grant appln revised: deadline wtorek 28.01 poludniu! more comments? - Cosmo-torun

27 Jan 2003


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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{flushleft}
\end{flushleft}
\begin{flushleft}
\textbf{State Committee for Scientific Research -- KBN
}{\footnotesize{}For KBN use only}
\end{flushleft}
\begin{flushleft}
\textbf{00-529 Warszawa
    						Nr.}
\end{flushleft}
\begin{flushleft}
\textbf{ul. Wsp'olna 1/3		Group}
\end{flushleft}
\begin{flushleft}
\textbf{POLAND} \
\end{flushleft}
\begin{center}
\textbf{GRANT APPLICATION}
\end{center}
\begin{flushleft}
\end{flushleft}
\begin{flushleft}
\textbf{Project Title:}
\centerline{\underline{Search for Topological Lensing}} \
\centerline{\underline{of Radio-Loud Active Galactic Nuclei and Galaxy
Clusters}}
\end{flushleft}
\begin{flushleft}
\end{flushleft}
\begin{flushleft}
\textbf{A. APPLICANT DATA}
\end{flushleft}
\begin{flushleft}
\end{flushleft}
\begin{flushleft}
{\em
1. Name and address of the organization where work will be
performed (include department, institute, laboratory, and chair,
as applicable):
}
\end{flushleft}
Toru'n Centre for Astronomy, Nicolas Copernicus University,
ul. Gagarina, 11, Toru'n 87-100; director prof. hab. dr Andrzej Kus
\begin{flushleft}
{\em
2. Principal Investigator (include title, first name, last name):
}
\end{flushleft}
dr Boudewijn Roukema
\begin{flushleft}
{\em
3. Principal Investigator's employer, if different from above
organization (include department, institute, laboratory, and chair,
as applicable):
}
\end{flushleft}
(same as above)
\begin{flushleft}
\textbf{B. GENERAL DATA}
\end{flushleft}
\begin{flushleft}
{\em 1. Funding period: }
{\bf \monthstotal}..months  (01.2004 -- 12.2006)
\end{flushleft}
\begin{flushleft}
{\em 2. Number of personnel involved in the project:} {\bf 6}
\end{flushleft}
\begin{flushleft}
{\em
3. Type of project (pick one):} \textbf{Individual Project}
\end{flushleft}
\begin{flushleft}
{\em 4. Requested funding amount
(in Polish z\l{}otys{\footnotesize{} Polish z\l{}oty
annual 2002 mid - rate against the euro is
estimated at 3,95 (Ministry of Finance - draft budget for the Year 2002)}
- z\l{}):}
\end{flushleft}
\grandtotal~PLN
\begin{flushleft}
{\em 5. Keywords:}
\end{flushleft}
observational cosmology, cosmic topology, radio-loud active galactic nuclei,
clusters of galaxies
\clearpage
\begin{flushleft}
6. \textbf{Project summary}
(not to exceed 1 page; may be published by KBN if grant is awarded):
\end{flushleft}
\begin{centering}
{\underline{Search for Topological Lensing
of Radio-Loud Active Galactic Nuclei and Galaxy
Clusters}}
\end{centering}
The Hilbert-Einstein equations are insufficient to describe the
geometry of the Universe, as they only constrain a local geometrical
property: curvature. A global knowledge of the geometry of space, if
possible, would require measurement of the topology of the
Universe. Since the subject was discussed in 1900 by Schwarzschild,
observational attempts to measure global topology have been rare for
most of this century, but have accelerated in the 1990's due to
the rapidly increasing amount of observations of non-negligible
fractions of the observational sphere.
The basic physical test for measuring the topology of the Universe
is simple from a na"{\i}ve theoretical point of view: it is sufficient
to see multiple images of extragalactic objects whose light travels
to the observer via straight lines (geodesics) in different directions,
or in other words that crosses the Universe from different directions or
more than once. Hence, the term ``topological lensing'', since whatever
theory might in the future explain the global shape of the Universe will
presumably be an extension of general relativity, and just as general
relativity is tested by gravitational lensing, where single objects such
as high redshift galaxies are seen several
times, the future theory (probably a theory of quantum gravity) should be
constrained by topological lensing.
