%Paper: 
%From: visitor@fnas08.fnal.gov (visitor)
%Date: Wed, 25 Nov 92 10:44:40 -0500
%Date (revised): Tue, 12 Oct 93 09:59:24 GMT-0500



\documentstyle[12pt,fleqn]{article}
\textheight 8.5in
\topmargin -.5in
\voffset 2 truecm
\hoffset 2 truecm


\textwidth 6.25in
\oddsidemargin 0.25in
\evensidemargin 0.25in
\topmargin -.25in
\begin{document}
\begin{titlepage}
\vspace*{-62pt}
\begin{flushright}
UCLAHEP-92-44\\
DART-HEP-92/06\\
Revised Sept. 1993
\end{flushright}

\vspace{0.75in}
\centerline{\bf KINETICS OF SUB-CRITICAL BUBBLES AND THE ELECTROWEAK
TRANSITION}
\vskip 0.5cm
\centerline{Graciela Gelmini$^a$ and Marcelo Gleiser$^b$ }

\vskip 0.5 cm
\centerline{\it $^a$ Department of Physics,}
\centerline{\it University of California, Los Angeles, CA 90024}
\vskip 0.5cm
\centerline{$^b$\it Department of Physics and Astronomy,}
\centerline{\it Dartmouth College, Hanover, NH 03755}

\baselineskip=12pt

\vskip 1.5 cm
\centerline{\bf ABSTRACT}
\vskip 0.5 cm
\begin{quote}
We investigate the role of large amplitude
sub-critical thermal fluctuations
in the dynamics of first order phase transitions.
In particular, we obtain a kinetic equation for
the number density of sub-critical fluctuations of the broken-symmetric phase
within the symmetric phase,
modeled as spherical bubbles, and solve it analytically
for temperatures above the critical
temperature.
We study the approach to
equilibrium and obtain the equilibrium distribution of sub-critical bubbles
of the unstable phase
by examining three possible mechanisms responsible for their removal;
their shrinking, their coupling to thermal noise, and by thermal
fluctuations of the true vacuum inside them.
We show that for sufficiently strong transitions, either
the shrinking or the coupling to thermal noise dominate the dynamics.
As the strength of the transition weakens we show that sub-critical
fluctuations become progressively more important, as a larger
fraction of the total volume is occupied by the broken-symmetric phase,
until the point where
our analytical approach breaks down.  Our investigation
suggests that pre-transitional
phenomena may considerably change the dynamics of sufficiently weak
first-order transitions. We apply our results to
the standard electroweak transition.

\end{quote}

\vspace{0.1in}
e-mail: gelmini@physics.ucla.edu; gleiser@peterpan.dartmouth.edu

\end{titlepage}

\def\la{\mathrel{\mathpalette\fun <}}
\def\ga{\mathrel{\mathpalette\fun >}}
\def\fun#1#2{\lower3.6pt\vbox{\baselineskip0pt\lineskip.9pt
        \ialign{$\mathsurround=0pt#1\hfill##\hfil$\crcr#2\crcr\sim\crcr}}}
\def\mpl{{m_{Pl}}}
\def\f{\phi}
\def\s{\sigma}
\def\l{\lambda}
\def\rf{\langle \f \rangle}
\def\t{\theta}
\def\n{n(R,t)}
\def\ksection{\arabic{section}}
\def\theequation{\ksection.\arabic{equation}}
\def\thesection{}

\def\beq{\begin{equation}}
\def\eeq{\end{equation}}
\def\ba{\begin{eqnarray}}
\def\ea{\end{eqnarray}}
\def\re#1{{$^{\ref{#1}}$}}

\baselineskip=24pt
\thesection{\bf 1. INTRODUCTION}
\setcounter{section}{1}
\setcounter{equation}{0}
\vspace{24pt}

The study of the kinetics of first order phase transitions is by no means
a new topic. Since the pioneer work of Becker and D\"oring, the condensation
of supersatured vapor has been understood to occur by the thermal nucleation
of droplets of the liquid phase which, when larger than a critical size, will
grow and coalesce completing the transition.\re{NUC} Despite all the effort
dedicated to the study of the kinetics of phase transitions, their
intrinsic non-linear nature makes progress slow and restricted to simple
systems. Even for simple systems in the same universality class of the
Ising model many questions remain unanswered, from a microscopic understanding
of coarse-graining to the description of the late stages of the
transition.\re{LAN}

% This is perhaps peculiar to researchers in condensed matter physics
%who are mainly interested in the behavior of systems after quenching it to
%{\it below} the critical temperature.

