diff --git a/docs/pdf/Makefile b/docs/pdf/Makefile new file mode 100644 index 00000000..c0e6d85f --- /dev/null +++ b/docs/pdf/Makefile @@ -0,0 +1,325 @@ +## $Id: Makefile 1524 2007-01-17 17:06:06Z sfilippo $ +##--------------------------------------------------------------------------- +## LaTeX Makefile +## Copyright (C) 1996-2001 Michael Forman Michael.Forman@Colorado.EDU +## +## This program is free software; you can redistribute it and/or +## modify it under the terms of the GNU General Public License +## as published by the Free Software Foundation; either version 2 +## of the License, or (at your option) any later version. +## +## This program is distributed in the hope that it will be useful, +## but WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +## GNU General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with this program; if not, write to the Free Software +## Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. +## +## This copyright applies to this Makefile, and all perl scripts. +## The GPL does NOT apply to the actual content of the paper or thesis. +##--------------------------------------------------------------------------- +## 01.Dec,1996 forman Initial Makefile +## 01.Jun,1997 forman Added support for print, preview, and bibtex +## 01.Jan,1998 stones tmp and lib directories to reduce clutter +## 05.Feb,1998 forman Added the following functions: +## .PHONY to prevent errors +## generic TEXFILE definition with following patsubst's +## vpath definitions +## gzip, gunzip, tar, ci +## search for \bibliography in tex file +## conditional ifeq omits bibtex if unnecessary +## documentation added +## 30.Nov,1998 forman Added TOPFILE and SECFILE definitions to support +## texfiles with "input" commands. +## 23.Dec,1998 marshats Added RCSFILES and ci/co capabilites for multiple files +## Now only runs makeindex if $(IDX) file exists. +## 15.Mar,1999 forman Added 'make wc' for papers with word quotas. +## 24.Aug,1999 forman Converted Makefile to use pdftex as the primary +## complier. Now generates true pdf and ps files. +## 09.Feb,2000 forman Simplified the documentation. Removed direct +## compilation of tex into DVI and PS. Conversion +## is done with PDF2PS now. +## 08.Aug,2000 forman Added define for figures directories. +## 18.Aug,2000 forman Removed the redundant code in the $(pdflatex) and +## $(pdflatex-bibtex) definitions by splitting them up +## into several smaller definitions which are called +## from a single set of "if-then" statements. +## 18.Aug,2000 forman Added support for glosstex and makeindex. +## 19.Aug,2000 forman To save space, all files in tmp are now links. +## 19.Aug,2000 forman Removed all postscript commands in favor of pdf. +##--------------------------------------------------------------------------- +## +## This Makefile expects the following directory structure: +## +## Makefile This file +## *.tex Put latex files in root directory. +## RCS/ Create an RCS directory for "ci" and "co". +## doc/ Document directory. Includes gpl.txt. +## lib/ Put all cls, sty, idx, gdf, and bib files in lib. +## figures/ Put all figures in the figures directory. +## tmp/ Never put anything in tmp -- it gets cleaned out. +## +##--------------------------------------------------------------------------- +## +## Normal Usage: +## make Run pdflatex +## make clean Remove all files in tmp and the pdf link in root. +## make preview Preview the compiled file +## make ci Check in the RCSFILES +## make co Check out the RCSFILES +## +## Advanced Usage: +## make gzip Recursively gzip all the files in the root directory +## make gunzip Reverse the above process +## make tar Tar and gzip the working directory +## make wc Count the number of words in your report +## +##--------------------------------------------------------------------------- +## WARNING: +## If "make ci" fails, "make co" will nuke your files! +## Don't put anything in tmp, "make clean" will delete everything! +##--------------------------------------------------------------------------- +# + +TOPFILE = userguide.tex +SECFILE = title.tex intro.tex methods.tex precs.tex +FIGDIR = figures + +XPDFFLAGS = +ACROFLAGS = #-- macos +#ACROFLAGS = -geometry 1234x1168+0+0 #-- new-sydney-wide +#ACROFLAGS = -geometry 1000x1000+0+0 #-- sydney-wide +#ACROFLAGS = -geometry 750x1000+0+0 #-- sydney +#ACROFLAGS = -geometry 1200x1200+0+0 #-- home-wide +#ACROFLAGS = -geometry 900x1200+0+0 #-- home + +##--------------------------------------------------------------------------- +## Change nothing below here (unless you're really really good). +#---------------------------------------------------------------------------- + +## +## Accounting +# +START = $(shell date) +WDIR = $(notdir $(shell pwd)) +DATE = $(shell date +%Y-%m-%d) + +## +## Programs +# +PDFLATEX = pdflatex +ACRO = evince +XPDF = xpdf +WC = wc +PDF2PS = pdf2ps +PDF2TEXT = pdftotext +MAKEIDX = makeindex +GLOSSTEX = glosstex +BIBTEX = bibtex +FILTER = ../bin/texfilter +FILTER = cat +CLEANIDX = ../bin/cleanidx + +## +## Files +# +TEXFILES = $(TOPFILE) $(SECFILE) +RCSFILES = $(TEXFILES) Makefile + +BASEFILE = $(patsubst %.tex,%,$(TOPFILE)) +IDX = $(join $(BASEFILE),.idx) +PDF = $(join $(BASEFILE),.pdf) +PS = $(join $(BASEFILE),.ps) +GXS = $(join $(BASEFILE),.gxs) +GLX = $(join $(BASEFILE),.glx) + +FIGURES = $(sort $(wildcard $(FIGDIR)/*)) +GLOFILES:= $(sort $(wildcard lib/*.gdf)) +GLOFILES:= $(patsubst lib/%,%,$(GLOFILES)) +BIBFILES:= $(shell grep ^.bibliography{ $(TOPFILE)|sed "s/,/ /g"|sed "s/%.*//g") +BIBFILES:= $(patsubst \bibliography{%,%,$(BIBFILES)) +BIBFILES:= $(patsubst %},%,$(BIBFILES)) +BIBFILES:= $(sort $(addsuffix .bib,$(BIBFILES))) + +LIBFILES = $(sort $(wildcard lib/*)) + +TEXLNFIL = $(addprefix $(PWD)/,$(TEXFILES)) + +#============================================================================ + +all: $(PDF) + @echo $(PDF) + +$(PDF): $(TEXFILES) $(LIBFILES) $(FIGURES) Makefile + $(header) + $(initialize) + $(pdflatex-filter) + ifneq ($(BIBFILES),) + $(bibtex) + $(pdflatex-filter) + endif + ifneq ($(GLOFILES),) + $(glosstex) + $(pdflatex-filter) + endif +# $(makeindex) + $(pdflatex-filter) + $(finish) + +$(PS): $(PDF) + $(PDF2PS) $< $(PS) + +ps: $(PS) + +#============================================================================ + +.PHONY: clean clean-tmp preview print gzip gunzip tar ci + +clean: + rm -f $(PDF) $(PS) + cd tmp ; rm -f * + +clean-tmp: + cd tmp ; rm -f * + +#---------------------------------------------------------------------------- + +preview: $(PDF) + $(ACRO) $(ACROFLAGS) $< & + +xpreview: $(PDF) + $(XPDF) $(XPDFFLAGS) $< & + +wc: $(PDF) + $(PDF2TEXT) $< | $(WC) + +#---------------------------------------------------------------------------- + +ci: $(RCSFILES) + $(shell for i in $(RCSFILES) ; do ci -u $$i ; done) + +co: $(RCSFILES) + $(shell for i in $(RCSFILES) ; do co -l $$i ; done) + +gzip: clean-tmp + gzip -r ./ + gunzip Makefile.gz + +gunzip: + gunzip -r ./ + +tar: clean-tmp + cd .. ; \ + tar cvf $(WDIR)-$(DATE).tar $(WDIR) ; \ + gzip $(WDIR)-$(DATE).tar + +info: + $(header) + +#============================================================================ + +define header + @echo + @echo "#---------------------------------------------------------------------" + @echo "MAKEFILE = LaTeX PDF Makefile" + @echo "AUTHOR = Alfredo Buttari" + @echo 'ID = $$Id: Makefile 1524 2007-01-17 17:06:06Z sfilippo $ ' + @echo "#---------------------------------------------------------------------" + @echo + @echo "ACRO = $(ACRO) $(ACROFLAGS) $(PDF)" + @echo "XPDF = $(XPDF) $(XPDFFLAGS) $(PDF)" + @echo "GV = $(GV) $(GVFLAGS) $(PS)" + @echo "LPR = $(LPR) $(LPRFLAGS) $(PS)" + @echo + @echo "WDIR = $(WDIR)" + @echo "DATE = $(DATE)" + @echo + @echo "TOPFILE = $(TOPFILE)" + @echo "SECFILE = $(SECFILE)" + @echo "TEXFILES = $(TEXFILES)" + @echo "PDF = $(PDF)" + @echo "PS = $(PS)" + @echo "BIBFILES = $(BIBFILES)" + @echo "GLOFILES = $(GLOFILES)" + @echo "IDXFILES = $(IDXFILES)" + @echo +endef +# @echo "FIGURES = $(FIGURES)" + +#---------------------------------------------------------------------------- + + +define initialize + @if test ! -d tmp; then mkdir tmp; fi + @ln -sf $(TEXLNFIL) tmp + @ln -sf $(PWD)/lib/* tmp + @ln -sf $(PWD)/$(FIGDIR) tmp +endef + +#---------------------------------------------------------------------------- + +define pdflatex + @echo + @echo "----- pdflatex -------------------------------------------------------" + @echo -n "Starting: "; date + @echo + cd tmp; $(PDFLATEX) $(TOPFILE) +endef + +#---------------------------------------------------------------------------- + +define pdflatex-filter + @echo + @echo "----- pdflatex -------------------------------------------------------" + @echo -n "Starting: "; date + @echo + cd tmp; ($(PDFLATEX) $(TOPFILE) 2>&1) | $(FILTER) +endef + +#---------------------------------------------------------------------------- + +define bibtex + @echo + @echo "----- bibtex ---------------------------------------------------------" + @echo -n "Starting: "; date + @echo + cd tmp; $(BIBTEX) $(BASEFILE) +endef + +#---------------------------------------------------------------------------- + +define glosstex + @echo + @echo "----- glosstex -------------------------------------------------------" + @echo -n "Starting: "; date + @echo + cd tmp; $(GLOSSTEX) $(BASEFILE) $(GLOFILES) + cd tmp; $(MAKEIDX) $(GXS) -o $(GLX) -s glosstex.ist +endef + +#---------------------------------------------------------------------------- + +define makeindex + @echo + @echo "----- makeindex ------------------------------------------------------" + @echo -n "Starting: "; date + @echo + cd tmp; mv $(IDX) $(IDX)-; $(CLEANIDX) < $(IDX)- > $(IDX) + cd tmp; $(MAKEIDX) $(IDX) +endef + +#---------------------------------------------------------------------------- + +define finish + @ln -sf tmp/$@ . + @echo + @echo "----- finish ---------------------------------------------------------" + @echo -n "Start: "$(START); echo + @echo -n "Finish: "; date + @echo -n "Output: "; ls -l -o tmp/$@ + @echo -n "Target: " +endef + + diff --git a/docs/pdf/intro.tex b/docs/pdf/intro.tex new file mode 100644 index 00000000..f8db18b6 --- /dev/null +++ b/docs/pdf/intro.tex @@ -0,0 +1,32 @@ +\section{Introduction}\label{sec:intro} + +The MLD2P4 library provides .... + + +\subsection{Programming model} + +The MLD2P4 librarary is based on the Single Program Multiple Data +(SPMD) programming model: each process participating in the +computation performs the same actions on a chunk of data. Parallelism +is thus data-driven. + +Because of this structure, many subroutines coordinate their action +across the various processes, thus providing an implicit +synchronization point, and therefore \emph{must} be +called simultaneously by all processes participating in the +computation. +However there are many cases where no synchronization, and indeed no +communication among processes, is implied. + +Throughout this user's guide each subroutine will be clearly indicated +as: +\begin{description} +\item[Synchronous:] must be called simultaneously by all the + processes in the relevant communication context; +\item[Asynchronous:] may be called in a totally independent manner. +\end{description} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "userguide" +%%% End: diff --git a/docs/pdf/methods.tex b/docs/pdf/methods.tex new file mode 100644 index 00000000..221ca03a --- /dev/null +++ b/docs/pdf/methods.tex @@ -0,0 +1,605 @@ +\section{Iterative Methods} +\label{sec:methods} + +In this chapter we provide routines for preconditioners and iterative +methods. The interfaces for Krylov subspace methods are available in +the module \verb|mld_krylov_mod|. The installation process of MLD2P4 +ensures that these may be used as a drop-in replacement for the PSBLAS +methods; they are accessible under the PSBLAS names (see the PSBLAS +documentation), + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% +% Krylov Methods driver routine +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\subroutine{mld\_krylov \label{krylov}}{Krylov Methods Driver Routine} + +This subroutine is a driver that provides a general interface for all +the Krylov-Subspace family methods. + +The stopping criterion is the normwise backward error, in the infinity +norm, i.e. the iteration is stopped when +\[ err = \frac{\|r_i\|}{(\|A\|\|x_i\|+\|b\|)} < eps \] +or the 2-norm residual reduction +\[ err = \frac{\|r_i\|}{\|b\|_2} < eps \] +according to the value passed through the istop argument (see +later). In the above formulae, $x_i$ is the tentative solution and +$r_i=b-Ax_i$ the corresponding residual at the $i$-th iteration. + + +\syntax{call psb\_krylov}{method,a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,irst,istop} + +\begin{description} +\item[Type:] Synchronous. +\item[\bf On Entry] +\item[method] a string that defines the iterative method to be + used. Supported values are: + \begin{description} + \item[CG]: the Conjugate Gradient method; + \item[CGS]:the Conjugate Gradient Stabilized method; + + \item[BICG]: the Bi-Conjugate Gradient method; + \item[BICGSTAB]: the Bi-Conjugate Gradient Stabilized method; + \item[BICGSTABL]: the Bi-Conjugate Gradient Stabilized method with restarting; + \item[RGMRES]: the Generalized Minimal Residual method with restarting. + \end{description} +\item[a] the local portion of global sparse matrix +$A$. \\ +Scope: {\bf local} \\ +Type: {\bf required}\\ +Intent: {\bf in}.\\ +Specified as: a structured data of type \spdata. +\item[prec] The data structure containing the preconditioner.\\ +Scope: {\bf local} \\ +Type: {\bf required}\\ +Intent: {\bf in}.\\ +Specified as: a structured data of type \precdata. +\item[b] The RHS vector. \\ +Scope: {\bf local} \\ +Type: {\bf required}\\ +Intent: {\bf in}.\\ +Specified as: a rank one array. +\item[x] The initial guess. \\ +Scope: {\bf local} \\ +Type: {\bf required}\\ +Intent: {\bf inout}.\\ +Specified as: a rank one array. +\item[eps] The stopping tolerance. \\ +Scope: {\bf global} \\ +Type: {\bf required}\\ +Intent: {\bf in}.\\ +Specified as: a real number. +\item[desc\_a] contains data structures for communications.\\ +Scope: {\bf local} \\ +Type: {\bf required}\\ +Intent: {\bf in}.\\ +Specified as: a structured data of type \descdata. +\item[itmax] The maximum number of iterations to perform.\\ +Scope: {\bf global} \\ +Type: {\bf optional}\\ +Intent: {\bf in}.\\ +Default: $itmax = 1000$.\\ +Specified as: an integer variable $itmax \ge 1$. +\item[itrace] If $>0$ print out an informational message about + convergence every $itrace$ iterations.\\ +Scope: {\bf global} \\ +Type: {\bf optional}\\ +Intent: {\bf in}.\\ +\item[irst] An integer specifying the restart parameter.\\ +Scope: {\bf global} \\ +Type: {\bf optional}.\\ +Intent: {\bf in}.\\ +Values: $irst>0$. This is employed for the BiCGSTABL or RGMRES +methods, otherwise it is ignored. + +\item[istop] An integer specifying the stopping criterion.\\ +Scope: {\bf global} \\ +Type: {\bf optional}.\\ +Intent: {\bf in}.\\ +Values: 1: use the normwise backward error, 2: use the scaled 2-norm +of the residual. Default: 1. +\item[\bf On Return] +\item[x] The computed solution. \\ +Scope: {\bf local} \\ +Type: {\bf required}\\ +Intent: {\bf inout}.\\ +Specified as: a rank one array. +\item[iter] The number of iterations performed.\\ +Scope: {\bf global} \\ +Type: {\bf optional}\\ +Intent: {\bf out}.\\ +Returned as: an integer variable. +\item[err] The convergence estimate on exit.\\ +Scope: {\bf global} \\ +Type: {\bf optional}\\ +Intent: {\bf out}.\\ +Returned as: a real number. +\item[info] Error code.\\ +Scope: {\bf local} \\ +Type: {\bf required} \\ +Intent: {\bf out}.\\ +An integer value; 0 means no error has been detected. +\end{description} + +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% % +%% % CG +%% % +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%% \subroutine{psb\_cg \label{cg}}{CG Iterative Method} + +%% This subroutine implements the CG method with restarting. The +%% stopping criterion is the normwise backward error, in the infinity +%% norm, i.e. the iteration is stopped when +%% \[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \] +%% or +%% \[ \frac{\|r_i\|}{\|b\|_2} < eps \] +%% according to the value passed through the istop argument (see later). + + +%% \syntax{call psb\_cg}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,istop} + +%% \begin{description} +%% \item[\bf On Entry] +%% \item[a] the local portion of global sparse matrix +%% $A$. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \spdata. +%% \item[prec] The data structure containing the preconditioner.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \precdata. +%% \item[b] The RHS vector. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[x] The initial guess. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[eps] The stopping tolerance. \\ +%% Scope: {\bf global} \\ +%% Type: {\bf required}\\ +%% Specified as: a real number. +%% \item[desc\_a] contains data structures for communications.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \descdata. +%% \item[itmax] The maximum number of iterations to perform.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Default: $itmax = 1000$.\\ +%% Specified as: an integer variable $itmax \ge 1$. +%% \item[itrace] If $>0$ print out an informational message about +%% convergence every $itrace$ iterations.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% \item[istop] An integer specifying the stopping criterion.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ + +%% \item[\bf On Return] +%% \item[x] The computed solution. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[iter] The number of iterations performed.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: an integer variable. +%% \item[err] The error estimate on exit.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: a real number. +%% \item[info] Error code.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required} \\ +%% An integer value; 0 means no error has been detected. +%% \end{description} +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% % +%% % CGS +%% % +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%% \subroutine{psb\_cgs \label{cgs}}{CGS Iterative Method} + +%% This subroutine implements the CGS method with restarting. The +%% stopping criterion is the normwise backward error, in the infinity +%% norm, i.e. the iteration is stopped when +%% \[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \] +%% or +%% \[ \frac{\|r_i\|}{\|b\|_2} < eps \] +%% according to the value passed through the istop argument (see later). + + +%% \syntax{call psb\_cgs}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,istop} + +%% \begin{description} +%% \item[\bf On Entry] +%% \item[a] the local portion of global sparse matrix +%% $A$. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \spdata. +%% \item[prec] The data structure containing the preconditioner.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \precdata. +%% \item[b] The RHS vector. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[x] The initial guess. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[eps] The stopping tolerance. \\ +%% Scope: {\bf global} \\ +%% Type: {\bf required}\\ +%% Specified as: a real number. +%% \item[desc\_a] contains data structures for communications.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \descdata. +%% \item[itmax] The maximum number of iterations to perform.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Default: $itmax = 1000$.\\ +%% Specified as: an integer variable $itmax \ge 1$. +%% \item[itrace] If $>0$ print out an informational message about +%% convergence every $itrace$ iterations.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% \item[istop] An integer specifying the stopping criterion.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ + +%% \item[\bf On Return] +%% \item[x] The computed solution. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[iter] The number of iterations performed.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: an integer variable. +%% \item[err] The error estimate on exit.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: a real number. +%% \item[info] Error code.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required} \\ +%% An integer value; 0 means no error has been detected. +%% \end{description} + +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% % +%% % BiCG +%% % +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% \subroutine{psb\_bicg \label{bicg}}{BiCG Iterative Method} + +%% This subroutine implements the BiCG method with restarting. The +%% stopping criterion is the normwise backward error, in the infinity +%% norm, i.e. the iteration is stopped when +%% \[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \] +%% or +%% \[ \frac{\|r_i\|}{\|b\|_2} < eps \] +%% according to the value passed through the istop argument (see later). + + +%% \syntax{call psb\_bicg}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,istop} + +%% \begin{description} +%% \item[\bf On Entry] +%% \item[a] the local portion of global sparse matrix +%% $A$. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \spdata. +%% \item[prec] The data structure containing the preconditioner.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \precdata. +%% \item[b] The RHS vector. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[x] The initial guess. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[eps] The stopping tolerance. \\ +%% Scope: {\bf global} \\ +%% Type: {\bf required}\\ +%% Specified as: a real number. +%% \item[desc\_a] contains data structures for communications.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \descdata. +%% \item[itmax] The maximum number of iterations to perform.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Default: $itmax = 1000$.\\ +%% Specified as: an integer variable $itmax \ge 1$. +%% \item[itrace] If $>0$ print out an informational message about +%% convergence every $itrace$ iterations.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% \item[istop] An integer specifying the stopping criterion.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ + +%% \item[\bf On Return] +%% \item[x] The computed solution. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[iter] The number of iterations performed.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: an integer variable. +%% \item[err] The error estimate on exit.