In practice, just as the individual and statistical observational properties
of extragalactic objects have made determination of local cosmological
parameters (such as the matter density parameter, the cosmological
constant and the Hubble constant) much more difficult than was hoped,
their properties make the search for topological lensing difficult.
The most promising objects at high redshifts for detecting topological
lensing are those we can see in large numbers and across large volumes
of space: (1) active galactic nuclei (AGNs) and (2) clusters of galaxies.
In the Toru'n Centre for Astronomy, we have a combination of
\begin{list}{(\roman{enumi})}{\usecounter{enumi}}
\item existing
observational expertise in  radio-loud AGNs (RLAGNs) including the study of
the evolution of RLAGNs (Marecki, Kunert, Gawro'nski); and
\item with the
OCRA (One-cm Receiver Array) project, we hope to soon obtain a catalogue
of thousands of clusters of galaxies at high redshifts via the
Sunyaev-Zel'dovich Effect (Soberski); and
\item  the PI (Roukema) has developed observational
strategies for investigating cosmic topology.
\end{list}
For this reason, we have an excellent opportunity at TCfA to excel
in this field. Although our focus will be on the use of RLAGNs and
clusters of galaxies, knowledge of cosmic microwave background (CMB)
observational analyses will be crucial for independently checking any
serious candidates for topological lensing. We are fortunate to have
the presence in our group of an expert in CMB data, Bartosz Lew,
who we expect to achieve the status of Magister during 2003.
\clearpage
\begin{flushleft}
\textbf{C. STAFF INFORMATION}
\end{flushleft}
\begin{flushleft}
\end{flushleft}
\begin{flushleft}
{\em
For the Principal Investigator and each senior staff member, provide the
following biographical information:}
\end{flushleft}
\begin{flushleft}
1. {\em Name}
\end{flushleft}
dr Boudewijn Roukema
\begin{flushleft}
2. {\em Educational history including, for each degree, the field,
institution, and date obtained}
\end{flushleft}
1989-93: Doctor of Philosophy (Ph.D.) in
Astronomy and Astrophysics,
Mt Stromlo and Siding Spring Observatories (M.S.S.S.O.),
 Australian National University (A.N.U.),
Canberra.
1985-88: Bachelor of Science (Hons), Australian National University,
Canberra, Australia
(awarded National Undergraduate Scholarship for this degree )
\begin{flushleft}
3. {\em Academic and professional
appointments, in reverse chronological order}
\end{flushleft}
\noin since 2002: adiunkt, Toru'n Centre for Astronomy, Uniwersytet
Miko\l{}aja Kopernika, Toru'n, Poland
\noin 2001: visitor, DARC/LUTH (Laboratoire de l'Univers et ses Th'eories),
Observatoire de Meudon, France
\noin 1998--2000: postdoctoral fellow, Inter-University Centre
for Astronomy & Astrophysics, Pune, India
\noin Feb--July 1998: visitor, CAMK, Warszawa
%\noin May-Sep 1997: Visitor, Institut d'Astrophysique
% de Paris, CNRS, France %(R)
%\noin April 1997: Visitor, Beijing
%Astronomical Observatory, Beijing, P.R.China  %(R)
\noin 1996--1997: Centre of Excellence foreign visiting fellow,
NAOJ, %  ďźĺ˝çŤĺ¤Šćĺ°ďź
Mitaka, Tokyo, %181,
Japan %(R)
%\smallskip
\noin 1994--1995: postdoctoral research fellow, Astronomy Centre,
University of Sussex, U.K. %(RT) %United Kingdom
%\smallskip
%\noin Aug/Sep 1994: Visitor, Dept of Astronomy, Bandung Institute of
%Technology,  Bandung, Indonesia %(T)
%\smallskip
\noin Jan/Feb 1994: visitor, Institute of Astronomy, University of
Cambridge, United Kingdom %(R)
%\smallskip
 \noin 1993: postdoctoral fellow, Institut d'Astrophysique
 de Paris, CNRS, France %(R)
\begin{flushleft}
4. {\em Brief descriptions of research projects completed in the last
four years, including up to 10 publications (provide publication data).}
\end{flushleft}
{Main Research Interests}
(i) {\em Observational Cosmology} and
(ii) {\em Galaxy Formation}:
(i) Observational constraints on statistics of
``large scale'' structure, observational constraints on local cosmological
parameters (such as the density parameter and the cosmological constant),
and observational programmes to try to constrain global cosmological
parameters; (ii)
Merging-history-tree based galaxy formation models in a cosmological
context and their comparison with observational galaxy statistics.