Our main interest is in the study of cosmological first order
transitions, where the cooling is enforced adiabatically by the expanding
Universe.\re{A}
In particular, we are only interested in
transitions where the expansion rate of the
Universe is much slower than typical fluctuation time-scales in the system,
{\it i.e.}, when $M_{Pl}\gg m$, where $M_{Pl}$ is the Planck mass, and $m$ is
the characteristic mass scale in the model.

In this work we will study analytically the early stages of a first
order phase transition.
That is, we will restrict our study to temperatures
above the critical
temperature $T_c$, which is defined as the temperature at which the homogeneous
part of the coarse-grained free energy density (the effective potential to some
order in perturbation theory) exhibits two degenerate minima. By focusing on
temperatures above the critical temperature, we will be examining the behavior
of thermal fluctuations around the high temperature equilibrium state of the
system. In particular, we will consider  models described by a potential
$V(\f,T)$ which at high temperatures has a minimum at $\rf=0$ and that, as the
temperature drops to some value $T_1$, develop a new minimum at
$\rf=\f_+(T)$.
At the critical temperature $T_c<T_1$, $V(0,T_c)=V(\f_+,T_c)$. We will examine
thermal fluctuations around $\rf=0$ as the temperature drops below $T_1$.

The reader may be wondering why should anyone be interested in studying the
kinetics of first order phase transitions above $T_c$. After all, it is a
well-known fact that first order transitions evolve through the nucleation
and subsequent percolation of
bubbles larger than a critical size as the temperature
drops below $T_c$.  This is indeed the
case for sufficiently strong transitions. However, for weak enough transitions
the critical bubble picture must be modified, as has been observed for several
condensed matter systems in the past two decades.  A particularly striking
example is the isotropic-nematic transition in certain
liquid crystals; the transition
is first order (there is a discontinuous jump of the order parameter)
even though there is no release of latent heat.\re{LQ} In fact, large amplitude
fluctuations of the nematic phase within the isotropic phase have been observed
{\it above} the critical temperature for the transition, a typical example of
the so-called pre-transitional phenomena in condensed matter
literature.\re{LQ2}
(Interestingly enough, the free energy density used to describe the
isotropic-nematic transition, the Landau-de Gennes free energy, is formally
identical to the effective potential obtained for the
electroweak transition.)
Here,
we would like to investigate this possibility within the context of hot field
theories.
The point is that the usual vacuum decay
mechanism for first order transitions relies on results obtained
within homogeneous nucleation calculations, which assume that below $T_c$
the system has
small fluctuations about the metastable phase. In other words,
it is assumed that the path integral controlling the transition rate is
dominated by its saddle point, given by the solution to the Euclidean
equations of motion. Small fluctuations are then incorporated by  evaluating
the path integral by a Gaussian approximation. But as the transition
grows weaker,
large amplitude fluctuations about equilibrium will become more probable and
the approximations used will break down.\re{GR} Instead of expanding about a
homogeneous metastable background, one should be expanding about an
inhomogeneous background consisting of these large amplitude sub-critical
fluctuations. This is clearly a very hard task which nevertheless must be
undertook if we are to better
understand the dynamics of weak first order transitions.
The present work is but a first step in this direction
as we attempt to obtain the equilibrium distribution
of sub-critical bubbles at temperatures above $T_c$. This way we can obtain
the fraction of the total volume which is occupied by the
broken symmetric phase as $T_c$ is approached from above, and thus examine
the validity of the homogeneous nucleation picture as a function of the
strength of the phase transition.
Gleiser, Kolb and Watkins \re{GKW} (GKW) have first suggested
this possibility,
concentrating on correlation volume bubbles, but they did not take into account
that subcritical bubbles are unstable and, therefore, shrink.  (See, however,
their comments in Section 3.3). Later, Anderson \re{CRITICS} remarked  that
subcritical bubbles may disappear not only by shrinking but also
due to thermal
noise. As a result of any of these two mechanisms he concluded that
the fraction of the total
volume filled by bubbles of the unstable phase will be much smaller than
proposed by GKW. Here we incorporate these two disappearance
mechanisms into a kinetic description of the transition in order to
investigate the importance of
sub-critical bubbles near the critical temperature. We find that
sub-critical fluctuations become progressively more
important as the strength of the transition weakens, until the point where
the approximations we use in order to treat the problem
analytically break down
and our analysis cannot be trusted quantitatively. However, we believe
that our results are indicative of the relevance of pre-transitional
phenomena in the study of sufficiently weak
phase transitions in hot field theories.