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: a real number. +%% \item[info] Error code.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required} \\ +%% An integer value; 0 means no error has been detected. +%% \end{description} + + +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% % +%% % BiCGSTAB +%% % +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% \subroutine{psb\_bicgstab \label{bicgstab}}{BiCGSTAB Iterative Method} + +%% This subroutine implements the BiCGSTAB method with restarting. The +%% stopping criterion is the normwise backward error, in the infinity +%% norm, i.e. the iteration is stopped when +%% \[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \] +%% or +%% \[ \frac{\|r_i\|}{\|b\|_2} < eps \] +%% according to the value passed through the istop argument (see later). + + +%% \syntax{call psb\_bicgstab}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,istop} + +%% \begin{description} +%% \item[\bf On Entry] +%% \item[a] the local portion of global sparse matrix +%% $A$. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \spdata. +%% \item[prec] The data structure containing the preconditioner.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \precdata. +%% \item[b] The RHS vector. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[x] The initial guess. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[eps] The stopping tolerance. \\ +%% Scope: {\bf global} \\ +%% Type: {\bf required}\\ +%% Specified as: a real number. +%% \item[desc\_a] contains data structures for communications.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \descdata. +%% \item[itmax] The maximum number of iterations to perform.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Default: $itmax = 1000$.\\ +%% Specified as: an integer variable $itmax \ge 1$. +%% \item[itrace] If $>0$ print out an informational message about +%% convergence every $itrace$ iterations.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% \item[istop] An integer specifying the stopping criterion.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ + +%% \item[\bf On Return] +%% \item[x] The computed solution. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[iter] The number of iterations performed.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: an integer variable. +%% \item[err] The error estimate on exit.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: a real number. +%% \item[info] Error code.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required} \\ +%% An integer value; 0 means no error has been detected. +%% \end{description} + + +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% % +%% % BiCGSTAB(L) +%% % +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% \subroutine{psb\_bicgstabl \label{bicgstabl}}{BiCGSTAB-$l$ Iterative Method} + +%% This subroutine implements the BiCGSTAB-$l$ method with restarting. The +%% stopping criterion is the normwise backward error, in the infinity +%% norm, i.e. the iteration is stopped when +%% \[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \] +%% or +%% \[ \frac{\|r_i\|}{\|b\|_2} < eps \] +%% according to the value passed through the istop argument (see later). + + +%% \syntax{call psb\_bicgstab}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,irst,istop} + +%% \begin{description} +%% \item[\bf On Entry] +%% \item[a] the local portion of global sparse matrix +%% $A$. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \spdata. +%% \item[prec] The data structure containing the preconditioner.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \precdata. +%% \item[b] The RHS vector. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[x] The initial guess. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[eps] The stopping tolerance. \\ +%% Scope: {\bf global} \\ +%% Type: {\bf required}\\ +%% Specified as: a real number. +%% \item[desc\_a] contains data structures for communications.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \descdata. +%% \item[itmax] The maximum number of iterations to perform.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Default: $itmax = 1000$.\\ +%% Specified as: an integer variable $itmax \ge 1$. +%% \item[itrace] If $>0$ print out an informational message about +%% convergence every $itrace$ iterations.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% \item[irst] An integer specifying the restarting iteration.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% \item[istop] An integer specifying the stopping criterion.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ + +%% \item[\bf On Return] +%% \item[x] The computed solution. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[iter] The number of iterations performed.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: an integer variable. +%% \item[err] The error estimate on exit.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: a real number. +%% \item[info] Error code.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required} \\ +%% An integer value; 0 means no error has been detected. +%% \end{description} + + +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% % +%% % GMRES +%% % +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% \subroutine{psb\_gmres \label{gmres}}{GMRES Iterative Method} + +%% This subroutine implements the GMRES method with restarting. The +%% stopping criterion is the normwise backward error, in the infinity +%% norm, i.e. the iteration is stopped when +%% \[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \] +%% or +%% \[ \frac{\|r_i\|}{\|b\|_2} < eps \] +%% according to the value passed through the istop argument (see later). + + +%% \syntax{call psb\_gmres}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,irst,istop} + +%% \begin{description} +%% \item[\bf On Entry] +%% \item[a] the local portion of global sparse matrix +%% $A$. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \spdata. +%% \item[prec] The data structure containing the preconditioner.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \precdata. +%% \item[b] The RHS vector. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[x] The initial guess. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[eps] The stopping tolerance. \\ +%% Scope: {\bf global} \\ +%% Type: {\bf required}\\ +%% Specified as: a real number. +%% \item[desc\_a] contains data structures for communications.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \descdata. +%% \item[itmax] The maximum number of iterations to perform.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Default: $itmax = 1000$.\\ +%% Specified as: an integer variable $itmax \ge 1$. +%% \item[itrace] If $>0$ print out an informational message about +%% convergence every $itrace$ iterations.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% \item[irst] An integer specifying the restart iteration.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% \item[istop] An integer specifying the stopping criterion.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ + +%% \item[\bf On Return] +%% \item[x] The computed solution. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[iter] The number of iterations performed.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: an integer variable. +%% \item[err] The error estimate on exit.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: a real number. +%% \item[info] Error code.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required} \\ +%% An integer value; 0 means no error has been detected. +%% \end{description} + + + + + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "userguide" +%%% End: diff --git a/docs/pdf/precs.tex b/docs/pdf/precs.tex new file mode 100644 index 00000000..6166b796 --- /dev/null +++ b/docs/pdf/precs.tex @@ -0,0 +1,278 @@ +\section{Preconditioner routines} +\label{sec:precs} + +% \section{Preconditioners} +\label{sec:psprecs} +The MLD2P4 library contains the implementation of many preconditioning +techniques. The preconditioners may be applied as normal ``base'' +preconditioners; alternatively multiple ``base'' preconditioners may +be combined in a multilevel framework. + +The base (one-level) preconditioners include: +\begin{itemize} +\item Diagonal Scaling +\item Block Jacobi +\item Additive Schwarz, Restricted Additive Schwarz and + Additive Schwarz with Harmonic extensions; +\end{itemize} +The Jacobi and Additive Schwarz preconditioners can make use of the +following solvers: +\begin{itemize} +\item Level-$p$ Incomplete LU factorization ($ILU(p)$); +\item Threshold Incomplete LU factorization ($ILU(\tau,p)$); +\item Complete LU factorization by means of the following optional + external packages: +\begin{itemize} +\item UMFPACK; +\item SuperLU; +\item SuperLU\_Dist. +\end{itemize} +\end{itemize} + +The supporting data type and subroutine interfaces are defined in the +module \verb|mld_prec_mod|; the module also overrides the variables +and tyep definitions of \verb|psb_prec_mod| so as to function as a +drop-in replacement for the PSBLAS methods. Thus if the user does not +wish to employ the additional MLD2P4 capabitlities, it is possible to +migrate an existing PSBLAS program without any source code +modifications, only a recompilation is needed. + +%% We also provide a companion package of multi-level Additive +%% Schwarz preconditioners called MD2P4; this is actually a family of +%% preconditioners since there is the possibility to choose between +%% many variants, and is currently in an experimental stateIts +%% documentation is planned to appear after stabilization of the +%% package, which will characterize release 2.1 of our library. + + + + +\subroutine{mld\_precinit}{Initialize a preconditioner} + +\syntax{call mld\_precinit}{prec, ptype, info} +\syntax*{call mld\_precinit}{prec, ptype, info, nlev} + +\begin{description} +\item[Type:] Asynchronous. +\item[\bf On Entry] +\item[ptype] the type of preconditioner. +Scope: {\bf global} \\ +Type: {\bf required}\\ +Intent: {\bf in}.\\ +Specified as: a character string, see usage notes. +\item[nlev] Number of levels in a multilevel precondtioner. +Scope: {\bf global} \\ +Type: {\bf optional}\\ +Specified as: an integer value, see usage notes. +%% \item[rs] +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Specified as: a long precision real number. +\item[\bf On Exit] + +\item[prec] +Scope: {\bf local} \\ +Type: {\bf required}\\ +Intent: {\bf inout}.\\ +Specified as: a preconditioner data structure \precdata. +\item[info] +Scope: {\bf global} \\ +Type: {\bf required}\\ +Intent: {\bf out}.