# LaTeX2HTML 2K.1beta (1.47)
# Associate images original text with physical files.


$key = q/n(s)simL,s^{-tau};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img80.png"
 ALT="$n(s) \sim L   s^{-\tau}$">|; 

$key = q/R_{itprice};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img115.png"
 ALT="$R_{\it price}$">|; 

$key = q/dollar10^8;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$\$10^8$">|; 

$key = q/17,500kdollar;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img136.png"
 ALT="$17 500k\$$">|; 

$key = q/Nslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$N/2$">|; 

$key = q/C;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$C$">|; 

$key = q/M;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img102.png"
 ALT="$M$">|; 

$key = q/{displaymath}c(i)=i{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="63" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="\begin{displaymath}
c(i) = i
\end{displaymath}">|; 

$key = q/Nslash2^ktimesNslash2^k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$N/2^k \times N/2^k$">|; 

$key = q/N(s)=s,n(s);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$N(s) = s   n(s)$">|; 

$key = q/1slashx;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img134.png"
 ALT="$1/x$">|; 

$key = q/simL^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img85.png"
 ALT="$\sim L^2$">|; 

$key = q/k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="$k$">|; 

$key = q/overlineS(tildet)=Nslashn(tildet)=1slash(1-tildetslashN);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="244" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$\overline S(\tilde t) = N / n(\tilde t) = 1 / (1 - \tilde t/N)$">|; 

$key = q/includegraphics[width=0.49hsize]{basic-scaling-gpl.eps};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="272" HEIGHT="188" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="\includegraphics[width=0.49\hsize]{basic-scaling-gpl.eps}">|; 

$key = q/R_x:=x(t)slashx(tmskip-thinmuskip-mskip-thinmuskip1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$R_x := x(t) / x(t\mskip -\thinmuskip -\mskip -\thinmuskip 1)$">|; 

$key = q/{displaymath}rho(x)propto{1overx},expbig[-(ln(x)-ln(mu))^2big]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="273" HEIGHT="82" BORDER="0"
 SRC="|."$dir".q|img133.png"
 ALT="\begin{displaymath}
\rho(x)
\propto {1 \over x}   \exp\big[ - ( \ln(x) - \ln(\mu) )^2 \big]
\end{displaymath}">|; 

$key = q/R_{itcost};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img116.png"
 ALT="$R_{\it
cost}$">|; 

$key = q/{itXcorr}(tau):=langleR_P(t)R_C(t!-!tau)rangle;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="245" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img118.png"
 ALT="${\it Xcorr}(\tau) := \langle R_P(t) R_C(t\!-\!\tau) \rangle$">|; 

$key = q/sqrt{s};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="$\sqrt{s}$">|; 

$key = q/s=2^k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$s=2^k$">|; 

$key = q/tauapprox3slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img92.png"
 ALT="$\tau \approx 3/2$">|; 

$key = q/n_*slashN=p_{{it{inj}-n_*slashN;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$n_*/N = p_{\it inj} - n_* / N$">|; 

$key = q/N(s)slashN(1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$N(s)/N(1)$">|; 

$key = q/{displaymath}n(s)propto(s-epsilonp_{{it{inj})^{-(1+epsilon)}sims^{-(1+epsilon)}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="275" HEIGHT="66" BORDER="0"
 SRC="|."$dir".q|img100.png"
 ALT="\begin{displaymath}
n(s) \propto (s - \epsilon p_{\it inj})^{-(1+\epsilon)}
\sim s^{-(1+\epsilon)}  .
\end{displaymath}">|; 

$key = q/P_j<1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img112.png"
 ALT="$P_j&lt;1$">|; 

$key = q/2=1+3slash2,(2-tau)<comment_mark>158Rightarrowtau=4slash3.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="283" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img91.png"
 ALT="$
2 = 1 + 3/2   (2-\tau) %% = 1 + 3 - 3 \tau/2
  \Rightarrow  \
\tau = 4/3  .
$">|; 

$key = q/Q_j=n_jMslashP_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img107.png"
 ALT="$Q_j = n_j M/P_j$">|; 

$key = q/2r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img130.png"
 ALT="$2r$">|; 

$key = q/-3slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img75.png"
 ALT="$-3/2$">|; 

$key = q/{displaymath}s_*=Nslashn_*=2slashp_{{it{inj}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="63" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="\begin{displaymath}
s_* = N/n_* = 2 / p_{\it inj}  .
\end{displaymath}">|; 

$key = q/p_{itinj}=0.1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$p_{\it inj}=0.1$">|; 