\begin{list}{\arabic{enumi}}{\usecounter{enumi}}
\item \pub \underline{Roukema, B.F.} & Bajtlik, S., 1999;;Transverse Galaxy
Velocities from Multiple Topological Images;;\mnras;;308;;309
\ (arXiv:astro-ph/9903038) %% CAMK, IAP, IUCAA %art
\item \pub \underline{Roukema, B.F.}, 2000a;;COBE and Global Topology:
An Example of the Application of the Circles Principle;;\mnras;;312;;712
\ (arXiv:astro-ph/9910272)  %% IUCAA  %ftp blacksci 15/10/99 %art
\mdcitem
%\item
\pub \underline{Roukema, B.F.} & Mamon, G.A., 2000;;Tangential
Large Scale Structure as a Standard Ruler:
Curvature Parameters from Quasars;;\AandA;;358;;395
\ (arXiv:astro-ph/9911413) %art %%395-408
%\item
\mdcitem
\pub \underline{Roukema, B.F.}, 2000b;;A Counterexample
to Claimed COBE Constraints on Compact
Toroidal Universe Models;;\cqg;;17;;3951
 \ (arXiv:astro-ph/0007140)
\item \pub \underline{Roukema, B.F.}, 2000c;;The
Topology of the Universe;;Bulletin
of the Astronomical Society of India;;28;;483
\ (arXiv:astro-ph/0010185)
\revinvit
\item \pub \underline{Roukema, B.F.} & Mamon, G.A., 2001;;Lifting
cosmic degeneracy within a single data set;;{\AandA};;366;;1
\ (arXiv:astro-ph/0010511)
\item \pub \underline{Roukema, B.F.}, 2001b;;How to distinguish a
nearly flat Universe from a flat Universe using the orientation
independence of a standard ruler;;{\AandA};;369;;729
\ (arXiv:astro-ph/0102095) %art
\item \pub \underline{Roukema, B.F.}, 2001d;;On the comoving distance
as an arc-length in four dimensions;;{\mnras};;325;;138
\ (arXiv:astro-ph/0102099)%art
\item \pub \underline{Roukema, B.F.}, Ninin, S., Devriendt, J.,
Bouchet, F.B.,
Guiderdoni, B., Mamon, G.A., 2001;;Star Formation Losses Due to
Tidal Debris in `Hierarchical' Galaxy Formation;;\AandA;;373;;494
\ (arXiv:astro-ph/0105152) %art
\item \pub \underline{Roukema, B.F.}, Mamon, G.A., &
Bajtlik, S., 2002;;The Cosmological Constant and Quintessence from a
Correlation Function Comoving Fine Feature in the 2dF Quasar
Redshift Survey;;{\AandA};;382;;397 \ (arXiv:astro-ph/0106135)
\end{list}
\begin{flushleft}
5. {\em Awards received}
\end{flushleft}
\begin{flushleft}
1. {\em Name}
\end{flushleft}
dr Andrzej Marecki
\begin{flushleft}
2. {\em Educational history including, for each degree, the field,
institution, and date obtained}
\end{flushleft}
1980 MSc (astronomy) UMK, Toru'n
1992 PhD (astronomy) UMK, Toru'n
\begin{flushleft}
3. {\em Academic and professional
appointments, in reverse chronological order}
\end{flushleft}
since 1992 adiunkt, Centrum Astronomii, UMK, Toru'n
\begin{flushleft}
4. {\em Brief descriptions of research projects completed in the last
four years, including up to 10 publications (provide publication data).}
\end{flushleft}
Brief description of research projects:
Interfermetric observations of radio-loud AGN (RLAGN) aimed to reveal
structures of compact i.e. {\it young} objects. Selection and observations
(MERLIN, VLBI) of a new sample of faint compact objects. Measurements of the
velocities of the components in such radio structures.
\begin{list}{\arabic{enumi}}{\usecounter{enumi}}
\item  \underline{Marecki, A.}, Falcke H., Niezgoda J.