In the next Section we will obtain the equation governing the kinetics of
sub-critical bubbles for temperatures just below $T_1$. In Section 3 we obtain
the expressions for the thermal nucleation rates needed to solve the kinetic
equation. In Section 4 we solve the kinetic equation in three
regimes; assuming
that  the shrinking  dominates the disappearance of subcritical bubbles,
assuming that thermal noise dominates, and finally neglecting
both shrinking and thermal noise.
Starting with the whole volume occupied only by the stable
phase, we obtain the equilibration time scale and the equilibrium number
density of bubbles of the unstable phase in the three  regimes at the
particular temperature considered, and establish the conditions for each
of the three processes to dominate the kinetics. In Section 5 we compare the
three time scales in the context of the standard electroweak model.
As expected,
for strong enough transitions shrinking or thermal noise dominate and the
sub-critical bubbles play a negligible role during the phase transition.
As the transition weakens we find that a larger fraction of the total
volume is occupied by the broken-symmetric phase. The
approximations we used to analytically solve the kinetic
equation break down when a large fraction of the volume is
occupied by sub-critical bubbles of the broken-symmetric phase,
and we
cannot carry our study into the limit of very weak transitions.
But our
results clearly suggest that for weak enough transitions a departure of the
usual vacuum decay mechanism is to be expected. Concluding remarks are
presented in Section 6.

\vspace{24pt}
\thesection{\bf 2. KINETIC EQUATION}
\setcounter{section}{2}
\setcounter{equation}{0}
\vspace{18pt}

Let $\n$ be the number density of sub-critical bubbles of radius $R$ at time
$t$. Thus, ${{\partial\n}\over {\partial R}} dR$
is the number per unit volume of bubbles of radii between $R$ and
$R+dR$. Since the bubbles can shrink, their radius $R$ is a function of time,
$R(t)$. We will only consider bubbles with $R\geq \xi$, where $\xi$ is the
correlation length for fluctuations around equilibrium, given by
\beq
\label{eq:XI}
\xi^{-2}(T)=V^{\prime \prime}(\f=0,T).
\eeq
Bubbles with $R\sim \xi$ will be statistically dominant since any larger
fluctuation has larger free-energy and is exponentially suppressed. (Recall
that for $T\geq T_c$ the free energy of bubbles is a monotonically increasing
function of $R$.\re{GKW})