$key = q/{keyword}econophysics;economics;simulation;markets{keyword};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="978" HEIGHT="1265" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="\begin{keyword}
econophysics; economics; simulation; markets
\end{keyword}">|; 

$key = q/{figure}[t]centercenterlineincludegraphics[width=0.49textwidth]series-gpl.epshfillincludegraphics[width=0.49textwidth]track-gpl.epslabelfig:adjustment-1center{figure}/;
$cached_env_img{$key} = q|<IMG WIDTH=541 HEIGHT=188 ALIGN=BOTTOM ALT="figure229" SRC="|."$dir".q|img7.gif">|; 

$key = q/{displaymath}n_*=N,p_{{it{inj}slash2.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="63" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="\begin{displaymath}
n_* = N   p_{\it inj} / 2  .
\end{displaymath}">|; 

$key = q/langle.rangle;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img121.png"
 ALT="$\langle . \rangle$">|; 

$key = q/2times10^9;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img141.png"
 ALT="$2 \times 10^9$">|; 

$key = q/Nslash2^{k-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$N/2^{k-1}$">|; 

$key = q/L;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img74.png"
 ALT="$L$">|; 

$key = q/Q;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img114.png"
 ALT="$Q$">|; 

$key = q/n(s)sims^{-2}hbox{or}n(>!s)sims^{-1},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="250" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="$
n(s) \sim s^{-2} \hbox{   or   } n(&gt;\!s) \sim s^{-1}  ,
$">|; 

$key = q/proptoL;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img79.png"
 ALT="$\propto L$">|; 

$key = q/R_x(t)=x(t)slashx(t-1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img119.png"
 ALT="$R_x(t)
= x(t) / x(t-1)$">|; 

$key = q/-1slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$-1/2$">|; 

$key = q/1024^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$1024^2$">|; 

$key = q/t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$t$">|; 

$key = q/epsilonsim1slashlanglesranglesimp_{{it{inj};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img97.png"
 ALT="$\epsilon \sim 1/\langle s \rangle \sim p_{\it inj}$">|; 

$key = q/N=LtimesL;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$N = L \times L$">|; 

$key = q/p_{{it{inj}=0.1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$p_{\it inj}=0.1$">|; 

$key = q/n(t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$n(t)$">|; 

$key = q/n_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img106.png"
 ALT="$n_j$">|; 

$key = q/{displaymath}r_{{it{del,eff}=n(t)slashN.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="63" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="\begin{displaymath}
r_{\it del,eff} = n(t)/N  .
\end{displaymath}">|; 

$key = q/Stoinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img83.png"
 ALT="$S \to \infty$">|; 

$key = q/Rightarrow;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img88.png"
 ALT="$ \Rightarrow $">|; 

$key = q/tau=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$\tau =0$">|; 

$key = q/2D;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img126.png"
 ALT="$2D$">|; 

$key = q/{figure}[t]centercenterlineincludegraphics[width=0.4textwidth]basic-1-gz.epshfilincludegraphics[height=0.4textwidth]basic-2-gz.epslabelfig:basic-snapshotcenter{figure}/;
$cached_env_img{$key} = q|<IMG WIDTH=475 HEIGHT=219 ALIGN=BOTTOM ALT="figure59" SRC="|."$dir".q|img2.gif">|; 

$key = q/1slashn(tildet);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$1/n(\tilde t)$">|; 

$key = q/simL^{3slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img86.png"
 ALT="$\sim L^{3/2}$">|; 

$key = q/D=(N-1)slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img127.png"
 ALT="$D=(N-1)/2$">|; 

$key = q/{frontmatter}titleSpatialcompetitionandpriceformationauthor[eth]KaiNagel,thanksrefknauthor[cowles]MartinShubik,thanksrefmsauthor[nbi]MayaPaczuski,thanksrefmpauthor[nbi]PerBakthanksrefpbaddress[eth]Dept.ofComputerScience,ETHZ"urich,Switzerlandaddress[cowles]CowlesFoundationforResearchinEconomics,YaleUniversity,NewHaven,Connecticutaddress[nbi]NielsBohrInstitute,UniversityofCopenhagen,Denmarkthanks[kn]nagel@inf.ethz.ch.ETHZentrumIFWB27.1,8092~Z"urich,Switzerlandthanks[ms]martin.shubik@yale.eduthanks[mp]paczuski@alf.nbi.dkthanks[pb]bak@alf.nbi.dkmaketitleabstractWelookatpriceformationinaretailsetting,thatis,companiessetprices,andconsumerseitheracceptpricesorgosomeplaceelse.Incontrasttomostothermodelsinthiscontext,weuseatwo-dimensionalspatialstructureforinformationtransmission,thatis,consumerscanonlylearnfromnearestneighbors.Manyaspectsofthiscanbeunderstoodintermsofgeneralizedevolutionarydynamics.Inconsequence,wefirstlookatspatialcompetitionandclusterformationwithoutprice.Thisleadstoestablishementsizedistributions,whichwecomparetoreality.Aftersometheoreticalconsiderations,whichatleastheuristicallyexplainoursimulationresults,wefinallyreturntopriceformation,wherewedemonstratethatoursimplemodelwithnearlynoorganizedplanningorrationalityonthepartofanyoftheagentsindeedleadstoaneconomicallyplausibleprice.abstractkeywordeconophysics;economics;simulation;marketskeyword{frontmatter}/;
$cached_env_img{$key} = q|<IMG WIDTH=78 HEIGHT=13 ALIGN=BOTTOM ALT="frontmatter8" SRC="|."$dir".q|img1.gif">|; 