\\ +Error code: if no error, 0 is returned. +\end{description} +\subsection*{Usage Notes} +%% The PSBLAS 2.0 contains a number of preconditioners, ranging from a +%% simple diagonal scaling to 2-level domain decomposition. These +%% preconditioners may use the SuperLU or the UMFPACK software, if +%% installed; see~\cite{SUPERLU,UMFPACK}. +Legal inputs to this subroutine are interpreted depending on the +$ptype$ string as follows\footnote{The string is case-insensitive}: +\begin{description} +\item[NONE] No preconditioning, i.e. the preconditioner is just a copy + operator. +\item[DIAG] Diagonal scaling; each entry of the input vector is + multiplied by the reciprocal of the sum of the absolute values of + the coefficients in the corresponding row of matrix $A$; +\item[BJAC] Precondition by a factorization of the + block-diagonal of matrix $A$, where block boundaries are determined + by the data allocation boundaries for each process; requires no + communication. +\item[AS] Additive Schwarz; default is to apply the Restricted + Additive Schwarz variant, with an $ILU(0)$ factorization +\item[ML] Multilevel preconditioner. +\end{description} + + + +\subroutine{mld\_precset}{Set preconditioner features} + +\syntax{call mld\_precset}{prec, what, val, info, ilev} + + +\begin{description} +\item[Type:] Asynchronous. +\item[\bf On Entry] +\item[prec] the preconditioner.\\ +Scope: {\bf local} \\ +Type: {\bf required}\\ +Intent: {\bf inout}.\\ +Specified as: an already initialized precondtioner data structure \precdata\\ +\item[what] The feature to be set. \\ +Scope: {\bf local} \\ +Type: {\bf required}\\ +Intent: {\bf in}.\\ +Specified as: an integer constants. Symbolic names are available in +the library module, see usage notes for legal values. +\item[val] The value to set the chosen feature to. \\ +Scope: {\bf local} \\ +Type: {\bf required}\\ +Intent: {\bf in}.\\ +Specified as: an integer, double precision or character variable. +Symbolic names for some choices are available in the library module, +see usage notes for legal values. +\item[ilev] The level of a multilevel preconditioner to which the + feature choice should apply.\\ +Scope: {\bf global} \\ +Type: {\bf optional}\\ +Specified as: an integer value, see usage notes. +\end{description} + +\begin{description} +\item[\bf On Return] +\item[prec] the preconditioner.\\ +Scope: {\bf local} \\ +Type: {\bf required}\\ +Intent: {\bf inout}.\\ +Specified as: a precondtioner data structure \precdata\\ +\item[info] Error code.\\ +Scope: {\bf local} \\ +Type: {\bf required} \\ +Intent: {\bf out}.\\ +An integer value; 0 means no error has been detected. +\end{description} + +\subsection*{Usage Notes} +Legal inputs to this subroutine are interpreted depending on the value +of \verb|what| input as follows +\begin{description} +\item[mld\_coarse\_mat\_] +\end{description} + + +\subroutine{mld\_precbld}{Builds a preconditioner} + +\syntax{call mld\_precbld}{a, desc\_a, prec, info} + +\begin{description} +\item[Type:] Synchronous. +\item[\bf On Entry] +\item[a] the system sparse matrix. +Scope: {\bf local} \\ +Type: {\bf required}\\ +Intent: {\bf in}, target.\\ +Specified as: a sparse matrix data structure \spdata. +\item[prec] the preconditioner.\\ +Scope: {\bf local} \\ +Type: {\bf required}\\ +Intent: {\bf inout}.\\ +Specified as: an already initialized precondtioner data structure \precdata\\ +\item[desc\_a] the problem communication descriptor. +Scope: {\bf local} \\ +Type: {\bf required}\\ +Intent: {\bf in}, target.\\ +Specified as: a communication descriptor data structure \descdata. +%% \item[upd] +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Intent: {\bf in}.\\ +%% Specified as: a character. +\end{description} + +\begin{description} +\item[\bf On Return] +\item[prec] the preconditioner.\\ +Scope: {\bf local} \\ +Type: {\bf required}\\ +Intent: {\bf inout}.\\ +Specified as: a precondtioner data structure \precdata\\ +\item[info] Error code.\\ +Scope: {\bf local} \\ +Type: {\bf required} \\ +Intent: {\bf out}.\\ +An integer value; 0 means no error has been detected. +\end{description} + + + +\subroutine{mld\_precaply}{Preconditioner application routine} + +\syntax{call mld\_precaply}{prec,x,y,desc\_a,info,trans,work} +\syntax*{call mld\_precaply}{prec,x,desc\_a,info,trans} + +\begin{description} +\item[Type:] Synchronous. +\item[\bf On Entry] +\item[prec] the preconditioner. +Scope: {\bf local} \\ +Type: {\bf required}\\ +Intent: {\bf in}.\\ +Specified as: a preconditioner data structure \precdata. +\item[x] the source vector. +Scope: {\bf local} \\ +Type: {\bf required}\\ +Intent: {\bf inout}.\\ +Specified as: a double precision array. +\item[desc\_a] the problem communication descriptor. +Scope: {\bf local} \\ +Type: {\bf required}\\ +Intent: {\bf in}.\\ +Specified as: a communication data structure \descdata. +\item[trans] +Scope: {\bf } \\ +Type: {\bf optional}\\ +Intent: {\bf in}.\\ +Specified as: a character. +\item[work] an optional work space +Scope: {\bf local} \\ +Type: {\bf optional}\\ +Intent: {\bf inout}.\\ +Specified as: a double precision array. +\end{description} + +\begin{description} +\item[\bf On Return] +\item[y] the destination vector. +Scope: {\bf local} \\ +Type: {\bf required}\\ +Intent: {\bf inout}.\\ +Specified as: a double precision array. +\item[info] Error code.\\ +Scope: {\bf local} \\ +Type: {\bf required} \\ +Intent: {\bf out}.\\ +An integer value; 0 means no error has been detected. +\end{description} + + + +\subroutine{mld\_prec\_descr}{Prints a description of current preconditioner} + +\syntax{call mld\_prec\_descr}{prec} + +\begin{description} +\item[Type:] Asynchronous. +\item[\bf On Entry] +\item[prec] the preconditioner. +Scope: {\bf local} \\ +Type: {\bf required}\\ +Intent: {\bf in}.\\ +Specified as: a preconditioner data structure \precdata. +\end{description} + + + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "userguide" +%%% End: diff --git a/docs/pdf/title.tex b/docs/pdf/title.tex new file mode 100644 index 00000000..89b9ec82 --- /dev/null +++ b/docs/pdf/title.tex @@ -0,0 +1,51 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Contents: The title page +% $Id: title.tex 1999 2007-10-29 15:25:27Z sfilippo $ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\ifx\pdfoutput\undefined % We're not running pdftex +\else +\pdfbookmark{MLD2P4-1.0 User's Guide}{title} +\fi +\newlength{\centeroffset} +\setlength{\centeroffset}{-0.5\oddsidemargin} +\addtolength{\centeroffset}{0.5\evensidemargin} +%\addtolength{\textwidth}{-\centeroffset} +\thispagestyle{empty} +\vspace*{\stretch{1}} +\noindent\hspace*{\centeroffset}\makebox[0pt][l]{\begin{minipage}{\textwidth} +\flushright +{\Huge\bfseries MLD2P4-1.0 User's guide +} +\noindent\rule[-1ex]{\textwidth}{5pt}\\[2.5ex] +\hfill\emph{\Large A reference guide for the MultiLevel Domain + Decomposition Parallel Preconditioners Package based on Parallel Sparse BLAS} +\end{minipage}} + +\vspace{\stretch{1}} +\noindent\hspace*{\centeroffset}\makebox[0pt][l]{\begin{minipage}{\textwidth} +\flushright +{\bfseries +by Salvatore Filippone\\ + Alfredo Buttari} \\ +University of Rome ``Tor Vergata'' \\[3ex] +{\bfseries Daniela di Serafino }\\ +Second University of Naples\\[3ex] +{\bfseries Pasqua D'Ambra}\\ +ICAR-CNR, Naples\\[3ex] +\today +\end{minipage}} + +%\addtolength{\textwidth}{\centeroffset} +\vspace{\stretch{2}} + +\endinput + +% + +% Local Variables: +% TeX-master: "userguide" +% mode: latex +% mode: flyspell +% End: + diff --git a/docs/pdf/userguide.tex b/docs/pdf/userguide.tex new file mode 100644 index 00000000..0ff357a7 --- /dev/null +++ b/docs/pdf/userguide.tex @@ -0,0 +1,255 @@ +\documentclass[10pt,a4paper,twoside]{article} +\usepackage{pstricks} +\usepackage{fancybox} +\usepackage{amsfonts} +% \usepackage{minitoc} +% \setcounter{minitocdepth}{2} +\usepackage[bookmarks=true, + bookmarksnumbered=true, + bookmarksopen=false, + plainpages=false, + pdfpagelabels, + colorlinks, + linkcolor=blue]{hyperref} +\usepackage{ifthen} +\usepackage{graphicx} +\newtheorem{theorem}{Theorem} +\newtheorem{corollary}{Corollary} + +%\newboolean{mtc} +%\setboolean{mtc}{true} + +\pdfoutput=1 +\relax +\pdfcompresslevel=0 %-- 0 = none, 9 = best +\pdfinfo{ %-- Info dictionary of PDF output /Author (Alfredo Buttari) + /Title ( MultiLevel Domain Decomposition Parallel Preconditioners Package + based on PSBLAS V. 1.0) + /Subject ( MultiLevel Domain Decomposition Parallel Preconditioners + Package) + /Keywords (Computer Science Linear Algebra Fluid Dynamics Parallel Linux MPI PSBLAS Iterative Solvers Preconditioners) + /Creator (pdfLaTeX) + /Producer ($Id: userguide.tex 1978 2007-10-19 14:51:12Z sfilippo $) +} +\pdfcatalog{ %-- Catalog dictionary of PDF output. + /URI (http://ce.uniroma2.it/psblas) +} + +\newcounter{subroutine}[subsection] +\newcounter{example}[subroutine] +\makeatletter +\def\subroutine{\@ifstar{\@subroutine}{\clearpage\@subroutine}}% +\def\@subroutine#1#2{% +\stepcounter{subroutine}% + \section*{\flushleft #1---#2 \endflushleft}% + \addcontentsline{toc}{subsection}{#1}% + \markright{#1}}% +\newcommand{\subsubroutine}[2]{% +\stepcounter{subroutine}% + \subsection*{\flushleft #1---#2 \endflushleft}% + \addcontentsline{toc}{subsubsection}{#1}% + \markright{#1}}% +\newcommand{\examplename}{Example} +\newcommand{\syntaxname}{Syntax} +\def\syntax{\@ifstar{\@ssyntax}{\@syntax}}% +\def\@syntax{\nobreak\section*{\syntaxname}% + \@ssyntax}% +\def\@ssyntax#1#2{% + \nobreak + \setbox\@tempboxa\hbox{#1\ {\em $($#2$)$}}% + \ifdim \wd\@tempboxa >\hsize + \setbox\@tempboxa\hbox{\em $($#2$)$} + \ifdim\wd\@tempboxa >\hsize + \begin{flushright}#1\ \em$($#2$)$\end{flushright}% + \else + \hbox to\hsize{#1\hfil}% + \hbox to\hsize{\hfil\box\@tempboxa}% + \fi + \else + \hbox to\hsize{\hfil\box\@tempboxa\hfil}% + \fi\par\vskip\baselineskip} +\makeatother +\newcommand{\example}{\stepcounter{example}% +\section*{\examplename~\theexample}} + +\newcommand{\precdata}{\hyperlink{precdata}{{\tt mld\_prec\_type}}} +\newcommand{\descdata}{\hyperlink{descdata}{{\tt psb\_desc\_type}}} +\newcommand{\spdata}{\hyperlink{spdata}{{\tt psb\_spmat\_type}}} + +\begin{document} +\include{title} +\cleardoublepage +\begingroup + \renewcommand*{\thepage}{toc} + \pagenumbering{roman} % Roman numbering + \setcounter{page}{1} % Abstract start on page ii + \tableofcontents +\endgroup + +\cleardoublepage + +\pagenumbering{arabic} % Arabic numbering +\setcounter{page}{1} % Chapters start on page 1 + +\include{intro} +\include{precs} +\include{methods} + +\cleardoublepage + +\begin{thebibliography}{99} + +\bibitem{PARA04FOREST} +G.~Bella, S.~Filippone, A.~De Maio and M.~Testa, +{\em A Simulation Model for Forest Fires}, +in J.~Dongarra, K.~Madsen, J.~Wasniewski, editors, +Proceedings of PARA~04 Workshop on State of the Art +in Scientific Computing, pp.~546--553, Lecture Notes in Computer Science, +Springer, 2005. +\bibitem{2007d} A. Buttari, D. di Serafino, P. D'Ambra, S. Filippone,\newblock +2LEV-D2P4: a package of high-performance preconditioners,\newblock +Applicable Algebra in Engineering, Communications and Computing, +Volume 18, Number 3, May, 2007, pp. 223-239 +%Published online: 13 February 2007, {\tt http://dx.doi.org/10.1007/s00200-007-0035-z} +% +\bibitem{2007c} P. D'Ambra, S. Filippone, D. Di Serafino\newblock +On the Development of PSBLAS-based Parallel Two-level Schwarz Preconditioners +\newblock +Applied Numerical Mathematics, Elsevier Science, +Volume 57, Issues 11-12, November-December 2007, Pages 1181-1196. +%published online 3 February 2007, {\tt +% http://dx.doi.org/10.1016/j.apnum.2007.01.006} + +\bibitem{BLAS2} + Dongarra, J. J., DuCroz, J., Hammarling, S. and Hanson, R., +An Extended Set of {F}ortran {B}asic {L}inear {A}lgebra {S}ubprograms, +{ACM Trans. Math. Softw.} vol.