Garrington, S.T., Patnaik A.R. (1999)
  "Gigahertz Peaked Spectrum sources from the Jodrell Bank-VLA Astrometric
  Survey" A&AS 135, 273
\item  Fanti, C. ... \underline{Marecki, A.}, et al. (2000)
"ISO observations of a sample of
  CSS and GHz Peaked Spectrum radio galaxies", A&A 358, 499
\item  Browne, I. W. \underline{Marecki, A.}, et al. (2000)
"OCRA: a one-centimeter receiver
  array" SPIE 4015, 299
\item  \underline{Kunert, M.}, \underline{Marecki, A.} et al. (2002)
"FIRST-based survey of Compact
  Steep Spectrum sources. I. MERLIN images of arc-second scale objects"
  A&A 391, 47
\item  \underline{Marecki, A.} et al. (2003)
"Location of Weak CSS Sources on the Evolutionary
  Path of Radio-Loud AGN", PASA 20, in press (astro-ph/0211253)
\item  \underline{Marecki, A.} et al. (2003)
"Weak CSS Sources from the FIRST Survey", PASA
  20, in press (astro-ph/0211249)
\item  \underline{Marecki, A.} et al. (2003)
"1245+676 - a CSO/GPS source being an extreme
  case of a double-double" PASA 20, in press (astro-ph/0209212)
\end{list}
\begin{flushleft}
5. {\em Awards received}
\end{flushleft}
\begin{flushleft}
\textbf{D. PROJECT DESCRIPTION, METHODOLOGY, AND EXPECTED RESULTS}
\end{flushleft}
\begin{flushleft}
\end{flushleft}
\begin{flushleft}
\textbf{	}{\em
What problem is being proposed and why?
Why should this work be undertaken in Poland?}
\end{flushleft}
The problem being posed is to try to measure the shape of the Universe.
This is important because the Universe is the object in which we live
and it is of obvious scientific and cultural interest to be aware of the
shape of the object in which we live.
It should be undertaken here because we have a combination of present
and developing observational expertise in radio-loud active galactic
nuclei (RLAGNs) and clusters of galaxies via the Sunyaev-Zel'dovich Effect
respectively, plus expertise in the development of observational strategies
for measuring cosmic topology.
Poland has obvious historical precedents in showing that the Earth is
not the centre of the Universe, and that planets around other stars exist.
It would clearly be good to continue the tradition on a much larger
length scale (Gigaparsecs).
\begin{flushleft}
{\em What is the present state of knowledge in the field, and to what
extent does this project verify it? How will the project advance
discovery and understanding in its field or across fields?  Is this a
new or a continued problem?  }
\end{flushleft}
It is clear that topological lensing on scales of a few hundred Megaparsecs
is extremely unlikely. Attempted constraints on scales from 1 Gigaparsec
(1$h^{-1}$Gpc) to the horizon diameter of about 20$h^{-1}$Gpc (comoving)
are much weaker and generally very model dependent.
This project will use RLAGNs and clusters of galaxies up to redshifts
of about $z\sim2-3$ as tracers, covering a volume of about half the
diameter of the observable Universe, i.e. about 10$h^{-1}$Gpc. It will
advance discovery and understanding by using these tracers as realistically
as possible given understanding of their evolution and properties.
This problem dates back to the pre-relativistic era (Schwarzschild 1900),
but has only been tackled non-trivially since the early 1990s. Work on
this theme is still in the pioneering stage.
\begin{flushleft}
{\em What is the proposed methodology? How will it solve the problem? What
equipment will be used? Does the applicant have the required equipment
skills and access?}
\end{flushleft}
The methodology is to use a range of methods, from studies of
individual objects to statistical studies of large catalogues, and to
parametrise understanding of the properties of the tracers in order to
make these methods as observationally correct and precise as
possible. Just as the supernova type Ia method was only one among many
methods proposed for measuring local cosmological parameters, but happened
to be the most dramatically successful, it is impossible
to predict beforehand which specific method for measuring topological
lensing will first yield highly significant results.