Consider a large volume $V$ filled by the stable phase $\rf=0$, which is cooled
down from high temperatures to a temperature just below $T_1$. Bubbles with
radius $R$ of the new phase with $\rf=\f_+$ will be thermally nucleated in the
background of the phase $\rf=0$ with number density $\n$; the bubbles are
energetically unfavored and will shrink away with some velocity $dR/dt$.
Shrinking will always be present, unless there is a stabilizing mechanism for
the bubbles, as in non-topological solitons. \re{NTS} [We would like to stress
though that not much is known about nonlinear bubble collapse.
Naively, one would expect small, unstable bubbles to collapse in a time
$\sim R$. In fact,
recent results on the evolution of unstable bubbles found a remarkable
{\it enhancement} of the lifetime of bubbles by 3 to 4 orders of magnitude,
as long as their initial radius
is larger than about $2.5\xi$ and their amplitude at the center probes the
nonlinearity of the potential.\re{PULSONS}]
Thermal noise
may also destroy small sub-critical bubbles.
The importance of this effect will depend both on the ratio of bubble size to
thermal length ($R/T^{-1}$), and
on the
strength of the coupling of the bubbles with the thermal background, which
we parameterize with a dimensionless coefficient $a$.
Anderson\re{CRITICS} wrote this ``thermal destruction''
rate as $ \simeq a T (RT)^3$.  This expression
would imply that
the rate of disappearance of a bubble due to thermal noise
increases with its size, a result we find counter-intuitive.
Instead, we will conservatively take this rate to be
of order $a T$, and thus independent of bubble size. As we are mostly
interested in small bubbles here,
we expect that this overestimate of the true rate will not
compromise our results. In any case, it will only make our final results
stronger, as the final fraction of volume occupied by sub-critical bubbles
will be larger than what we obtain.
This expression yields a lower rate than that of Ref. \ref{CRITICS}, since
 $T > R^{-1}$.
We take, therefore, the rate per unit volume
of disappearance of sub-critical bubbles due to thermal noise to be
$\Gamma_{TN} (R) \simeq a
T/\frac{4}{3} \pi R^3$.

We now proceed to obtain the rate equation.
We can say, quite generally, that the number of bubbles that at time $t+dt$
have radius $R+dR$ in a volume $V\gg\xi$ is equal to the number of bubbles at
time $t$ with radius $R$ plus the net change in the number of bubbles in the
range ($R$, $R+dR$)  due to thermal nucleation,
%%%%%%%changes%%%%%%%%%%%%
disappearance due to thermal noise
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
and shrinking in the time interval $dt$,
\begin{eqnarray}
n(R+dR,t+dt)V= \n V+\left ({{V_0}\over V}\right )\Gamma_{0\rightarrow +}(R)Vdt
 \nonumber\\  -\left ({{V_+}\over V}\right )\Gamma_{+\rightarrow 0}(R)Vdt
- \left(\frac{V_+}{V}\right) \Gamma_{TN} (R) Vdt.
\end{eqnarray}

Thus, to first order in $dR$ and $dt$ we obtain, after
subtracting $n(R+dR,t)$ to both terms and dividing by $Vdt$,
\begin{eqnarray}
\label{eq:KIN}
{{\partial \n}\over {\partial t}}=-{{\partial \n}\over {\partial R}}
\left ({{dR}\over {dt}}\right )+\left ({{V_0}\over V}\right )\Gamma_{0
\rightarrow +}(R)  \nonumber\\
 - \left ({{V_+}\over V}\right )\Gamma_{+\rightarrow 0}(R)
- \left(\frac{V_+}{V}\right) \Gamma_{TN} (R)
\end{eqnarray}
Here, $\Gamma_{0\rightarrow +}(R)$ ($\Gamma_{+\rightarrow 0}(R)$)
is the rate per unit volume for
the thermal nucleation of a bubble of radius $R$ of phase $\f=\f_+$ within
the phase $\f=0$ (phase $\f=0$ within
the phase $\f_+$).
These were the only two rates considered in GKW.\re{GKW}
The volume ratios $V_{0(+)}/V$ take into account the
fact that the total volume in each phase changes in time due to the evolution
of $\n$. The initial conditions we choose are
\beq
V_0(t=0)=V~~~~~~~~{\rm and}~~~~~~~~V_+(t=0)=0~~,
\eeq
that is, all volume $V$ is initially in the phase $\f=0$. Also, $V_+$
must be understood as the volume of the (+)--phase in bubbles of radius $R$
{\it only}, since we are following the evolution of $\n$.
 Thus $\left(
\frac{V_+}{V}\right) = \frac{4}{3} \pi R^3 n (R,t)$.
In Eq.~(\ref{eq:KIN})  bubbles of radius $R$ can disappear due to their
shrinking (accounted for by the first term in the right-hand side with
$dR/dt<0$), due to thermal noise (last term in the right-hand side),
and due
to the nucleation of bubbles of the (0)--phase in their interior.
This latter process will, in general, involve bubbles of (0)--phase of
different radii as we will discuss later on.