~{14}, 1--17, 1988. +\bibitem{BLAS3} + Dongarra, J., DuCroz, J., Hammarling, S. and Duff, I., +A Set of level 3 Basic Linear Algebra Subprograms, +{ACM Trans. Math. Softw.} vol.~{16}, 1--17, 1990. +%% \bibitem{DOUGLAS} +%% R.E.~Bank and C.C.~Douglas, +%% {\em SMMP: Sparse Matrix Multiplication Package}, +%% Advances in Computational Mathematics, 1993, 1, 127-137. +%% (See also {\tt http://www.mgnet.org/~douglas/ccd-codes.html}) +% +% +%% \bibitem{PARA04} +%% A.~Buttari, P.~D'Ambra, D.~di Serafino and S.~Filippone, +%% {\em Extending PSBLAS to Build Parallel Schwarz Preconditioners}, +%% in , J.~Dongarra, K.~Madsen, J.~Wasniewski, editors, +%% Proceedings of PARA~04 Workshop on State of the Art +%% in Scientific Computing, pp.~593--602, Lecture Notes in Computer Science, +%% Springer, 2005. +% +%% \bibitem{CAI_SAAD} +%% X.~C.~Cai and Y.~Saad, +%% {\em Overlapping Domain Decomposition Algorithms for General Sparse Matrices}, +%% Numerical Linear Algebra with Applications, 3(3), pp.~221--237, 1996. +%% % +%% \bibitem{CAI_SARKIS} +%% X.C.~Cai and M.~Sarkis, +%% {\em A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems}, +%% SIAM Journal on Scientific Computing, 21(2), pp.~792--797, 1999. +% +%% \bibitem{CAI_WIDLUND} +%% X.C.~Cai and O.~B.~Widlund, +%% {\em Domain Decomposition Algorithms for Indefinite Elliptic Problems}, +%% SIAM Journal on Scientific and Statistical Computing, 13(1), pp.~243--258, 1992. +% +%% \bibitem{DD1} +%% T.~Chan and T.~Mathew, +%% {\em Domain Decomposition Algorithms}, +%% in A.~Iserles, editor, Acta Numerica 1994, pp.~61--143, 1994. +%% Cambridge University Press. +%% % +%% \bibitem{APNUM06} +%% P.~D'Ambra, D.~di Serafino and S.~Filippone, +%% On the Development of PSBLAS-based Parallel Two-level Schwarz Preconditioners, +%% Applied Numerical Mathematics, to appear, 2007. +% +%% \bibitem{UMFPACK} +%% T.A.~Davis, +%% {\em Algorithm 832: UMFPACK - an Unsymmetric-pattern Multifrontal +%% Method with a Column Pre-ordering Strategy}, +%% ACM Transactions on Mathematical Software, 30, pp.~196--199, 2004. +%% (See also {\tt http://www.cise.ufl.edu/~davis/}) +%% % +%% \bibitem{SUPERLU} +%% J.W.~Demmel, S.C.~Eisenstat, J.R.~Gilbert, X.S.~Li and J.W.H.~Liu, +%% A supernodal approach to sparse partial pivoting, +%% SIAM Journal on Matrix Analysis and Applications, 20(3), pp.~720--755, 1999. +% +\bibitem{BLACS} +J.~J.~Dongarra and R.~C.~Whaley, +{\em A User's Guide to the BLACS v.~1.1}, +Lapack Working Note 94, Tech.\ Rep.\ UT-CS-95-281, University of +Tennessee, March 1995 (updated May 1997). +% +\bibitem{sblas97} +I.~Duff, M.~Marrone, G.~Radicati and C.~Vittoli, +{\em Level 3 Basic Linear Algebra Subprograms for Sparse Matrices: +a User Level Interface}, +ACM Transactions on Mathematical Software, 23(3), pp.~379--401, 1997. +% +\bibitem{sblas02} +I.~Duff, M.~Heroux and R.~Pozo, +{\em An Overview of the Sparse Basic Linear +Algebra Subprograms: the New Standard from the BLAS Technical Forum}, +ACM Transactions on Mathematical Software, 28(2), pp.~239--267, 2002. +\bibitem{PSBLAS} +S.~Filippone and M.~Colajanni, +{\em PSBLAS: A Library for Parallel Linear Algebra +Computation on Sparse Matrices}, +\newblock +ACM Transactions on Mathematical Software, 26(4), pp.~527--550, 2000. +% +\bibitem{KIVA3PSBLAS} +S.~Filippone, P.~D'Ambra, M.~Colajanni, +{\em Using a Parallel Library of Sparse Linear Algebra in a Fluid Dynamics +Applications Code on Linux Clusters}, +in G.~Joubert, A.~Murli, F.~Peters, M.~Vanneschi, editors, +Parallel Computing - Advances \& Current Issues, +pp.~441--448, Imperial College Press, 2002. +% +\bibitem{METIS} +Karypis, G. and Kumar, V., +{\em {METIS}: Unstructured Graph Partitioning and Sparse Matrix + Ordering System}. +Minneapolis, MN 55455: University of Minnesota, Department of + Computer Science, 1995. +Internet Address: {\verb|http://www.cs.umn.edu/~karypis|}. +\bibitem{BLAS1} +Lawson, C., Hanson, R., Kincaid, D. and Krogh, F., + Basic {L}inear {A}lgebra {S}ubprograms for {F}ortran usage, +{ACM Trans. Math. Softw.} vol.~{5}, 38--329, 1979. + +\bibitem{machiels} +{Machiels, L. and Deville, M.} +{\em Fortran 90: An entry to object-oriented programming for the solution + of partial differential equations.} +{ACM Trans. Math. Softw.} vol.~{23}, 32--49. +\bibitem{metcalf} +{Metcalf, M., Reid, J. and Cohen, M.} +{\em Fortran 95/2003 explained.} +{Oxford University Press}, 2004. +% +%% \bibitem{DD2} +%% B.~Smith, P.~Bjorstad and W.~Gropp, +%% {\em Domain Decomposition: Parallel Multilevel Methods for Elliptic +%% Partial Differential Equations}, +%% Cambridge University Press, 1996. +% +\bibitem{MPI1} +M.~Snir, S.~Otto, S.~Huss-Lederman, D.~Walker and J.~Dongarra, +{\em MPI: The Complete Reference. Volume 1 - The MPI Core}, second edition, +MIT Press, 1998. +% +\end{thebibliography} + +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: 'userguide' +%%% End: diff --git a/docs/userguide.pdf b/docs/userguide.pdf new file mode 100644 index 00000000..8d64e33a --- /dev/null +++ b/docs/userguide.pdf @@ -0,0 +1,5174 @@ +%PDF-1.4 +5 0 obj +<< /S /GoTo /D (title.0) >> +endobj +8 0 obj +(MLD2P4-1.0 User's Guide) +endobj +9 0 obj +<< /S /GoTo /D (section.1) >> +endobj +12 0 obj +(1 Introduction) +endobj +13 0 obj +<< /S /GoTo /D (subsection.1.1) >> +endobj +16 0 obj +(1.1 Programming model) +endobj +17 0 obj +<< /S /GoTo /D (section.2) >> +endobj +20 0 obj +(2 Preconditioner routines) +endobj +21 0 obj +<< /S /GoTo /D (section*.2) >> +endobj +24 0 obj +(mld\137precinit) +endobj +25 0 obj +<< /S /GoTo /D (section*.5) >> +endobj +28 0 obj +(mld\137precset) +endobj +29 0 obj +<< /S /GoTo /D (section*.8) >> +endobj +32 0 obj +(mld\137precbld) +endobj +33 0 obj +<< /S /GoTo /D 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI7) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /BVYXMW+CMMI7 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 105 /i put +readonly def +/FontBBox{0 -250 1171 750}readonly def +currentdict end +currentfile eexec +oc;j~EЪ)s̾;.;rTejiK/df5A|{S/ )Sc\^ȟmp+#vL17~k d# +]LeVߐGoo٥\k 9Mv92#:iQ?.n>%jzGm >NjS])7uևUQh4)-×p#z{8YаGP9 )"Pƣ3ГzYYZgp_PC߬CܔDC'<|(Rl/IxXMYzntԟlAv)|*iQP3|TxL" ʃ?Aw·pҋ:r)6,N{?JoA剳Js(0T9$ն''0j%&4LwQcKHpY Bֶ6$bZXZmX>B#9xҥ6IUJeG#݆>@P1o(ߋUcCо"[D.)>;@LyB Gp^yc96d{f'(~z[ܸQRn|48!΍eϟg'_$R;pb>زX _|M%r8U{^^1="\[dZB6CoK8/Gƪ86g84ʹLeoI4&>NU[pf[ž@vam(8a.Qr T+IFdj=aY@O)UQ4c,>inY( (o +V!gJb`B*g9!+spҞ @1YaČd_*\hIլ-$u0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +endstream +endobj +180 0 obj << +/Type /Font +/Subtype /Type1 +/Encoding 222 0 R +/FirstChar 105 +/LastChar 105 +/Widths 223 0 R +/BaseFont /BVYXMW+CMMI7 +/FontDescriptor 178 0 R +>> endobj +178 0 obj << +/Ascent 694 +/CapHeight 683 +/Descent -194 +/FontName /BVYXMW+CMMI7 +/ItalicAngle -14.04 +/StemV 81 +/XHeight 431 +/FontBBox [0 -250 1171 750] +/Flags 4 +/CharSet (/i) +/FontFile 179 0 R +>> endobj +223 0 obj +[404 ] +endobj +222 0 obj << +/Type /Encoding +/Differences [ 0 /.notdef 105/i 106/.notdef] +>> endobj +125 0 obj << +/Length1 915 +/Length2 2883 +/Length3 532 +/Length 4330 +>> +stream +%!PS-AdobeFont-1.1: CMR8 1.0 +%%CreationDate: 1991 Aug 20 16:39:40 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR8) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /OELLFO+CMR8 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 45 /hyphen put +dup 84 /T put +dup 97 /a put +dup 99 /c put +dup 101 /e put +dup 103 /g put +dup 104 /h put +dup 105 /i put +dup 110 /n put +dup 114 /r put +dup 115 /s put +dup 116 /t put +dup 118 /v put +readonly def +/FontBBox{-36 -250 1070 750}readonly def +currentdict end +currentfile eexec +oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou\@[6]nhmlhaH+4/?3&n=a6E#|~.ԅˡw,"rg[eHi>u +Wת>~ӖѿJmdvA +[4|ܾ.Vz_1. Ff |X9^Rw] +ۊ31S\DKZW` P^3 eێ 8`2?l;Ȋ!eXxh +Df@=$*IBXԏ!Wx-b1 C; p}hQi=HXbgbmǣR,>_Q! +Z؞Ar]< Qjt8?B,mN3v լǵ+K6 t{AJcQ%r?v60RmXsŤ+pǸi:Us)kPW\~; 7T.N }.&:D~zp0C_HOzCByAOve1k`G|f28'j0&®uk6sw, I5&{oP}p2d +CA!8Z⓪٦ǎaBLebG\[F_}+w!JLz>:<,?˲s =,Fj#V?" y(=D{qPƷC6w"B ҥ!aN arE[##oS)MUL*sI8<0_?k`ˠE女 vFyx8Ԑ%6lF"aJ^wtBy͖gV~J 2g/dƦ+]:KU¡S8D( $"ۀ"36y0%b9y]5 q4aB>I~]\q޼sSWP4k[A6GXzBA74eUa t$.WPH*SFI[U7X; +B~,A6`)M> !]}Ȗ =-2#Nmh,0\)E52 8S+\%jQρyJ>R4*׿z6zuF+OfRɻy3FJ":>T@3T?߄jم +w{]5ρcP`%h,P$s'6HܚFLQnf{۫ +'%lU[Ode@Etl>OgGQZb D,DsǴ#r %j!u]} ӆ}!Ʉ ]jy+)P['%t=1:՘o#\>ڃ +yQu3u\:Yڶ3Et>Gb%^6X? :6"Y iKΡv1b \Wh~oC>̎EػffPf#48#|Nǿaԫ#O=QiP d=אkŷЗF-1".V!svyȣLcpDn<g8$kxl!凌eb:#܏4^B)@?~nb*>RlSY4~dz?S*$:R_C^%f?,:yji~DPDl> `&յCǗn$MFħucKkD&ʼa@ӹ2`,QuBpAdk*3ԓuɬ$ꦋU`]|J"4=iM_XGKs[#i[^]+GsN6;>5XMqA^gw!Pc-SH.t#@zA] +:w+b> endobj +124 0 obj << +/Ascent 694 +/CapHeight 683 +/Descent -194 +/FontName /OELLFO+CMR8 +/ItalicAngle 0 +/StemV 76 +/XHeight 431 +/FontBBox [-36 -250 1070 750] +/Flags 4 +/CharSet (/hyphen/T/a/c/e/g/h/i/n/r/s/t/v) +/FontFile 125 0 R +>> endobj +225 0 obj +[354 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 767 0 0 0 0 0 0 0 0 0 0 0 0 531 0 472 0 472 0 531 590 295 0 0 0 0 590 0 0 0 414 419 413 0 561 ] +endobj +224 0 obj << +/Type /Encoding +/Differences [ 0 /.notdef 45/hyphen 46/.notdef 84/T 85/.notdef 97/a 98/.notdef 99/c 100/.notdef 101/e 102/.notdef 103/g/h/i 106/.notdef 110/n 111/.notdef 114/r/s/t 117/.notdef 118/v 119/.notdef] +>> endobj +121 0 obj << +/Length1 735 +/Length2 1052 +/Length3 532 +/Length 2319 +>> +stream +%!PS-AdobeFont-1.1: CMR6 1.0 +%%CreationDate: 1991 Aug 20 16:39:02 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR6) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /ICOPRL+CMR6 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 49 /one put +readonly def +/FontBBox{-20 -250 1193 750}readonly def +currentdict end +currentfile eexec +oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou\@[6]nhmlhaH+4/?3&n=a6E#|~.ԅˡ}_B$~\|"4Pxҍ>P% ~ߏ4q.C3s蛼q翈by?Z72z6LpHC1D"28s B +~ OPQ +O\O}';Pǂ;߉~ I;^קf5)P)6Ö9}ln~E1 k N|dEmϫNO3h>vM83M- ۃB3?(qJ9k7I%֧N93πh.