Although the TCfA 32m telescope will be used for part of the general
understanding of RLAGNs and for the OCRA project, which should in the
long term yield
large numbers of high-redshift clusters of galaxies, use of existing
public catalogues such as those
available at the Centre de Donn'ees astronomiques
de Strasbourg (CDS) and the information processing analysis requires
the use of computers and computer peripherals.
We do have access to these telescopes and databases and have experience
managing computer resources.
\begin{flushleft}
{\em What are the expected results of this project (``know-how'', patents,
methods, equipment), and how will they be disseminated (publications,
conference presentations, PhD theses)?}
\end{flushleft}
This is a {\bf research} project, not a {\bf development} project, and
the required theory which goes beyond general relativity has not yet
been developed, so while we would hope to detect topological lensing,
the results cannot be predicted before they are found.
Articles on the results will of course be published in refereed
journals, presented at conferences, and professionals and
non-professionals will be able to follow (and maybe participate) in the
research on our web pages via the normal methods of internet culture
such as publicly archived mailing lists and wiki pages.
\begin{flushleft}
\textbf{E.} \textbf{SOLICITED
PROJECTS ONLY: DOES THE APPLICANT MEET THE CALL CRITERIA,
PARTICULARLY THOSE CONCERNING INTERNATIONAL COOPERATION?}
\end{flushleft}
N/A
\begin{flushleft}
\textbf{F. PROJECT}  \textbf{SCHEDULE}  \textbf{- ANTICIPATED TASKS}
\end{flushleft}
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\usecounter{enumi}
\begin{center}
\begin{tabular}{clrr}
\hline \
No.  &
Name and description of task & \multicolumn{1}{c}{Expected} &
Expected cost (z\l{})  \
  & & \multicolumn{1}{c}{completion} \
  & & \multicolumn{1}{c}{date (mm/yy)} \
\ \addtocounter{enumi}{1} \arabic{enumi}
& parametric modelling of projection \
& and evolution effects of multiple images  & 6/2004 & \x~PLN
%
\ \addtocounter{enumi}{1} \arabic{enumi}
& application to individual candidate pairs   & 12/2004 & \x~PLN
\ \addtocounter{enumi}{1} \arabic{enumi}
%
& purchase computer items & 12/2004 & \equip~PLN
\ \addtocounter{enumi}{1} \arabic{enumi}
& international cosmology consultants   & 12/2004 & \z~PLN
\ \addtocounter{enumi}{1} \arabic{enumi}
& conferences, public relations   & 12/2004 & \allconferyear~PLN
%
\ \addtocounter{enumi}{1} \arabic{enumi}
& predictions of further images  & 6/2005 & \x~PLN
%
\ \addtocounter{enumi}{1} \arabic{enumi}
& statistical analysis of RLAGN catalogues  & 12/2005 & \x~PLN
\ \addtocounter{enumi}{1} \arabic{enumi}
& international cosmology consultants   & 12/2005 & \z~PLN
\ \addtocounter{enumi}{1} \arabic{enumi}
& conferences, public relations   & 12/2005 & \allconferyear~PLN
%
\ \addtocounter{enumi}{1} \arabic{enumi}
& statistical analysis of cluster catalogues, \
& OCRA predictions & 6/2006& \x~PLN
%
\ \addtocounter{enumi}{1} \arabic{enumi}
& predictions of further images   & 12/2006 & \x~PLN
\ \addtocounter{enumi}{1} \arabic{enumi}
& international cosmology consultants   & 12/2006 & \z~PLN
\ \addtocounter{enumi}{1} \arabic{enumi}
& conferences, public relations   & 12/2006 & \allconferyear~PLN
%
%
\
\hline Total & & & \w~PLN \ \hline