$key = q/c(i)=C;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$c(i) = C$">|; 

$key = q/256^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$256^2$">|; 

$key = q/s,n(s)-(s-1),n(s-1)approx{doverds}(s,n(s));MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="305" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img98.png"
 ALT="$s   n(s) - (s-1)   n(s-1) \approx {d \over ds} (s   n(s))$">|; 

$key = q/includegraphics[width=0.49hsize]{rnd-inj-gpl.eps};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="272" HEIGHT="186" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="\includegraphics[width=0.49\hsize]{rnd-inj-gpl.eps}">|; 

$key = q/L^2simL;(L^2)^{2-tau};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img87.png"
 ALT="$L^2 \sim L \; (L^2)^{2-\tau}$">|; 

$key = q/{displaymath}intds,s,n(s),{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="79" BORDER="0"
 SRC="|."$dir".q|img77.png"
 ALT="\begin{displaymath}
\int ds   s   n(s)  ,
\end{displaymath}">|; 

$key = q/{{it{Xcorr}(tau):=delimiter"426830AR_P(t)R_C(tmskip-thinmuskip-mskip-thinmuskiptau)delimiter"526930B;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="245" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="${\it Xcorr}(\tau ) := \delimiter ''426830A R_P(t) R_C(t\mskip -\thinmuskip -\mskip -\thinmuskip \tau ) \delimiter ''526930B $">|; 

$key = q/1slashN;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$1/N$">|; 

$key = q/2^D;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img131.png"
 ALT="$2^D$">|; 

$key = q/s_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img94.png"
 ALT="$s_i$">|; 

$key = q/tau=3slash2.;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img90.png"
 ALT="$
\tau = 3/2  .
$">|; 

$key = q/s_{i+1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img137.png"
 ALT="$s_{i+1}$">|; 

$key = q/n(s)sims^{-3slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$n(s) \sim s^{-3/2}$">|; 

$key = q/Nslash2^k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$N/2^k$">|; 

$key = q/i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$i$">|; 

$key = q/{displaymath}0=-n-s,{dnoverds}-epsilon,n+epsilon,p_{{it{inj},{dnoverds}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="83" BORDER="0"
 SRC="|."$dir".q|img99.png"
 ALT="\begin{displaymath}
0 = - n - s   {dn \over ds} - \epsilon   n
+ \epsilon   p_{\it inj}   {dn \over ds}  .
\end{displaymath}">|; 

$key = q/s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$s$">|; 

$key = q/x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img135.png"
 ALT="$x$">|; 

$key = q/tildet;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$\tilde t$">|; 

$key = q/log(sqrt{s})=log(s)slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$\log(\sqrt{s}) = \log(s)/2$">|; 

$key = q/tau<2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img82.png"
 ALT="$\tau &lt; 2$">|; 

$key = q/128^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$128^2$">|; 

$key = q/n(tildet)=N-tildet;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$n(\tilde t) = N - \tilde t$">|; 

$key = q/1slashp_{{it{inj};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$1/p_{\it inj}$">|; 

$key = q/epsilon;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img96.png"
 ALT="$\epsilon$">|; 

$key = q/{displaymath}n(s)sims^{-2}hbox{or}n(>!s)sims^{-1}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="64" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="\begin{displaymath}
n(s) \sim s^{-2} \hbox{ or } n(&gt;\!s) \sim s^{-1}  .
\end{displaymath}">|; 

$key = q/2^{k-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="$2^{k-1}$">|; 

$key = q/{figure}[t]centercenterlineincludegraphics[width=0.4textwidth]snap-line-gz.epshfilincludegraphics[width=0.55textwidth]line-scaling-gpl.epslabelfig:snap:linecenter{figure}/;
$cached_env_img{$key} = q|<IMG WIDTH=532 HEIGHT=226 ALIGN=BOTTOM ALT="figure122" SRC="|."$dir".q|img4.gif">|; 