ÉV6k#8"++=fw6Naʹn'`goNq#./eJ[$2E;ԣ *z͕Qt1kBa\ye`90000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +endstream +endobj +122 0 obj << +/Type /Font +/Subtype /Type1 +/Encoding 226 0 R +/FirstChar 49 +/LastChar 49 +/Widths 227 0 R +/BaseFont /ICOPRL+CMR6 +/FontDescriptor 120 0 R +>> endobj +120 0 obj << +/Ascent 694 +/CapHeight 683 +/Descent -194 +/FontName /ICOPRL+CMR6 +/ItalicAngle 0 +/StemV 83 +/XHeight 431 +/FontBBox [-20 -250 1193 750] +/Flags 4 +/CharSet (/one) +/FontFile 121 0 R +>> endobj +227 0 obj +[611 ] +endobj +226 0 obj << +/Type /Encoding +/Differences [ 0 /.notdef 49/one 50/.notdef] +>> endobj +118 0 obj << +/Length1 751 +/Length2 1203 +/Length3 532 +/Length 2486 +>> +stream +%!PS-AdobeFont-1.1: CMR7 1.0 +%%CreationDate: 1991 Aug 20 16:39:21 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR7) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /MGZAWE+CMR7 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 49 /one put +dup 50 /two put +readonly def +/FontBBox{-27 -250 1122 750}readonly def +currentdict end +currentfile eexec +oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou\ʻl24`}IRB s\pzEGAۋa4_p0uAEG)Q|8B*dGWj'0Vix#(=@'qIT5i +(Ѵt` ?E)4E^yҴF+$8&G"Yl?eYjt+TI2! nXKt`˱~h]{>Qaiσ\mFU#Gvh2un8W;R4Ej1B4b ;b9y[lV:P񕈇9g`\J~ O>%V0 ݬ;cJԺjYrt6yql4Qo٫~o_=6xqw,",kϷo +#vI7_ fz!y(3)5*кYb#aM?3G%wG*L4}. f0Fp)_@ڴ +.E z~Fi_F $oG^b=09u61%7ZKUe.E'fe 0cGy\ɑk+zz;U5{CNjvcr0&=Xw;7/LJgz}8̚ug> endobj +117 0 obj << +/Ascent 694 +/CapHeight 683 +/Descent -194 +/FontName /MGZAWE+CMR7 +/ItalicAngle 0 +/StemV 79 +/XHeight 431 +/FontBBox [-27 -250 1122 750] +/Flags 4 +/CharSet (/one/two) +/FontFile 118 0 R +>> endobj +229 0 obj +[569 569 ] +endobj +228 0 obj << +/Type /Encoding +/Differences [ 0 /.notdef 49/one/two 51/.notdef] +>> endobj +107 0 obj << +/Length1 1125 +/Length2 4973 +/Length3 532 +/Length 6630 +>> +stream +%!PS-AdobeFont-1.1: CMTT10 1.00B +%%CreationDate: 1992 Apr 26 10:42:42 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMTT10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch true def +end readonly def +/FontName /VCYLXU+CMTT10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 46 /period put +dup 47 /slash put +dup 58 /colon put +dup 95 /underscore put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 100 /d put +dup 101 /e put +dup 104 /h put +dup 105 /i put +dup 107 /k put +dup 108 /l put +dup 109 /m put +dup 110 /n put +dup 111 /o put +dup 112 /p put +dup 114 /r put +dup 115 /s put +dup 116 /t put +dup 117 /u put +dup 118 /v put +dup 119 /w put +dup 121 /y put +dup 126 /asciitilde put +readonly def +/FontBBox{-4 -235 731 800}readonly def +currentdict end +currentfile eexec +oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou_c2Bطj=-8\Dg݌] /%bԺnٻڿSy b*L(9sWF R:EMksH02E?Oe+Z'zK΃оif <,EDNZ|J#BW3ϗMp(%5%~(5Bk}Aj c'S-8*!iy$G.w g J0nr +;଍ Kr^ox7p4= CyO#y[49'n*xx/J}o֯p6Oޏe}hà1W6Ϋ%(i]Ii +텴""b3=5sJzbJ>[Wе H 2"ێ0Oy9.t:=$EǪ ]to`% +'EKKfrRK^y`vO^v~ZwR iNMW3HSp+T,q!s0(ع;U+3"J8q3dJ`77+IuؿhH<=!'T́2.r% +v y*S\L$r)Xm!UgWyD3y#<+iYPo+e=a.q%B )z=v"1); t -x<b?a,~JDgpt1UsOi1y +E|Kڤڵ8 ar|z(B]KpWSF ~p}+__EqfEXXE\:~*Ys}G[`Рb`4mWUи+ᰁKVdNzqm=7zj +h6 1 xoMgR2, ns4 BtߚC2x`ZBq2avSfW)G e?wb+M4BW6)iO.]%`N[0J;}]_a&Tn`[kFB|xpB4:Ye Xba521gcUbBq cۺkiYQEϲb^Ṋg X컄 `Ĥ1&DΨя:x7fH!ɫ2nU.o {yku p$ibzԶ.^DIБ-4gȲrS#iQ|-X j3bSc+ZiGq0eΪ[egWճic?Us2oi6fu5- ݆zmSArf?$O(ϐ$X[zmhv6}|nP+QcR +:-X2ڡ厫내EXP <ANqe +)V}=XfZ˥|cJCQئ]jS!i @6L-a?{Ʒ~zwLMsImh%k|K@‰E8)Mwl +E"rX{v-r/?IbL]a4ĺfCi6z#qi~%'m:iXRTQt]#h &oh0PD6X6Ө‘^c7h^9nƑpu>&. +Ū;ZƟo崖gH&ё2LlD!uTQ O&*zg)rI` p 25qF 3<\I|2|oa._AS<7h%CiZTۃC/}m8?!0^ݘFvY/Ӧ+&˄F[X AO`9uC/9!ɒ &k-]5 _:vcm5xCZD.,-F EY+28d rDNoQmg%"ڠ¡B(Ÿ\lGEtOocs.nq[}`Q4.#E.}sTU׋(Ud!>f*%tQ~z QcV5\J/M>lHD*v kf`BZzd)<إJU z=x(|#$n} ]*Kc|~̆YqG{|~Zw!6-C.!Bޖ: H~-]DCM;zrIH+c)2*G9DBR4x 6n= DvTs( 6evSuN^oN+MK|vhQ7lXCVO Yj9`idpȼ_*ٽN/g[i@2] ҧU}4KU(ԸPfKb@T_ ##.*H7@^?H=̪j\H5\D6<ҳt{JN(8Y@5G{*vce-ⲶFi՚{Wh}p1CjNTl6Y_ĪM8<)|QRtы~_ddYu3w#Qkld +՗:JI˖&Q)K[u#1fM,@YX譻)-~6 Wmk8<[ōZ)@c8k% w8ZDb Y8.o1Du\7N5^ >6ieUmV[T%^pH?58pކG/9hȕi&OiLY@  'J@ozlSAGX-N`hB(}aX;O +gɭI!k$p'  +iot% T-=%`؂v1zCZXNh)_ d.y__ĺW-fK;LʌcHO y8R[kk 'x*] #Ow)JuVEH{dQ_ YSs iv3Fyk܈&sI)"{ +2 g6<!{A٢џ|"ErK[}`Vh4D ؕ;˻%~6p p4MgCUG]n]KskEHzZ?YIwk;+>d ,MvW$5u/E2 vH|6Už/z)gVsK[4ğ}T'oKkKlMiQ?\G MqPi6 +mrgºC!P/ZNl ӻ YX}`:!nE !lBK*n;fʠh{zS*slvg?pdj=8'(Z\0vӜZ#C] hʊ !-~/T B(i9gԴ.+#FYqSԷ,s >bUIܪک +!D~$oD'MOFBA^guNZGrFan ]_C+E +\2ȗ\t¬#u3m҇j3G({ <ֿwnU;w ǒ0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +endstream +endobj +108 0 obj << +/Type /Font +/Subtype /Type1 +/Encoding 230 0 R +/FirstChar 46 +/LastChar 126 +/Widths 231 0 R +/BaseFont /VCYLXU+CMTT10 +/FontDescriptor 106 0 R +>> endobj +106 0 obj << +/Ascent 611 +/CapHeight 611 +/Descent -222 +/FontName /VCYLXU+CMTT10 +/ItalicAngle 0 +/StemV 69 +/XHeight 431 +/FontBBox [-4 -235 731 800] +/Flags 4 +/CharSet (/period/slash/colon/underscore/a/b/c/d/e/h/i/k/l/m/n/o/p/r/s/t/u/v/w/y/asciitilde) +/FontFile 107 0 R +>> endobj +231 0 obj +[525 525 0 0 0 0 0 0 0 0 0 0 525 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 525 0 525 525 525 525 525 0 0 525 525 0 525 525 525 525 525 525 0 525 525 525 525 525 525 0 525 0 0 0 0 525 ] +endobj +230 0 obj << +/Type /Encoding +/Differences [ 0 /.notdef 46/period/slash 48/.notdef 58/colon 59/.notdef 95/underscore 96/.notdef 97/a/b/c/d/e 102/.notdef 104/h/i 106/.notdef 107/k/l/m/n/o/p 113/.notdef 114/r/s/t/u/v/w 120/.notdef 121/y 122/.notdef 126/asciitilde 127/.notdef] +>> endobj +104 0 obj << +/Length1 1038 +/Length2 4549 +/Length3 532 +/Length 6119 +>> +stream +%!PS-AdobeFont-1.1: CMMI10 1.100 +%%CreationDate: 1996 Jul 23 07:53:57 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /RFRKVT+CMMI10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 28 /tau put +dup 59 /comma put +dup 60 /less put +dup 62 /greater put +dup 65 /A put +dup 73 /I put +dup 76 /L put +dup 85 /U put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 101 /e put +dup 105 /i put +dup 109 /m put +dup 112 /p put +dup 114 /r put +dup 115 /s put +dup 116 /t put +dup 120 /x put +dup 121 /y put +readonly def +/FontBBox{-32 -250 1048 750}readonly def +currentdict end +currentfile eexec +oc;j~EЪ)s̾;.;rTejiK/df5A|{S/ )Sc\^ȟmp+#vL17~k d# +]LeVߐGoo٥\k 9Mՙ= 0)xf +1kX9JS:6V =!X>KM)9! I}HWIUcl=GeZm>nQk2=1p%R`%$]c{!W+8?v(+)0ӈ!YahtA?H @m?|M X9Հ֨#2 +:m,MZ+ǒ\Ex9Yn<Ŀ2^FC[`T+ȬD]ǸFF$oB!>;A\T hxh|5:6;ϖUǷ6~k.T*{8K`y8'dT|-QkKmy9 91|Afr (K*)%_ʬtP`.rY?nrn{v2O_5;\g>R{4_ +: 9pEz~Gu E[n窙i9ヽu#=X&>@Q-2fT{0lY+%dm%dBag(MInǹpFt%V/~@6!tL:nS&Il*rH7d?ܡPZ=uۻ3MfM[S`fvuԳ3Ttw~^QbamM`c4Z7ʺ!@ s9G!t!-_a@Tp[SͰ5s|DmCB@uDT6QU)x2.5BEU;ɉjK#vB -e x9H}#;% u/^7Yȭ[SdtNGbBpV'@!zudL&>te?Bj%1O HKEO 53AOPpg fdxȿ)K VqnpQ, xX C ] ᣛ6;@%A3D8pT#!FD -kYDA|ۊ]Xj,GRohvgN.)9 )* +t״nߦ&_k䑏eKv%D/5Wa_eǡ̦j &":.9dolc:^_>4/MC +s'|CYȖD +_s^>@dc2W \zMvG:QOmGX~Ն]L 3SK |s 24+V\ +~bŌ m~4~Gȩ +'|1Փ~ pQOp?NCL[@'`-pq}1+0U?bSpT ~к̑K**qU{ +_[`w F6&!';uHDn7EXخԘ`U'0ߛUY^=s?t)up"dd!.;d52~ OĮdf?E+d2m~qfR$$*O@dA:7] ,FuT:,qIUDx +G^_NwÅɼ; 0Vt +vOWY2 b<o[-_hᆽR (A:gOK~xm@vʙϳS"p +m? ! 6ɤlQa` ǰ\$)o鸷[BƉM'N_sK1K K THCYViFum NvrƒȪLl-w1l,N xE{w$ T M1>cnۢ[Ar쿎'Қ]`%v; >'/C&%/M*pxވqUu/ƂQ*DeY{42c\7}$9I-ow5a!<\`tH%g>l!+1sGy+1jp9o ktHh2쁆tC~[ uT\R$@Ce]"2Gļjɶg~GhŦ'3ÍM^eI=O τM%ƍxj jCz#Aˊ3B^n>A41 4Ĕ}4b-p\\Lb 0R΃}܍[}LI3 ȨI<8WۭE5zç̦Pb>p'mK Lzr?EQ7f{E6W Aa?:+| +*:l0000>ΡJʴhWP)[\J0l%/41G,pD5%:?h0,dR91ɩ6Y/T7vFI@E0['vB.b_ Nn?'INTZsE7Mc?Lxvu{SM^ZrJ>STqR5YO~fpk}nc(Ծ)~}I؞7F9y{ZL;f= :(u H)(sS)(GDy[oV>{k"\YwU>E $;ҷb{$*@䉌+̹ ҀVUɀM6?;B+=(ɜb혧<*M!bã 3jtgUUűoMf9nxnҝffC9nbg;#7Y?f7*X-Ju⡘®8eG_lb[51(T^\{Ϟ2f$?8'N)@uȉMW#3n}b <˶`&HN3n.c41h r.yMTiʼFӗ셼qIMTA0aZ 1:QxCM5!Vd*muBy()oHHPsqzr\Qj;!dcr**D7BXWϦ8<5.fs@[B! ?f_xx +/.VSM1F|S5Rq|z5=ܒ/_3RB1Xqrȫ\O8H~8=4a d)n\)ʜ>vɕtXI {#s*NQ?otI/*=WLy&")> endobj +103 0 obj << +/Ascent 694 +/CapHeight 683 +/Descent -194 +/FontName /RFRKVT+CMMI10 +/ItalicAngle -14.04 +/StemV 72 +/XHeight 431 +/FontBBox [-32 -250 1048 750] +/Flags 4 +/CharSet (/tau/comma/less/greater/A/I/L/U/a/b/c/e/i/m/p/r/s/t/x/y) +/FontFile 104 0 R +>> endobj +233 0 obj +[437 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 278 778 0 778 0 0 750 0 0 0 0 0 0 0 440 0 0 681 0 0 0 0 0 0 0 0 683 0 0 0 0 0 0 0 0 0 0 0 529 429 433 0 466 0 0 0 345 0 0 0 878 0 0 503 0 451 469 361 0 0 0 572 490 ] +endobj +232 0 obj << +/Type /Encoding +/Differences [ 0 /.notdef 28/tau 29/.notdef 59/comma/less 61/.notdef 62/greater 63/.notdef 65/A 66/.notdef 73/I 74/.notdef 76/L 77/.notdef 85/U 86/.notdef 97/a/b/c 100/.notdef 101/e 102/.notdef 105/i 106/.notdef 109/m 110/.notdef 112/p 113/.notdef 114/r/s/t 117/.notdef 120/x/y 122/.notdef] +>> endobj +101 0 obj << +/Length1 812 +/Length2 902 +/Length3 532 +/Length 2246 +>> +stream +%!PS-AdobeFont-1.1: CMSY10 1.0 +%%CreationDate: 1991 Aug 15 07:20:57 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMSY10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.035 def +/isFixedPitch false def +end readonly def +/FontName /GDGSMG+CMSY10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /minus put +dup 15 /bullet put +dup 21 /greaterequal put +dup 107 /bardbl put +readonly def +/FontBBox{-29 -960 1116 775}readonly def +currentdict end +currentfile eexec +oc;j~EЪ/ ȭX~id}S5Q!gtⵎkJc;rN^X5.Sy +'IqV:r㚉#,# dBZ *R*"7٨y=cLIPsF'f> ba +]fv+QAwdO[x"%Sx~{p҈덡|O +BÄ/GL3h+Ng03jU1~akDzq=U}.KY碌 ֻ1?C N2Muh/4Gm |Q] +OaFދp0z +1ɛQx%:.~e`Q} t-;CH']0NbܒN4٭ +So~.,ԼʴQCMbΞ0+G7<E9˦c/H˥A.gM:^ӽÑp 8nTGU H|P A_HMNi#aj{of凣+z2(Wq^""XG0$BX;[ϸ 2W'^&* Ō@Y`)zJr8kgi˰v/bL(:dZ\h&I% 5̗n$=ɶHA^twwߔ*xnhߩX"CEX/˷f\M5>;γ}P&·ՇPͽcMqݏA;~0es8-Nqt6 7₇2AVkbELyc?RZgz֮ ef0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +endstream +endobj +102 0 obj << +/Type /Font +/Subtype /Type1 +/Encoding 234 0 R +/FirstChar 0 +/LastChar 107 +/Widths 235 0 R +/BaseFont /GDGSMG+CMSY10 +/FontDescriptor 100 0 R +>> endobj +100 0 obj << +/Ascent 750 +/CapHeight 683 +/Descent -194 +/FontName /GDGSMG+CMSY10 +/ItalicAngle -14.035 +/StemV 85 +/XHeight 431 +/FontBBox [-29 -960 1116 775] +/Flags 4 +/CharSet (/minus/bullet/greaterequal/bardbl) +/FontFile 101 0 R +>> endobj +235 0 obj +[778 0 0 0 0 0 0 0 0 0 0 0 0 0 0 500 0 0 0 0 0 778 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 500 ] +endobj +234 0 obj << +/Type /Encoding +/Differences [ 0 /minus 1/.notdef 15/bullet 16/.notdef 21/greaterequal 22/.notdef 107/bardbl 108/.notdef] +>> endobj +95 0 obj << +/Length1 1590 +/Length2 12214 +/Length3 532 +/Length 14336 +>> +stream +%!PS-AdobeFont-1.1: CMTI10 1.00B +%%CreationDate: 1992 Feb 19 19:56:16 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMTI10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CDONCR+CMTI10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 11 /ff put +dup 39 /quoteright put +dup 44 /comma put +dup 45 /hyphen put +dup 46 /period put +dup 47 /slash put +dup 48 /zero put +dup 49 /one put +dup 50 /two put +dup 51 /three put +dup 53 /five put +dup 57 /nine put +dup 58 /colon put +dup 65 /A put +dup 66 /B put +dup 67 /C put +dup 68 /D put +dup 69 /E put +dup 70 /F put +dup 71 /G put +dup 73 /I put +dup 76 /L put +dup 77 /M put +dup 78 /N put +dup 79 /O put +dup 80 /P put +dup 82 /R put +dup 83 /S put +dup 84 /T put +dup 85 /U put +dup 86 /V put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 100 /d put +dup 101 /e put +dup 102 /f put +dup 103 /g put +dup 104 /h put +dup 105 /i put +dup 106 /j put +dup 107 /k put +dup 108 /l put +dup 109 /m put +dup 110 /n put +dup 111 /o put +dup 112 /p put +dup 113 /q put +dup 114 /r put +dup 115 /s put +dup 116 /t put +dup 117 /u put +dup 118 /v put +dup 119 /w put +dup 120 /x put +dup 121 /y put +readonly def +/FontBBox{-163 -250 1146 969}readonly def +currentdict end +currentfile eexec +oc;j~EЪ)s̾;.;rTejiK/df5A|{S/ )Sc\^ȟmp+#vL17~k d# +]LeVߐGoo٥\k 9Mՙ= 0)xf +1kX9H!.vPN 7qjj7!6CɫTw.]ʂԬ/J1]0': fqdU24tԡ?@^g+0[ +KTB/UٝFMz7 .U{7K.=UٯI C^$O7Û-tGrz J:"ia~ +T"*^MMчff0EM +z8uwi*?rw5(*5nZ٫ +4*RX&RTdRM3m ѫ& .Pd8;]F |H!%T [-͘ޞ E|pV$MU]n11RP} +d +.{IQ7^N-+C #̲]\M؅1 +pk2 +\t,o)2TTڮw}Ҏvq `;lSgs3c-h}W9;ڤ9Ö`2 ${};;m򉅘^l1'C*~O`XUn0x|cɾ'iD%WNCەU.9R*R?nLWˆs/[趡ۆ8>H@#ٻx wf} ayBR C1|P|'r,߰INJU`DkUQe ]Am\"GmFO )2rIuW\SW,'vdy]eqXH0#~Z9|pŞPOHau`Cb鬅<=?t8!-~C0VY-aht`rxK[3,f @=]wG2C#܎dVe"τ~fFE"ʨ IlB#{ FV<,L0 AXF,M19r@3Ipl,S~bF![=ҩ]co%5 x\Ґ|wfdG@ +_N(C*8h\k +ڮEKLK?eF[N#7)if(?e`o {K+\/ Bc T#< kTv\&Fȍez]3 k>!0[l~TE& 2j7Hmu.CE] e8 ?)X#'JvkRkJ7#Yֵfa9i#8!VOP~z30{chU!aDL24H\qtc5_U3oؕ8##[t4D6e> 4l[1:f~1G%M_fH~u1pbc1C PQ$j8#pbJN:L mqڣ BMĂd2\&?1J݊K$4m$[&>/EXPe&+ ` mLDg%/]uUٻa6߆`}o1p@` s(26Z8To `$Q%޺gnKa חXө ={tUNԏ(Lˊjjff0*r}s/ڈK63.``~_MLOt A;ed0b:d>\6j䂼 + P(!"JyAksDQƃ@qMMN8: F}ˀ8\$Dmn$Ph +'%p錬C<t헴ՊTG6{}G!~-6UB=`NFfvoEbzaG +<&fhqLiS8zF"TE@z 1Jŕ: ~럪nX!`aV=SQ7W, t=̪nL?oXב1 \GXcyBp; cW2~fZ;r-<,f|(rY +C~~b/oܻU2?B'Y ^h3d jLG`f"?ثf4 ¶h8^}PӬ`SlJphc\ib9~LGNx9}pi+FrCfIIa=,dbLX8+eQ>,444HVXڕ /Fdx%mȄn8㓖zX}ggL$GJ&ZjJ¶Ȧw`-Q|~v}/G4vjRS%wŸk˸L28 +&bYEɮ/^t""' U` bQ>Q*p]W%2+]|)c|~5O LO喩D̓+VG^>n\Y pl̈́ma}PdX/nCOA0 +"1~%FGQn3ՑvnLaqG5m5r +,,zlVg9su&5:z(!