\end{tabular}
\end{center}
\smallskip
\begin{flushleft}
\textbf{G. PROPOSED BUDGET}
\end{flushleft}
\begin{center}
\begin{spacing}{1.24}
\setcounter{y}{\saltotalyear + \saltotalyear + \saltotalyear}
\renewcommand\y{\arabic{y}}
\setcounter{z}{\consult /3} \renewcommand\z{\arabic{z}}
\begin{tabular}{lrrr|r}
\hline
No. Item  & \multicolumn{3}{c}{Funds for each budget year (z\l{})}
  & Total \
 & 2004 & 2005 & 2006 \
%
{\bf 1} Direct costs, including:  &&&& \
{\footnotesize{}1/ }Salaries and benefits
& \saltotalyear & \saltotalyear & \saltotalyear & \y~PLN \
%
%
{\footnotesize{}2/} Equipment      & \equip &  & &  \equip~PLN\
%
{\footnotesize{}3/} Other direct costs &&&&\
%
international cosmology consultants &
\z &\z &\z &  \consult~PLN  \
%
conferences, public relations &
\allconferyear &\allconferyear &\allconferyear & \allconfer~PLN  \
\hline
%
Subtotal: & \subone & \subtwo& \subthree  & \suball~PLN \
&&&&\
\multicolumn{4}{l|}{{\bf 2} Indirect costs
(admin costs to UMK - 25% 1st yr; 30% 2nd, 3rd yrs)} &\
& \adminone & \admintwo & \adminthree & \adminall~PLN \
\hline
{\bf 3} Total costs (1+2) & \totalone &\totaltwo &\totalthree&
\totalall~PLN  \
\hline
\end{tabular}
\end{spacing}
\end{center}
\begin{flushleft}
\begin{spacing}{1.24}
Details of direct cost items
\end{spacing}
\end{flushleft}
\begin{flushleft}
1) {\em Salaries and benefits}
\end{flushleft}
\begin{flushleft}
{\em Principal Investigator {\bf \monthstotal} person-months}
\end{flushleft}
Based on KBN guidelines, 100% of \salrate{}PLN/annum for the principal
investigator if dr.,
75% for other investigators if dr.,
50% of \salrate{}PLN/annum for other investigators if mgr.
Hence:
\begin{list}{(\roman{enumi})}{\usecounter{enumi}}
\setcounter{x}{\salrate *3} \renewcommand\x{\arabic{x}}
\item dr Boudewijn Roukema \salrate{}PLN *3 =  \x~PLN
\end{list}
\begin{flushleft}
\setcounter{x}{(\monthstotal *(\persontotal-100))/100}
\renewcommand\x{\arabic{x}}
{\em Staff {\bf \x} person-months}
\end{flushleft}
\begin{list}{(\roman{enumi})}{\usecounter{enumi}}
\addtocounter{enumi}{1}
\setcounter{x}{(\salrate *67)/100} \renewcommand\x{\arabic{x}}
\setcounter{y}{\x *3} \renewcommand\y{\arabic{y}}
%
\item dr Andrzej Marecki \x~PLN *3 = \y~PLN
%
\setcounter{x}{(\salrate *50)/100} \renewcommand\x{\arabic{x}}
\setcounter{y}{\x *3} \renewcommand\y{\arabic{y}}
%
\item mgr Magdalena Kunert \x~PLN *3 = \y~PLN
\item mgr Sebastian Soberski \x~PLN *3 = \y~PLN
\item mgr Marcin Gawro'nski \x~PLN *3 = \y~PLN
\item (2003 mgr) Bartosz Lew \x~PLN *3 = \y~PLN
\end{list}
\setcounter{x}{(\salrate *(\monthstotal/12)*(\persontotal))/100}
\renewcommand\x{\arabic{x}}
Total: \x~PLN
\smallskip
\begin{flushleft}
2)
{\em Equipment
(type, estimated cost, planned month of purchase, and justification)}
\end{flushleft}
Justification: These computing facilities are needed for synthesis and
analysis of empirical data, and for creating added value of the
scientific products of the project (presenting and communicating
results).  Comparison of pairs of objects in a large catalogue is
an $N^2$ operation, i.e. it is CPU intensive. It can be speeded up
by making introducing prior assumptions. However, the history of
astronomy shows that making reasonable, but wrong, assumptions often
leads to missing a real signal, so having good CPU power would be an
advantage to the project.
