelwidth 6pt}} \item No target list required \item Documentation on the available VLT instruments can be obtained from the ESO coordinator \item Please attach figures to the form and send an electronic version to the ESO coordinator \item Deadline: 30. April 1996, please indicate in written form by 20. January that you are planning to provide a test case. \item For information please contact either Alvio Renzini (arenzini@eso.org) or Bruno Leibundgut (bleibundgut@eso.org) \end{list} \normalsize %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % end of page 1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \newpage %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Pages 2 and 3 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Scientific Rational (not more than two pages) % !!!! \rationale{This proposal intends to address two main problems: the stellar populations at early cosmological epoch, and the relationship between environment and activity, and its evolution. Both of these questions can be addressed by studying the clusters of galaxies around high redshift radio galaxies (HzRG) and radio quasars (RQ). Up to now almost all information on objects in the early Universe has been obtained from active objects, because it is easier to detect them, and to measure their redshifts and their main physical properties. However if one wishes to study the formation and early evolution of most galaxies that we see in the local Universe, which are non--active, these active galaxies have the disadvantage that their morphology and spectra are influenced by the activity. The case of quasars is very clear, since tha strong nuclear source overwhelmes the stellar light. Also in HzRG the morphological and spectral signatures of activity are clear (eg, McCarthy, 1993, ARAA, 31, 639). Although for HzRG spectropolarimetry can help in disentangling the stellar component from the active one (di Serego Alighieri et al., 1994, ApJ, 431, 123; see also test case c), the measurement of the stellar SED and absorptions is inhevitably more difficult, and one is left with the doubt that even the stellar component can be influenced by the activity and therefore cannot give information applicable to the majority of galaxies. AGN (particularly the radio-loud objects) can nevertheless be used as signposts for galaxies more in general. We know that they occour in clusters and groups (Yee, ... , Dickinson, 1996...): looking around AGN we can surely find other more normal galaxies, and most of them will be at the same redshift. We then propose to study these cluster galaxies to obtain information on their stellar populations from the morphology and spectra. The aim is to determine the age of the stars (in particular of the oldest ones), its evolution with redshift and its spread in a single cluster, in order to provide constraints on the formation and early evolution of normal galaxies. An important analysis tool will be the spectral synthesis codes developed to reproduce both the general shape and the detailed features of the spectra of stellar populations (eg, Bressan et al., 1994, ApJSS, 94, 63, and 1995, A\&A, ...). The second main theme of this proposal is the relationship between activity and environment. It has often been claimed that activity is triggered by the interaction between the active galaxy and one or more companions and even that the material necessary to fuel the activity comes from companions . Indeed some nearby AGN have double nuclei and companions with distorted morphology. On the other hand it is also clear that an AGN influences the environment, eg, with the radio plasma and with strong anisotropic ionizing radiation. We intend to study these interactions on the most powerful AGN and on the youngest ones, where the causes and effects can be hopefully separated and shed light on the properties of the central power source. The necessary data again are images, to look for distorted morphologies, and spectra, to study the kinematics of the cluster and of individual members and the ionization as a function of the distance of the companion and of its direction with respect to the axes of the AGN. We believe that addressing this second problem we can also give constraints on the possibility that most galaxies, also those that are not active now, have had an active phase in the past. Clearly, if all galaxies have been active and if the triggering of the activity requires a strong galaxy-to-galaxy interaction, which leaves long-lasting traces, we should see these today. On the other hand, if most of the distorsions and peculiar spectra which we see around AGN are a temporary effect of the activity (like illumination and ionization) then we do not expect to see much of it after the activity is finished. (nb. this may require a more detailed discussion of the duration of effects: eg, kinematical effects may last longer than ionization). } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Done with pages 2 and 3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \newpage %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Page 4 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Technical requirements % % Describe your observations in some technical detail % !!!! \observations{The observations necessary are of two types: first imaging, to find the cluster members and to study their morphology, second spectroscopy to study the SED, stellar spectral features, and emission lines. The morphology can best be studied with the HST (eg, Dickinson, 1996...). However the search for companions, in particular for those useful for the study of stellar populations at the highest redshifts, is probably best accomplished in the near IR from the ground (some simulations to quantify this would be very useful). The most important stellar spectral features for the old stellar population occur between 3500 and 6000 \AA , which is moved in the near IR for z=2-4. So we need spectroscopy in the JHK bands (ISAAC). Multiobject spectroscopy in JHK would be a very big advantage, as well as OH suppression. The younger OB stellar features require the optical range (FORS) for the same redshift range. } % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Which instruments are needed? % % Describe your observations in some technical detail (filters, % gratings, throughput, stability, etc.) % !!!! \techniques{Single and multi-object spectroscopy with resolutions from a few hundred to a few thousand. Requirements are to identify and measure stellar absorption features and to measure stellar velocity dispersions. Principal instruments will be FORS and ISAAC. } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Done with page 4 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \newpage %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Page 5 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Describe your required calibration to achieve the science goal % !!!! \calibration{tbd } % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Limitation of the current instrumentation of the VLT and % possible extensions of the observing program % % % Describe limitations of the current ESO instrumentation program % and possible extensions of the observational project % !!!! \limitations{Needs further discussion --- possibly need more objects per multi-object field. } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Done with page 5 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Done with the form %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \end{document} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Finis % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%