{ +w7]n;*x&B::ݩOmW2`pG[cQHn{5zqam. ͩUr VH hS9W+ |3wBϪlg Cu*ǰou@rnNj;!9T[5EVo@zࣆN Pp;&UDm +.g'K+? V~5hG#Ԡ +B&P C/JqNR2tr8gS_kv`g\K1\?6Vl$up0GvvnjY;"/){:xzdd[2`y*α}5D`."R *#aq8xuƪ6^\2L¤Mo-OLSNj&q)<YѽɝNF@w>Iq"~m9py=GlެS?lEѩOC[u3}@׭wg-"Ug}F؏ɦƞ˚oK}DÍMr<J4}L +v+`H&QSh-p<fe¿\z'm3>ɖd +X,U~MMb'N5aTJ#U8?]M ׭[$< T˳I;&6*=tR6bSk)m>d ׺eǰ%Mޏ +n /ɼ̙4i:UsbQ{_G)Z +:~FCzB!ǔBl|oflUحɓe@%BHҥ;ۨu+^]H%ZUQ=ތ7U +p%WkC -a'dj黒@訆'e_Z|n+J-W%#c 3r,-I\_(p3*ZaPeԒ Vjfhȿg5ɝCN+W2HˠnLs7?f:Ł)mwt J;.6x4⫏{fF@GQ1JwE{gD2Dg>WyaǗ|%Lme&3Ɍ6T/|k 9rqe5p$4W;]N:hc[yٌ6тxs1n #5+}+@+ѐ:6aDj"/uNpi3ޒW +u4b9$ȗ!QKbq.8 :2e m9m9FXz$dA&Po c*[BbF9 \psY w0uְ/שiL 1,atSU@ۧS[Xۿ/!WIinm_yTDg+?)%" j݋C*4p UHАGL/~7"ݨK`ʷ&IT8> +p~9؄39S,ta͇@k˜:LɒoJ{B"JE/>Zy?aX2q?Y{^C> +!cQxБo,?uCcFn<}hIcH& |7Nn[@$h#< zKNz#un E$L<t);Z9(KJ~ ͥ(#k2L_8N&WnP 1I,A)bFIk!!LS(Z{7hd-rMD S9s*i=\9=vؒbz^U}.w}xtW}ifٴ]cmŷjek*U>BqUeXԭqS_\=[П:q`rH,U =N%,p}G^ +A?pyg46]?cx -H|9?GFa27&StvR5'~ a}&mȧ0ʷ*GF ¯~MȬ{ dKVtH֭_zCeL.o/AiF~GLrhp4^J]EA +")@aYaty^k;ׅV.#,[kãwvnjJbS($j^I!KpUfVBdŨ[hE!z䗳 ~ %I},x 9aV[zawD <cy'U֜(Iw:TƒSڗeU@mҵ;@w1F?nyb6m[ H"@BL2/tW+Ld4PLmIM001}^bNGr rz ЈjJo$Q -%5h}] A{# /9cZ Ti8)XvqVj^oi8U1U-*Vl^t:Z3'JxEۿ}(B7 Ж ENiVw<{\ݪ|5Ӆi 9p&CEv<-g1?ݹ1" Y^1>϶;܁IՐ/#1db5νH )f`/)S V +'^lN[ %!_F; +1Ca6&\өDWM0K<`[7#0 "/0OC i[m|iqQ`@:}"t'_Ehkf2|`;~jߠ"̧l5=AwQJu}3fscRЖ@7<\9O+8YV_SYhu懝ޜIWmŔ9Ja/PS!ThH Ů~)Xr,2nI~|#og!x +\ (/"3&.Ѩ^u&K}nWqI 3 aO!-p=Y`._Սt;ּҰ7'ϴ˃9sPPcCù{o{ܠ!/\8V!6Hr:0G\!?7L:of-ҬM0 ?eR4]7 ˳5Pר&ا/d(2rGj$51$+ +nQXO4s,/"`!5ewksT`aV~o@Vi-I7q7WHs9Ƹ? ~ΑPid?pSPY7֯ dqϕ噎DRp޸*B' +h!:L,yEQ4W*-EqaiYz+\'mbBpvzc[!m*R4VtӢKݓZ7-|,c`z>Q3v~n-Gvp%fEJ~xd9}TNT(2D@NP0OxJD:USR.P^MΫ.CcZ"sOLJQD隘PWQ矵XgP0˓:cI5-#oRIL(4Ϊ0K0A8h}.mԘyGup +Ff+aG2Y{h +Ps#6%}Bʆe8b-j2#:t6K|iA:)L}R'`G{_F}߉a:P&%w@{(쫓E'ݔoj@F+3X_~2pElb +**^3uˇS"4KpX G\Q}$\k+%^RXao$)R6|\&Ӭ#vž^'k6OP5 w!AϾx_ GtX_/wl?#׏kC4d \feR#Xy+m+Axvc(#ΓqLi暦uLJ*B+B6F;MG/~xy>G3ZSu벀h%CկGtL Pdx"@ WشMs-+H`$EyV[7ȫ;hT\BYˑS7hWlɋ_}R H9uN+<h7ݰ~~ +B<߬p^׀s֭>{b D,&VRʥNYJ컙\Q%ПDo<}{c}5=X "ysGJM:Q! B\¸4$_%<$l z$BEJBfʬXcbt~dnS+Z[aȘ=˧V|(IqPisr{VdxS"$9cmvjV]_]o{l&EBWܫx.S=3SON7!0f1xM@SGZ(gp ԫ%Q叿</bV5nvGRsAeg&Ԛk8([8[A}:?k܉u@jF^k=jd0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +endstream +endobj +96 0 obj << +/Type /Font +/Subtype /Type1 +/Encoding 236 0 R +/FirstChar 11 +/LastChar 121 +/Widths 237 0 R +/BaseFont /CDONCR+CMTI10 +/FontDescriptor 94 0 R +>> endobj +94 0 obj << +/Ascent 694 +/CapHeight 683 +/Descent -194 +/FontName /CDONCR+CMTI10 +/ItalicAngle -14.04 +/StemV 68 +/XHeight 431 +/FontBBox [-163 -250 1146 969] +/Flags 4 +/CharSet (/ff/quoteright/comma/hyphen/period/slash/zero/one/two/three/five/nine/colon/A/B/C/D/E/F/G/I/L/M/N/O/P/R/S/T/U/V/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y) +/FontFile 95 0 R +>> endobj +237 0 obj +[613 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 307 0 0 0 0 307 358 307 511 511 511 511 511 0 511 0 0 0 511 307 0 0 0 0 0 0 743 704 716 755 678 653 774 0 386 0 0 627 897 743 767 678 0 729 562 716 743 743 0 0 0 0 0 0 0 0 0 0 511 460 460 511 460 307 460 511 307 307 460 256 818 562 511 511 460 422 409 332 537 460 664 464 486 ] +endobj +236 0 obj << +/Type /Encoding +/Differences [ 0 /.notdef 11/ff 12/.notdef 39/quoteright 40/.notdef 44/comma/hyphen/period/slash/zero/one/two/three 52/.notdef 53/five 54/.notdef 57/nine/colon 59/.notdef 65/A/B/C/D/E/F/G 72/.notdef 73/I 74/.notdef 76/L/M/N/O/P 81/.notdef 82/R/S/T/U/V 87/.notdef 97/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y 122/.notdef] +>> endobj +65 0 obj << +/Length1 1979 +/Length2 14326 +/Length3 532 +/Length 16837 +>> +stream +%!PS-AdobeFont-1.1: CMR10 1.00B +%%CreationDate: 1992 Feb 19 19:54:52 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /PQEPRA+CMR10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 11 /ff put +dup 12 /fi put +dup 14 /ffi put +dup 34 /quotedblright put +dup 38 /ampersand put +dup 39 /quoteright put +dup 40 /parenleft put +dup 41 /parenright put +dup 43 /plus put +dup 44 /comma put +dup 45 /hyphen put +dup 46 /period put +dup 48 /zero put +dup 49 /one put +dup 50 /two put +dup 51 /three put +dup 52 /four put +dup 53 /five put +dup 54 /six put +dup 55 /seven put +dup 56 /eight put +dup 57 /nine put +dup 58 /colon put +dup 59 /semicolon put +dup 61 /equal put +dup 65 /A put +dup 66 /B put +dup 67 /C put +dup 68 /D put +dup 69 /E put +dup 70 /F put +dup 71 /G put +dup 72 /H put +dup 73 /I put +dup 74 /J put +dup 75 /K put +dup 76 /L put +dup 77 /M put +dup 78 /N put +dup 79 /O put +dup 80 /P put +dup 82 /R put +dup 83 /S put +dup 84 /T put +dup 85 /U put +dup 86 /V put +dup 87 /W put +dup 91 /bracketleft put +dup 92 /quotedblleft put +dup 93 /bracketright put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 100 /d put +dup 101 /e put +dup 102 /f put +dup 103 /g put +dup 104 /h put +dup 105 /i put +dup 106 /j put +dup 107 /k put +dup 108 /l put +dup 109 /m put +dup 110 /n put +dup 111 /o put +dup 112 /p put +dup 113 /q put +dup 114 /r put +dup 115 /s put +dup 116 /t put +dup 117 /u put +dup 118 /v put +dup 119 /w put +dup 120 /x put +dup 121 /y put +dup 122 /z put +dup 123 /endash put +readonly def +/FontBBox{-251 -250 1009 969}readonly def +currentdict end +currentfile eexec +oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou\c3R*R?쨤ȯ@ gSr RIzE_EMv,X!%6]ަ_3+_hJإ0o'z 9K$|tV\)Z! j#ZŚz1UA~ +"p?{u@]A}s +ijB)~Ob {z;O9mT[Ğ^dUl$Wh: ?Ƃ(r6;Bt6cFCr$/;!,KqLeWuG h7IQ[u20uZ8*#qP|̖I̓pe}#YۇW{ +Hs(}CE c;[e/SmV& +i2ǡmc\0kC'sp)X0@$2jOGG9%fLJD@m2b5\cdy!iz+lxa+2S@uIY5F>qgROEowK*;/sDGǡx=>J ujLDfdžk-j_~hNa0GF{Bad&p+ZlN>#\S ;rCԿk Yce2->fBi߬,uOLu #s6-;s Jt%K|pX;p+,ArwV\jU<6^ YS|?Ɯu`x*,ܺvdz`;t/nQ ,՟=)uv1Q|Afg] 0)``[ߺAv&eӈPmayak3,OD(,de5lN,n@Uy;ye +<OK3`r +h I&@e/JHx1iZiPt&9Be8=^gl%Q/2T^G[ojDeQ#o?B9$3% 'ݨmL |/U 8BQ3;:& %#La}Z.b ohm\ʅ9&ˈ}¢MpUndE: z$wIS 8FQ^lJ@QA\/ "4#;}/ƔFExh `Oq?1D߀œf1ޡɊ`Ћ%>5h?|zKW%r?R!ZйuD2 uxO!&7%Fw'kn%5r?Mr>J2ט̥._uy=4#ج)2sP~YB.jj0^ +Mh8{jHjL4QU=seE֏^ȶ vĺ[D9*Pp SU;'PPSNf $_ b[Z,رξjë}06%XPb?aٷ=!Y3TxC Hp yw̘ͽyH2Y }S0qǧ<;sIG|Oγ 'BegpNVtԙ Rp -܇Kg97"״\pZ_IjseAA7s:vӅ7dHNՂ OՂ_,+ Nx\2` Xkp85opݠkJ݉A&|O(Y UR11 5\xm7]ܸʂY>BWPr2..KaI+B%EH +O$]үWD'6^t:?cM*O (?r"l=op@@h`3)xrx( W~] =b:\Юh K^&ӕnss\Oq: 0F0߿t,|#sE0ҍ#[*dhhe*բbt vhNTW_PNyOBUwzBYuZo\xQx@{&  )/mkխLy jC[PceGso9}}̻1?mlef}) 127 =ltpDb'SDt5&d[-y8^ [r +rn;=kZGv"ac +}r&+Mk'Tа \{ 8S{Z=랁_*!gQ#QKf hv9&%xK%ǿpBSmYPJCK KchA?CF ( $Vy-΁A{6t`DH̞Hc?AU#`J;J/!_ s@g5#$rT`Y38!%UW^?*_w O +ѹkzzad+%pyHCo0fna(+Gc P_¶Ʉv.39j )i{Aϲd]{շbHG׍:8ݩP<:~ iQJZ尛cDP1keόK#RZV: '@l6K6n^hgUpx|`K܂% .si/jɥiOCF t#>KB͇/x??)*"4}XL,$Ϩ}űRQEfn2eQL5ƃC wn*IPX6,YnޡT|B@ܧ/&s`ܓ - >* +1B ^Tv !a8IFBTny@!җ! MeuMmd+6FI,+=G]51)\_܏P'D\uO`hà!Cw'|ϛN~3LMHlE +6Le:+06\N$}*l ŧI8HoO[M1ͷq:*w-nO) 68g*|nCk3YHNJdzGf.85ӚHvgN#)ǖ|'c=qJ֤iF4z |\| 8Af(>% h߈I42ۋf1+QOy+})ۛ|<=$fS ;U4,؛s>[GY72ǟڇ|{9f ̛\ꠇQ(h7w'ˑB'QJ_\Lԫ8)bRfZ*.G+mC~!gY;U EMk+w L.R9C4\.2Pgyx,%)av!SQjX5So#}h͊$( Skk[ 8QwwDmJ2,(LsKf>IL.BDT7lDYh.|&=&tb9Y0Y. v$gv^bE-ZT2]oJ\ztbRyDr%gzv6~5!e(D,@'hmWW'[E"8׭Q1"yݲ9BAΖD*n3 GeSB˚$:.qI?[ Y^Љ5>YPRi fr-f8)q`BYj5jxT{- 'ُ%/"x]@GGkj + m#,p+3/Pu: E&O),SiLg[YTDm5Rf*r[פ/o~"ka ޞYڔĨaY +z!Kw=#5 +D\kj_UjԋXUa(C+F)3J1ri{$mGK-z /hseoA +ƶN,OhTk/]P g8$'A&])8bI +~CeIAlZ T_2ehȷlDT*ȵh?L-: %[?%A"~=Iq?sM?8>t_8Ok#J+~gÕX{}:GbVΖsVrӴq~YH , NTsd +4Sf4^A=sK_|۹\j3l'r@V69ݾkK/='?h͈v$#~W o]^R.%vv2':^#\0Uɡe.0^.rb,bs Bo[#ցXҼ`CN(v՚D +dIeg¾?-~W1Y# +=ϗ]WFUѤgi3GwI\p_'>k9MΞOhX<^ ڰ Q_+)mS,6YYpY>8\Oq~k[[l-')2 DlŮuQkmi \jaqà0w?"-C҈b`Js#l)~vEn:ж{7kYbϠ dT+Y)$^$*n44I]*P* R݃/}şтE6HE3UvӐ3R=0O⾑IW6@WƔ;-C &_.1 +FꜮbH',õқr71dT6O{K@Pfv/Mw3ŤS 鲹?SZ~1I;fd~se-"-ehz7`B{hvC,;@~d`0 `0~MS +UBUzW'- x3w7> CnT-2֩UuH a/yx6G}9PUT:1QX46" Y*0Sc_ӑIғ # 3MhluVV77bSķ3-x.ILg5wp[BD9ԵٛjMJPbgSCcWVi?^'K|CIqUvcϖ*ꠁ_̄U͋QgSVȞ3c}S00OY|oA3Hl;WʘmԨަaaC\)r񼯋$EX~/8j+^T>cǩ-{,my/7*n1c}Y*gɓ,@z_I @xiX2[Lf.z&N=xnkuNW2"ȚG0|`Ӄcfh۳]#I{wqC}N|i'<#%NJh3/\*)b b@*:M$V=K^^8CWP/ąaVg䗔މ?nz]+uvCPs5K/&s2=~D]4feeVRkIB1.Z!|,$*_\,ScU.o+ H Nk(iFOxx_` yp{UR%C$}z4hw.ah6Y׈ު|9 $)N:U;Y!wwh(j&+=r UbEL,c+=ݲel|r杻#fxl Cɢ;UX*es'\yw1<\Jj|(Z:r]KƤ B7Kg]l2[c@׽`(ng#BPոU3Vb'mu2ɁF$v O9H6왻1*g2Dž+{VVhC5-_ՠPpln/b#pDKX. +H:)^]å,F?9l9S'_u<k;ZcJHnXз:gQ7c^.MF&K&aYvPfty, +:1rkN-cϤ5TmlK@3Z0x}e_A&-Lg 4<8Bf|e_D3SQg@zm[6ÈƓEb;Lp5 GTvph_]:BV69hZL{; FLJbBįA] OKzF,6Uq&`82O#m-1~8q%27!Q"ۃfyg+a+M*Gf*mCP]zIY +yI Zc_;;>mv&b(}P/gE QATD7F޸XP\̗ T#d;T᩹`fJTfrDWFsZI K՟H*Cy<aчҕx5. E _7l[_q"D!8o+v +\퓶Nd*Amh4U^@ ނ oB +[yEMeR R,t[͛5f`%@cTz픊QZsCK,7Bڪ4-hTSZٗa6KG3Ԩ35f "!{(&P8q3Lf xcslJ}siVLeL>*`\΢R5Rk|wZO?19!6Y>@:%£-aG#OCħaCPZ#]>6=vR."Y1O Iʚ>-Iؿ y>ff> +dbY]Ÿlg7T/#BcSvMl(#IMmWr#`P[se(;EJc:|91c0; ﱄ:ޏ8R {fhtP`@-lbE+Upd@[l@ʉ^8O)7pűxZ OI sDx/rOpTCص\ i/6C vM$}@n8t_fC_+*p'%n`W[LK1l39O짪W;8YJY̧vpy '=n_?Y@]l=J;SϷ_E +Tcl¢OHwYK݄8}ʂKErhbҕ$+RFf%CA1DŽ)mK ܵrz[h >o%WMLg.'9c..Cfy eWݘ*vG5&m{追ݧoSڮ;$~)r:J1|K(< Y|A2~Wy/iOؿ_ߗòh@ʒۺI)Oe/MWEYԥS +}(cj kfp2{"614S8@b>w 38/_st2^jn<&K("0tFQ'."s]\^~ ] 2-dw=>$+7pT/i g\Ym `TI A\EqSk ~&Jd0SoMq~[A5<2d#EܥQ8Ka>H}\d|9 0N5?/Shbc =Qī + p%~>qٖ "w&ζ7x؇dӘ´KGXFx< ֜B4 'gIMQ ';F5r5)} uvl?-7,dBZX )F 9A3+t D/TD,}IF%H#+N.߿wzmtaߐeH(?_W_D:<*')k]Oa +3IB4mЕOMxM&=$D\Ȭ +mt#Q 97B2ρ/ӈI6?BO ;°g\GV^4O:"l?հnOq38,\3ָeG0h#a+EW Lɤo@qkVCgQ*t ̗o9!.TCA$8!˓.2b +aVWAJO.H uD1[!ː%4;בuuFݙL׫1\~U{)Dz!a1RVt츍ORX*Hؓ,qIYVOPO 66M>D$ +ϔ̟TT) ?pot@'P0v?;#=v1My0yu3[֮rc}V6, V&Y'W0*g!!^ +ijYXe$L}ȷq_0@]c<`R=mz~Z(`ퟩ_`ZHoxG81BɌ'S}EHN +k2g1}r0dvp/tYv+AVP#u"w<0eX<2xю=n|t92 z"G 'i82@O,F6IYF,5T|w4F/_DsZٟ iUߴK@| +640CyTL7sܨKĠj|xK(ۧ~L.p@4N[_3E ,!1S{sb ē2Xoy X|vdyՐG4OS eoϫp>=  c*"'v%J=xw0 #kP$S 8-> 4`B-B6kwحO Cu'";랫{9KѤ%ﰕGzv~6LU#o9/fJe.I~<etVgFB`c4IvB^=Hº^@V\Uhۏ։Àauc %iU=u +^FxE Q$qhۘ +(2 t7֛ndӰK +`+d2J;=&5|fG=n.%K%1CЀ@-.,OݺS9.Ʒ2 hBr8GحB%ND#T"bX-y,}]˹xCBM(ғ{i@D@?RQN]U_- +)D}8wIAc'TL:=zyM@&d`I|gg/x`:%Un DC7ީThay S5EPӴ!E 6˕-ot!gwn4x?<㦹̞ɿѓho^P,[MQ9ӋlrtL>ܮs`v}R#4<sƅwmS]V.7'V0&**f0qSdlq !̅qnoxsLI2²XSJc'.v;g0ԠJ:ݼ mu3 %<y&juEp±{8(Vܾ'=V?؋3%9tb$\gםN4eOp7f\#{Ԟ%_ Q9ఒO2cN[s +aϭaFx|9x'q2ό6Աܘtfpµ:}oA\]Oys|ݎbVbO9bH"Krx#KHhi!;{ QꆓQN1aDcylTtb*t4ű`Q{_!ᭈ[ߕWֿRuC ~鞹y, Ѓeiw6`Q,njixLg#MJFҥe=fW7oSd6/8b>RV8S@҇ )!FwxHf^CU&A}GgD<̭ +\:}DܣH|x/'2}1;O +N83!jE{9c9x.9QT)/y=AתSo1xДw&g5  zp_Ԡ_Tvti`S#-*j2aSIS+IHf-wZ?