Purchases are planned for 2004.
\begin{list}{(\roman{enumi})}{\usecounter{enumi}}
\item inkjet scanner/copier/printer + 3yrs insurance (loss/theft/etc.)
(an inkjet PSC 750 costs 900PLN; recycled cartridges cost about
35~PLN B/W, 50~PLN colour) 1~kPLN
\item colour laserwriter/scanner/copier   + 3yrs insurance (loss/theft/etc.)
7~kPLN
\item computer (Gawro'nski) - AMD Athlon, 2GHz, 512Mb RAM, 100Gb hard disk,
CD burner, ethernet card, 19'' screen
 + 3yrs insurance (loss/theft/etc.)
\perso~kPLN
\item computer (Lew) - AMD Athlon, 2GHz, 512Mb RAM, 100Gb hard disk,
CD burner, ethernet card, 19'' screen
 + 3yrs insurance (loss/theft/etc.)
\perso~kPLN
\item computer (Kunert) - AMD Athlon, 2GHz, 512Mb RAM, 100Gb hard disk,
CD burner, ethernet card, 19'' screen
 + 3yrs insurance (loss/theft/etc.)
\perso~kPLN
\item computer peripherals (Marecki) - 2 SCSI 73Gb disks
 + 3yrs insurance (loss/theft/etc.)
\scsi~kPLN
\item computer peripheral (Soberski) - CD burner 200~PLN, 512Mb RAM 500~PLN,
total \sober~PLN
\item portable computer (``notebook'') (available to all members of the group)
 + 3yrs insurance (loss/theft/etc.)
\portable~kPLN
\end{list}
Total:  \equip~PLN
\smallskip
\begin{flushleft}
3) {\em Other direct costs
(type of expenditure, amount, and relation to project plan)}
\end{flushleft}
These relate to the project plan in that the project is internationally
competitive research and so (1) international consultants are required
for providing theoretical insights and observational strategies
regarding the ways in which
RLAGNs and clusters of galaxies can be used as candidate topologically
lensed objects, and (2) we need to be able to present our results
at international conferences and consult international experts at
their home research institutes.
\smallskip
(1) The research environment for an internationally
competitive research project
requires consultations from international experts for periods
of between 1 week and a few months. Three people each for one month,
and four people each for a week, per year, yields a total of
\consultpm{}
person-months
over the three-year period of the project.
At a rate of
\consultrate~PLN/month for international consultants in cosmology, we
have
Total: \consult~PLN
\smallskip
(2) In order to present our results at conferences and other
public relations exercises, attendance at two international
conferences per fractional person per year would be consistent with
international standards.
One conference: typical economy class flight costs ($3.5$~kPLN) $+$ 1
week's accommodation and per diem in Europe/US/Japan/Australia
(2~kPLN) $+$ registration fees (1~kPLN) $\Rightarrow$ \oneconfer~kPLN.
Hence, two conferences/year for a 100% person are within the recommended
spending limits.
\setcounter{x}{\persontotal/100} \renewcommand\x{\arabic{x}}
\setcounter{y}{\persontotal-100*(\persontotal/100)}
\renewcommand\x{\arabic{x}}
At a rate of \confperyear  per effective person,
and \x{}.\y{} effective people over 3 years, this implies:
Total: \allconfer~PLN.
\begin{flushleft}
\end{flushleft}
\begin{flushleft}
\end{flushleft}
\begin{flushleft}
\begin{tabular}{cccc}
 {\em  Date} & \multicolumn{2}{c}{\em  Grantee organization	}&
  {\em Principal Investigator}; \
 & Kierownik: &    Kwestor &dr Boudewijn Roukema \
 & Prorektor ds Nauki i Wsp'o\l{}pracy&mgr Henryk Heldt &  \
 & z Zagranic\c{a}   \
 & prof dr. hab. Marek Zaidlewicz & \
\ \
\
\
& Signature			&	Signature  & Signature
\end{tabular}
\end{flushleft}
\begin{flushleft}
\end{flushleft}
\begin{flushleft}
\end{flushleft}
\begin{flushleft}
\end{flushleft}
\begin{flushleft}
\end{flushleft}
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\end{flushleft}
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\end{flushleft}
\end{document}