$key = q/C(Q);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img109.png"
 ALT="$C(Q)$">|; 

$key = q/p_{itinj}=0.01;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$p_{\it inj} = 0.01$">|; 

$key = q/{displaymath}n(s)sims^{-1.5}hbox{or}n(>!s)sims^{-0.5}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="64" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="\begin{displaymath}
n(s) \sim s^{-1.5} \hbox{ or } n(&gt;\!s) \sim s^{-0.5}  .
\end{displaymath}">|; 

$key = q/(25,000~kdollar-10,000~kdollar)=15,000~kdollar;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="291" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img132.png"
 ALT="$(25 000&nbsp;k\$ - 10 000&nbsp;k\$) = 15 000&nbsp;k\$$">|; 

$key = q/{displaymath}r_{{it{inj,eff}=p_{{it{inj}-n(t)slashN.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="192" HEIGHT="63" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="\begin{displaymath}
r_{\it inj,eff} = p_{\it inj} - n(t)/N  .
\end{displaymath}">|; 

$key = q/{displaymath}L^2simintds,s,L,s^{-tau}=L,intds,s^{1-tau}simL,s^{2-tau}big|_0^S.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="361" HEIGHT="79" BORDER="0"
 SRC="|."$dir".q|img81.png"
 ALT="\begin{displaymath}
L^2 \sim \int ds   s   L   s^{-\tau}
= L   \int ds   s^{1-\tau}
\sim L   s^{2-\tau} \big\vert _0^S  .
\end{displaymath}">|; 

$key = q/512^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$512^2$">|; 

$key = q/n(>!s)sims^{-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$n(&gt;\!s)
\sim s^{-1}$">|; 

$key = q/1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$1$">|; 

$key = q/k-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$k-1$">|; 

$key = q/2=1+2,(2-tau)<comment_mark>156;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img89.png"
 ALT="$
2 = 1 + 2   (2-\tau) %%= 1 + 4 - 2 \tau
$">|; 

$key = q/N_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img138.png"
 ALT="$N_i$">|; 

$key = q/p_{{it{inj}=0.01;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$p_{\it inj} = 0.01$">|; 

$key = q/{displaymath}tildeN_i={N_iovers_{i+1}-s_i},{s_i+s_{i+1}over2}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="87" BORDER="0"
 SRC="|."$dir".q|img140.png"
 ALT="\begin{displaymath}
\tilde N_i = {N_i \over s_{i+1} - s_i}   {s_i + s_{i+1} \over 2}  .
\end{displaymath}">|; 

$key = q/{figure}[t]centerhboxincludegraphics[width=0.49hsize]basic-scaling-gpl.epshfillincludegraphics[width=0.49hsize]rnd-inj-gpl.epslabelfig:basic-scalingcenter{figure}/;
$cached_env_img{$key} = q|<IMG WIDTH=542 HEIGHT=185 ALIGN=BOTTOM ALT="figure83" SRC="|."$dir".q|img3.gif">|; 

$key = q/sims^{-3slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img93.png"
 ALT="$\sim s^{-3/2}$">|; 

$key = q/p_{{it{ch};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img123.png"
 ALT="$p_{\it ch}$">|; 

$key = q/2^k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$2^k$">|; 

$key = q/p_{{it{ch}to0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img124.png"
 ALT="$p_{\it ch} \to 0$">|; 

$key = q/r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img129.png"
 ALT="$r$">|; 

$key = q/{displaymath}n(>!s)sims^{-1}hbox{correspondingto}n(s)sims^{-2}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="342" HEIGHT="64" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="\begin{displaymath}
n(&gt;\!s) \sim s^{-1} \hbox{  corresponding to   } n(s) \sim s^{-2}
\end{displaymath}">|; 

$key = q/i=1..N;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$i=1..N$">|; 

$key = q/{figure}[t]centercenterlineincludegraphics[width=0.49hsize]nsptl-p10-gpl.epshfilincludegraphics[width=0.49hsize]nsptl-p01-gpl.epslabelfig:non-spatial-gplcenter{figure}/;
$cached_env_img{$key} = q|<IMG WIDTH=543 HEIGHT=185 ALIGN=BOTTOM ALT="figure133" SRC="|."$dir".q|img5.gif">|; 

$key = q/n(s)sims^{-tau};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img78.png"
 ALT="$n(s) \sim s^{-\tau}$">|; 

$key = q/delta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img113.png"
 ALT="$\delta$">|; 