~QһY^Zl9ReAkgeX;s4qzR\M#tbcuT6Zhcw5/բ94*gL牖*.6zmi_ewhJipgtcV@Wy:"@f Tm=_X0ݿ[1t6$*Md.RAB<1Q;R @%dˊnz szK=ni*,Nº=0诤q ^B#+ (6 [Ӟ^[IWupYF +(4D[4 Č֣Aʴ +䎳"|kfi*CV]TKr7 *& Hg wTQ Rd/ fp +wOMJ%xozFy㹖D^(t\` XlɃ{Cg`#:bx5wf8GƔle2X7P_q#nTʂJ&q c, KF4?q&&O:%40Fh;/8L +& + ՂQÖuȅlox +ఱy z11ҋpSᅴ`PwGV}Ğ)VZѫ#C:DʦKyKcH-U6 X;_jKj/ґKFsoBg٫S0\C̒|igDIF~wF;9guңQqA5bq:9XmFA6l\Y?Ej%:)dP]~#MZwÑ +SA3OcCN홌UUKn|Ucu( +WJ}o1^> hoUho[gzg9(&mr 3U33'QH-f1`ہ)[=^3s}#H%q|iQ@5s݂p:4[+ޒo~e>DQL?s=I|4jѡ.VG?A|Y IN磰JNyPńYj/s"xi]3'<ϕ=X"px7Mqi 1Z$ 'N܏"Sq0M\; 'U}GDzMcQHQO\GCGX3'寄zW0>"(X0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +endstream +endobj +66 0 obj << +/Type /Font +/Subtype /Type1 +/Encoding 238 0 R +/FirstChar 11 +/LastChar 123 +/Widths 239 0 R +/BaseFont /PQEPRA+CMR10 +/FontDescriptor 64 0 R +>> endobj +64 0 obj << +/Ascent 694 +/CapHeight 683 +/Descent -194 +/FontName /PQEPRA+CMR10 +/ItalicAngle 0 +/StemV 69 +/XHeight 431 +/FontBBox [-251 -250 1009 969] +/Flags 4 +/CharSet (/ff/fi/ffi/quotedblright/ampersand/quoteright/parenleft/parenright/plus/comma/hyphen/period/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/equal/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/R/S/T/U/V/W/bracketleft/quotedblleft/bracketright/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash) +/FontFile 65 0 R +>> endobj +239 0 obj +[583 556 0 833 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 500 0 0 0 778 278 389 389 0 778 278 333 278 0 500 500 500 500 500 500 500 500 500 500 278 278 0 778 0 0 0 750 708 722 764 681 653 785 750 361 514 778 625 917 750 778 681 0 736 556 722 750 750 1028 0 0 0 278 500 278 0 0 0 500 556 444 556 444 306 500 556 278 306 528 278 833 556 500 556 528 392 394 389 556 528 722 528 528 444 500 ] +endobj +238 0 obj << +/Type /Encoding +/Differences [ 0 /.notdef 11/ff/fi 13/.notdef 14/ffi 15/.notdef 34/quotedblright 35/.notdef 38/ampersand/quoteright/parenleft/parenright 42/.notdef 43/plus/comma/hyphen/period 47/.notdef 48/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon 60/.notdef 61/equal 62/.notdef 65/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P 81/.notdef 82/R/S/T/U/V/W 88/.notdef 91/bracketleft/quotedblleft/bracketright 94/.notdef 97/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash 124/.notdef] +>> endobj +62 0 obj << +/Length1 1466 +/Length2 9551 +/Length3 532 +/Length 11549 +>> +stream +%!PS-AdobeFont-1.1: CMBX10 1.00B +%%CreationDate: 1992 Feb 19 19:54:06 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMBX10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Bold) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /SLFAMK+CMBX10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 12 /fi put +dup 39 /quoteright put +dup 48 /zero put +dup 49 /one put +dup 50 /two put +dup 51 /three put +dup 58 /colon put +dup 65 /A put +dup 66 /B put +dup 67 /C put +dup 68 /D put +dup 69 /E put +dup 70 /F put +dup 71 /G put +dup 73 /I put +dup 74 /J put +dup 76 /L put +dup 77 /M put +dup 78 /N put +dup 79 /O put +dup 80 /P put +dup 82 /R put +dup 83 /S put +dup 84 /T put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 100 /d put +dup 101 /e put +dup 102 /f put +dup 103 /g put +dup 104 /h put +dup 105 /i put +dup 107 /k put +dup 108 /l put +dup 109 /m put +dup 110 /n put +dup 111 /o put +dup 112 /p put +dup 113 /q put +dup 114 /r put +dup 115 /s put +dup 116 /t put +dup 117 /u put +dup 118 /v put +dup 119 /w put +dup 120 /x put +dup 121 /y put +dup 123 /endash put +readonly def +/FontBBox{-301 -250 1164 946}readonly def +currentdict end +currentfile eexec +oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou_cst ?}ߴ7-95†笟M/Z+FCxw\#㺴DɫN^?0^~o&fZ9-(*ϟVV9 +|J7@s.$DFYMi+M즒DSW['1qy4qZ;]6y@F< +V&N3n]Db a[sK kԃ9$[F=e,&Ȩ)uv1DVIjaIç# +5k~QaMjFJL3.0lVem; YnⱪyRyh$&'gYx Qi- o 7kacg92X3]*#5sJ^fXגbA>!đkLa\wi\p d³JKWpt+2~-OC=<ߨ7H'4FDS٤d4isCD3M`=eO7mfz~6H36&Uԍ&23`}VBr![/9tp'iq$$+ʼ1> ҐRQE+9d-$CkdH5 +ASHHmmK9>SU$7=ڍu4 DKLW_<|ha 6b-D^N"cMJHԶ>W Z 6(;XhǺW^1m#a19F!|(nou[B A2tϚnLo׺i ML 2+> +^MBܷGIPCQ94+"?8 +( +$o-7Dz2WU)GЄRj~qp ŃpBR,bF#q'KI3C0P\lj?%o sYʦX3Onؑ{`~b$9/U +Wa#TA,ǣz!wȆZeӏD}HƇƺd"a03ݔK\<3? 4PW[S>&ΡGpu`V]"d04}\bt0'Mtuô˶eL淵lj?yK4$wNlzPZF(5KQYfCjCA).A\TWݩ=;\|O_rLI ΚM\vLf擾qNO^gp𠑢>OmvDc5Jff[EG䤒Oϯ/s#UQ7/>΁# ]AibF.O9:Kb=,w;@ #0PB1UMDy +#0^BJ֪Hl؁ZE &t⺶2e't7 ٕ`HѨ(۹fo e9eQ?aN ѵF8AhR;-[2M oX&*J) .Ϩ,yoJf19Jezu:J?<Ǚ9*r/Wq4)4~k2*׆g作S \[V ڀ4U 8O>)fK{?DP8(Hǀ%p1$=!]”ٹ.n0)zu{@QEe* os/CrT \06Sk/ v[;0(^eBٷc&;#AZY# I׼Xѓ 3 g`jS6 +j&f +eV )z$SM;7)ŴI]vTYtR +$HRT3U6%-2'!5'hWa>Ez#ǁ +ߍ[筘ʰ vZD5tz +{i 翋LoF#<Ȃc)9(_1fH\,klF`<īi߷m~|SD!}VJmн(.?SYb[<_=^wY~*%?e6o2@Y[W7.<0̰4sԢ:n/>X-Ɓ^D WV]M.&>}'!97;cXMQf4pU!-%,n~pG%?Q} ʏ ίS_Q寽jŸ~\v2ύ>OAQŧ7P"j@_9/っ6_N'@{7?U +ɏxjTU+Z#aHt!+o!+LR̤VP8"ڡQM7e`2PQgЛuʇ Elg\<#u$It{3gAJmE9`@l( /ШV涰S>tX8ݮ-@.| Msxq`n]V&uw@|/-yiGϒ=G]uLnR%+@-7FE_)hd( 81NV03P0S4y +#߶Gz'-}EfVXs%O~\?{IS?>|8yJ{ωp\?./h{/gDUG +8瀋>ӇMXu_z>DC^A,StL3Ҡu{O櫅ࠛ&Q)\30 ^dYʼn)gŵ4?etkL)#ہ|_x[kiHyՍO^~)BlB+sXHsvFijOF)P _Q_aOrRaNk,iL7UojC[1 C ?*_j`]|pȅ*}/H}zfhq07R&몚E$Ljtb$o cV>[< 3/?X+ Q5 +岩RcǑw +CDJ0I*:V lGg俥wL+õuj[JBm>7U +Bre8#ّٝ$|!E, 'Jt 3ї4Rd$@[`# '8w7QgFn=Tʮ?IZ :2 `7C"Wx;E= BqAFo׸|QBC6] +XAߟlf3 +u |:7 +sQpn9' C,EF"7f ' 0 ɰ]Q+(xo6L+?D*^$3\lS[[j cbE!EV.dRm~ZI{@.;,9"{,哥9E}jz>N04ӱ,!Ʌ)\Ɣ'_NdڠvZhB-M[1=t?gJ5_lHCfDrXN"@NMcd5!lM|X[FGӤQ;U|czzNuqS!GyL GcK/6=YC;\ y^aً䵎8rQ5•Gٚ.kXHS#c &9FHR(<[o!Z=Q#rt '{MJ_=7ȩnb@G3s,YW1)Y*+KHPpYqx&8_.u[Ld_<>c0%kHqHۧmM./ТŻqV 7G%:Y욅P5HU׌%<΍J:n/}yzݴ}+Tc:<70aJ1:vmN> ‹Ut߅dL"p0`u\Ō=!ʦztMb/챝@lݧ",'%ҍHEr`6H O-MK"2^CΗQ/qC<MW(xo3ñ֡c14b oVe#&A@] \L#mS)jؚM@CC$jK֮ЦٙxcاϹoϤykX'X_>~9P}n %ex`wcղwv"&qKwBVJ[$&백:D=b"ۧg1ٍِ%x-dg /~1йn5vK>?J@E$TGb( +xg 0G`9.RQ dcZnb>{y$Šk[9)cԤz"jaPdƊ#mA#GCgB='0OpVA͵jvˎ[GC)cM6:^ܸ[8B<2P`MסF5߯)0U5g2#lD' LIj]i}T/_!BRE?5+4 k,HU)bVqԾuL4H^J.λa|XA5FJ_%c6OJ/TD T>wqɕE D7yg?U|]v,Qa 8q̑ᶫ A7pۄdFvjGB +ǥ3%Ѳoٴa=`\Z}TNd;=]ߗ[z3>![< ;GCTv @ (sćMVl=*x|,ЎokP&@B Uo:TRˁ݂Q=}IޜP7bݹ5:wtMr Q6W(Eg8jplD >~Jϼ%)dD`mlk!ʔȅHA'*%vȌ k&y O/7AFfO|n~.\(,C!ZLǽ'~Յq;bglZ*+iڧIWoG띢/VR׉l Ogwwyrf~MyrsGZ/cSgN[HS-XQzOZ3g3A\,s"C<܄h'6 +&hR+C*ّZݠ6rzab!b7TKqAH 3wn"x-B tCM1IS!a;WT}C΁7f@Hof5]3Ku k&2k˳$Z"&U%0gHZஉTC<8E?E6Mvlen;סq4 z/i*O/ [myxUvz񫄉MS=!EL6jK(jYWq\tY,DE(8?҈c 5x$lse^(қl e- u ÍpN֯ #2$R,KOptSՉYBK/#dF?lȀ;S{EQQ2 uXސ2^ߦBCB=6WX/䓫?KU8. ~>g ='Pvז_)$A;CwZ'@,00h-V v6}hEUf-űm-ڴM:/ MG4c\eWD6eBMmq#|RnZ52p۷8@bu8K|mvhKYT]B"w)\!$)[1y*g'~jXbw#9v10!'a\N`qŲ~Xm16ݸhF1].\'-HI>:}g&e}\@Tu2UDStGCy\Ъu=j"%EP (Z`1_ UU"q7[~N@=d:0(L2CAY-}(fd1N%W^zH@puZL9 .Q(a<)`@HQڔ~"VQ~կ,z,،v𡯦+o;!B0GbS&P~0:yx~G#3\lw 1ϥ9a9=3;M_6)h,Il׽oPo<}hYOo4P D MڐOt-KIt+=}zW׌CfQ +~kni*乺{Vߘ3 ]%ռmA +|BGCp@9WR|9u)gf} \+# ^idXJOSS 0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +endstream +endobj +63 0 obj << +/Type /Font +/Subtype /Type1 +/Encoding 240 0 R +/FirstChar 12 +/LastChar 123 +/Widths 241 0 R +/BaseFont /SLFAMK+CMBX10 +/FontDescriptor 61 0 R +>> endobj +61 0 obj << +/Ascent 694 +/CapHeight 686 +/Descent -194 +/FontName /SLFAMK+CMBX10 +/ItalicAngle 0 +/StemV 114 +/XHeight 444 +/FontBBox [-301 -250 1164 946] +/Flags 4 +/CharSet (/fi/quoteright/zero/one/two/three/colon/A/B/C/D/E/F/G/I/J/L/M/N/O/P/R/S/T/a/b/c/d/e/f/g/h/i/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/endash) +/FontFile 62 0 R +>> endobj +241 0 obj +[639 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 319 0 0 0 0 0 0 0 0 575 575 575 575 0 0 0 0 0 0 319 0 0 0 0 0 0 869 818 831 882 756 724 904 0 436 594 0 692 1092 900 864 786 0 862 639 800 0 0 0 0 0 0 0 0 0 0 0 0 559 639 511 639 527 351 575 639 319 0 607 319 958 639 575 639 607 474 454 447 639 607 831 607 607 0 575 ] +endobj +240 0 obj << +/Type /Encoding +/Differences [ 0 /.notdef 12/fi 13/.notdef 39/quoteright 40/.notdef 48/zero/one/two/three 52/.notdef 58/colon 59/.notdef 65/A/B/C/D/E/F/G 72/.notdef 73/I/J 75/.notdef 76/L/M/N/O/P 81/.notdef 82/R/S/T 85/.notdef 97/a/b/c/d/e/f/g/h/i 106/.notdef 107/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y 122/.notdef 123/endash 124/.notdef] +>> endobj +59 0 obj << +/Length1 1125 +/Length2 6015 +/Length3 532 +/Length 7672 +>> +stream +%!PS-AdobeFont-1.1: CMTI12 1.0 +%%CreationDate: 1991 Aug 18 21:06:53 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMTI12) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /TSJTZG+CMTI12 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 65 /A put +dup 66 /B put +dup 68 /D put +dup 76 /L put +dup 77 /M put +dup 80 /P put +dup 83 /S put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 100 /d put +dup 101 /e put +dup 102 /f put +dup 103 /g put +dup 104 /h put +dup 105 /i put +dup 107 /k put +dup 108 /l put +dup 109 /m put +dup 110 /n put +dup 111 /o put +dup 112 /p put +dup 114 /r put +dup 115 /s put +dup 116 /t put +dup 117 /u put +dup 118 /v put +readonly def +/FontBBox{-36 -251 1103 750}readonly def +currentdict end +currentfile eexec +oc;j~EЪ)s̾;.;rTejiK/df5A|{S/ )Sc\^ȟmp+#vL17~k d# +]LeVߐGoo٥\k 9M֨[G(aܘ|RP>f}|Zx'5+jۊz3p3`/gtJ8)&ho%̸{sCVah~I"Y0'Ӷg; 怦#Ӝոgl;O6jyg +H@n΅ +l2qŽwޗMe]}Aq}_oyѣg+JIua;5m˺ڳŞppX!cs|:J#5պ )jYN,~[Y\! $a7{_-l Ɍ@ec!Eo-}гR#w9O,;rЮm;xx]JTeSB@b"e':NR)mHdʮ7hAܗx|}/k*b\TW}JIR=D>ܸZykx^tlʩ`̪y?k:Z"T?S%Nd7P,AXHȎYj.B5[c:´@W~N#+0[yuG"oYBn +I=Aƛ9Ia& 86E(Fzܷ!"@%Ӻ=Mw1Y$"HI~; +8"T2rsaiƧC9'`ƚevKNYJn{( vz2VHjm|"9{ZC㻂{BǖPGF & [rã3L(N:oNSfД8|XҤ -G> hSlK*EJ J1; >/w;Jе& Rt8>3X8']MB4VΒ?? o.3xaBi}bHܼ8{4^_P:|0!ˡ7&lYB"?Omb{1 aбNP8@GV YrUTWXҿX掍i7 iOvX,m0R|-jX.JI| J{ yy +8UЛ%Țȓli4L@H|堽w=ArϏC5 ~.m@8bo 1uXMAMH4`;}"@RoGT짴E9-mcn;OгTOkI +kM 07gozW +@ +7vO `D'$"$R 2Y~ +}!k]ws'aQG6;(&8_E"OjT\ܟ`KcǞHo\pw/Q]3df8iqҺXQӷ(-aɌl|.LHՉS.GY?z%{[73O;c"_aHΤi#}err3~bXWqޔu틉Ow+Pw?JTLVM +4PA{ֵ!e0@UJ-*X6C8GlC߃a՛%AO)(cF9ez$р6|tmSruECXC1dDGF`:ܒEqܩ)Aũ{Q7xhRR1/.$"h'hteq8eG}GUy lP&hmԁ4MHH:K PӁӘvvkuBiET*QtZgZ\S&g:ˆ {km"ipkG)ROG?y^aHWȦ~bկc1]fh!sKXkoEY _R#"(.̶f~F!S#}QTTWx5ziϣR^6 ,tY< +e%wL2 o >5E6䩇RNt: +X0F-(l#W9d_{]6*u9V̂h'@kBѕIVID"ȓS&eIo LWc/sn=ӅV͋rrQ֦n%/$jt ca)^A(".0v.`#,4"dSر;!ղ+V.sCBk=Խ;|6U-s Fe?iaݘnQA^זO@շx+f 9^'mu+t!lD= +0k$j;SX6ddL:/G0?B|\9?ŚpIjI~ +0ۺ7#Ld]5W)S`L!zC!;w&Q*p& 9^l)1M,N[% +#EjƤQ+c%5F8+n $M<3Wj/}/xa-qîf KcᲆӒ +xIvG?Ҧ 5\.fuDpuLS벖wK{vƻ Lz8:&#d Iî Z09(=-wbB޹ֲy`TBmƺ%D:b}zU2NHe^aIKߤ{*ҥUt!hJSlAr(39jY(ongwT.з.`41JD*k ? pQE`꿯>kOC>-F",6F?{͚)pJ3M2$>/tDdT'"Q4,(m3K2<N&a&t|cY w6Ls-Br7/Dg1ЙIu'XX+%jޫ #[nQ\k: C}tFKrsLm;rAà _zgMэ.F2'4, +q U;8Ĺc+ P!M||\$%L=T_m(~Bl;V@ '+֨+5z$v'HSa5XG$ (Gq5xt2l)`:b螵K|DŽF:ڠ`v^B YkJK0!2z}B"JCtPs{O-6Z0ퟦ+Zdx~EwQF48 ';)H-_Kh@XqA:8d[2YJidē\&äYMIAPM䉇{. 8p~I=> endobj +58 0 obj << +/Ascent 694 +/CapHeight 683 +/Descent -194 +/FontName /TSJTZG+CMTI12 +/ItalicAngle -14.04 +/StemV 63 +/XHeight 431 +/FontBBox [-36 -251 1103 750] +/Flags 4 +/CharSet (/A/B/D/L/M/P/S/a/b/c/d/e/f/g/h/i/k/l/m/n/o/p/r/s/t/u/v) +/FontFile 59 0 R +>> endobj +243 0 obj +[727 688 0 738 0 0 0 0 0 0 0 613 877 0 0 663 0 0 550 0 0 0 0 0 0 0 0 0 0 0 0 0 500 450 450 500 450 300 450 500 300 0 450 250 800 550 500 500 0 413 400 325 525 450 ] +endobj +242 0 obj << +/Type /Encoding +/Differences [ 0 /.notdef 65/A/B 67/.notdef 68/D 69/.notdef 76/L/M 78/.notdef 80/P 81/.notdef 83/S 84/.notdef 97/a/b/c/d/e/f/g/h/i 106/.notdef 107/k/l/m/n/o/p 113/.notdef 114/r/s/t/u/v 119/.notdef] +>> endobj +56 0 obj << +/Length1 1398 +/Length2 7256 +/Length3 532 +/Length 9186 +>> +stream +%!PS-AdobeFont-1.1: CMBX12 1.0 +%%CreationDate: 1991 Aug 20 16:34:54 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMBX12) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Bold) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /ZRPMDE+CMBX12 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 39 /quoteright put +dup 45 /hyphen put +dup 46 /period put +dup 48 /zero put +dup 49 /one put +dup 50 /two put +dup 51 /three put +dup 52 /four put +dup 66 /B put +dup 67 /C put +dup 68 /D put +dup 73 /I put +dup 75 /K put +dup 76 /L put +dup 77 /M put +dup 78 /N put +dup 80 /P put +dup 82 /R put +dup 83 /S put +dup 85 /U put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 100 /d put +dup 101 /e put +dup 102 /f put +dup 103 /g put +dup 104 /h put +dup 105 /i put +dup 107 /k put +dup 108 /l put +dup 109 /m put +dup 110 /n put +dup 111 /o put +dup 112 /p put +dup 114 /r put +dup 115 /s put +dup 116 /t put +dup 117 /u put +dup 118 /v put +dup 120 /x put +dup 121 /y put +dup 122 /z put +dup 124 /emdash put +readonly def +/FontBBox{-53 -251 1139 750}readonly def +currentdict end +currentfile eexec +oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou_dV`Ky Z]uMYb[1[l',t\pڮԞZO4GJ7 i!U&Ϸݢh`ZṆhKGz; #1&()$J3KُօEsjFf"P$-I޵˕B +6=hqDV<` EkENrraƌJG ~L{6IE6U'y 0gK>&)o>2\U]$XW-1f@'B 1mW=L%5t.O-]N CT4>&wvNXŅCf עr1fׁVCȖ~q0 Xf^^$ӷ%G7dȱ\lFc0]g<銷_&W{>}N|ӷ 054H4ܞlG>T_cќ6Y1 nUr-u$zq1k.s+6'F2炁.rq5#3|u)pվc Nr3 p<~s?aG:m+-뢅^dҭG)qQE;%鬎F02y'9N#`=gh7+eC:é&2k(]9YW-f&AدʴE'l:Gqs)'bR!fv@@#['#*DuD<%n3<D.RR}셛%]5|gB?="u:U}`qv|0Kуa>h> ^O:j^RĿɭ/Й)?OFLD|@zd P i[tL5N7d~Csj̸!GS)}+8TջH2UeBU̘D B`3FU8F۟h_zB5foJ}y85Ka]oN jri~y7o[G7 +*-MC}Կ\8U`5#m}w(O6xЏ{bA?9pwtxYMoŽTTR`18Gdo\@!>v/#xcFSN*i$zMIcK~R{FDlZBi0MOrfm0Jd/`b +Qʭh4fYznPy#2*SMn>kHAܤ6Oe#zX$5N +YZ+xkxHn_q=IU^h v$-T ZewX||#* Kɖ|[m }$mnbb’~:\Z_iBtTӸRF (;-1xhAU)9P9@o;H7mOه:YO胇ҳb)It1 * HfpfEDpŧu5@FT̴~$Mbxdpx&^YO͍vN1J [W~ {DȒFzE+n'O'ZF8IMD 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