$key = q/n(>!s);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$n(&gt;\!s)$">|; 

$key = q/64^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$64^2$">|; 

$key = q/L^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img76.png"
 ALT="$L^2$">|; 

$key = q/N=L^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$N = L^2$">|; 

$key = q/P_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img105.png"
 ALT="$P_j$">|; 

$key = q/c(i)=i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$c(i) = i$">|; 

$key = q/Q_i=MslashP_j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img104.png"
 ALT="$Q_i = M/P_j$">|; 

$key = q/sims^{-2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="$\sim s^{-2}$">|; 

$key = q/R_{{it{cost};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$R_{\it cost}$">|; 

$key = q/{displaymath}{dn(s)overdt}=(s!-!1),n(s!!-!!1)-s,n(s)-epsilon,n(s)-epsilon,p_{{it{inj},n(s)+epsilon,p_{{it{inj},n(s!!+!!1).{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="545" HEIGHT="84" BORDER="0"
 SRC="|."$dir".q|img95.png"
 ALT="\begin{displaymath}
{d n(s) \over dt}
= (s\!-\!1)   n(s\!\!-\!\!1) - s   n(s) ...
...t inj}   n(s)
+ \epsilon   p_{\it inj}   n(s\!\!+\!\!1)  .
\end{displaymath}">|; 

$key = q/C(Q)=Q;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img111.png"
 ALT="$C(Q)=Q$">|; 

$key = q/D;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img125.png"
 ALT="$D$">|; 

$key = q/tilden(s)sims^{-3}hbox{or}tilden(>!s)sims^{-2},;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="231" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$
\tilde n(s) \sim s^{-3} \hbox{ or } \tilde n(&gt;\!s) \sim s^{-2}  ,
$">|; 

$key = q/{displaymath}{{it{Xcorr}(tau)=langleR_P(t),R_C(t-tau)rangle,{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="253" HEIGHT="63" BORDER="0"
 SRC="|."$dir".q|img120.png"
 ALT="\begin{displaymath}
{\it Xcorr}(\tau) = \langle R_P(t)   R_C(t-\tau) \rangle  ,
\end{displaymath}">|; 

$key = q/N;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$N$">|; 

$key = q/S;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img84.png"
 ALT="$S$">|; 

$key = q/n=2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$n=2$">|; 

$key = q/j=f(i);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img103.png"
 ALT="$j=f(i)$">|; 

$key = q/{figure}[t]centercenterlineincludegraphics[width=0.49hsize]s-corr-gz.epshfillincludegraphics[width=0.49hsize]f-corr-gz.epslabelfig:xcorrcenter{figure}/;
$cached_env_img{$key} = q|<IMG WIDTH=542 HEIGHT=183 ALIGN=BOTTOM ALT="figure239" SRC="|."$dir".q|img8.gif">|; 

$key = q/p_{{it{inj}to0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img101.png"
 ALT="$p_{\it inj} \to 0$">|; 

$key = q/n(s);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$n(s)$">|; 

$key = q/c(i);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$c(i)$">|; 

$key = q/{{it{XCorr}(-tau);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img122.png"
 ALT="${\it XCorr}(-\tau)$">|; 

$key = q/Dtoinfty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img128.png"
 ALT="$D
\to \infty$">|; 

$key = q/Pi_j:=n_j,M-C(n_j,MslashP_j);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img110.png"
 ALT="$\Pi_j
:= n_j   M - C(n_j   M/P_j)$">|; 

$key = q/n(t)slashN;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$n(t)/N$">|; 

$key = q/log(s);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="$\log(s)$">|; 

$key = q/R_{{it{price};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$R_{\it price}$">|; 

$key = q/R_x:=x(t)slashx(t!-!1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img117.png"
 ALT="$R_x := x(t) / x(t\!-\!1)$">|; 

$key = q/n_jM;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img108.png"
 ALT="$n_j M$">|; 

$key = q/n(s)sims^{-2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$n(s) \sim s^{-2}$">|; 

$key = q/-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$-1$">|; 

$key = q/{figure}[t]centercenterlineincludegraphics[width=0.49textwidth]sales-loglog-gpl.epshfillincludegraphics[width=0.49textwidth]sales-accum-gpl.epslabelfig:salescenter{figure}/;
$cached_env_img{$key} = q|<IMG WIDTH=541 HEIGHT=187 ALIGN=BOTTOM ALT="figure156" SRC="|."$dir".q|img6.gif">|; 

$key = q/p_{{it{inj};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$p_{\it inj}$">|; 

$key = q/tildeN_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img139.png"
 ALT="$\tilde N_i$">|; 

1;