Because
\beq
\left ({{V_0}\over V}\right )=1 - \int_{\xi}^{\infty}dR\left[-{4\over 3}\pi
R^3{{\partial\n}\over {\partial R}}\right]~~,
%\equiv 1-|I|\simeq 1~~.
\eeq
Eq.~(\ref{eq:KIN})  is an integro-differential equation and must be solved
within certain approximations, as with any Boltzmann-like equation. In a
complete treatment of the kinetics we should also write an equation for the
fluctuating regions of the (0)--phase within the (+)--phase. Furthermore, there
would be two contributions to $V_0$, a connected background volume
and a bubble-like, disconnected volume. The topology of the two-phase system
will, in general, be very complicated. Thus, we choose the range of
temperatures in which it is consistent to restrict the (0)--phase to the
background, as will be clear later.

Before we move on, we comment on two other possible contributions to $\n$ which
we will not discuss here; a)Induced nucleation: small bubbles may act as seeds
for the nucleation of other bubbles in their neighborhood due to the gain in
surface energy. There should be an enhancement of the nucleation
rate due to the presence of small bubbles in the background,
very much like the presence of impurities in condensed matter systems.
b)Collision of
bubbles: small bubbles may acquire a thermal velocity and collide forming
larger bubbles. Of course, for very short lived bubbles none of these processes
should be very important. However, we again stress that large enough bubbles
can be quite long-lived, and that a truly realistic scenario of weak first
order transitions will be much more complicated than our simple model.
The worth of the present effort relies on it being the first attempt to go
beyond GKW, by
incorporating more complicated out-of-equilibrium processes in the usual
description of phase transitions in field theories.


\vspace{24pt}
\thesection{\bf 3. THERMAL NUCLEATION RATES}
\setcounter{section}{3}
\setcounter{equation}{0}
\vspace{18pt}

In order to solve Eq.~(\ref{eq:KIN}) we need to determine the thermal
nucleation rates $\Gamma_{0(+)\rightarrow +(0)}$. For temperatures $T\la T_1$,
it is reasonable to assume that most bubbles will be nucleated with radius
$R\ga \xi$, where $\xi$ was defined
in Eq.~(\ref{eq:XI}).
%will be small with respect to critical bubbles.
For simplicity we will assume the same correlation
length for fluctuations around both minima, even though at $T_1$ the
correlations about $\f_+$ diverge. Following GKW we write for the rates,
\beq
\label{eq:RATES}
\Gamma_{0(+)\rightarrow +(0)}(R)=AT^4{\rm exp}\left [-F\left ({\bar \f}_{+(0)}
\right )/T\right ]~~~,
\eeq
where $A$ is a constant of order unity and the  ansatz for the sub-critical
bubble configurations ${\bar \f}$ is
\beq
\label{eq:BUB}
{\bar \f}_+(r)=\f_+{\rm exp} \left [-r^2/R^2\right ]~~~;~~~
{\bar \f}_0(r)=\f_+\left (1-{\rm exp}\left [-r^2/R^2\right ]\right ),
\eeq
with the free energy functional $F({\bar \f})$ of the bubble configuration
given by
\beq
\label{eq:FREE}
F\left ({\bar \f}\right )=4\pi\int r^2dr\left [{1\over 2}\left ({{d{\bar \f}}
\over {dr}}\right )^2 + V\left ({\bar \f},T\right )\right ]~~.
\eeq
In order to move on, we will choose a specific (but quite general) potential,
\beq
\label{eq:POT}
V(\f,T)={{m^2(T)}\over 2}\f^2 - \gamma(T)\f^3 +{{\l(T)}\over 4}\f^4~~,
\eeq
where $\gamma(T)$ and $\l(T)$ are positive definite functions of $T$ and
$m^2(T)$ can be negative below a certain temperature $T_2<T_c$. This potential
has a minimum at $\f=0$ as long as $m^2(T)>0$, and a local minimum at
$\f_+=\left[3\gamma(T)+\sqrt{9\gamma^2(T)-4m^2(T)\l(T)}~\right]/2\l(T)$, which
appears at a temperature $T_1$ given by the solution of $\gamma^2(T_1)=
4m^2(T_1)\l(T_1)/9$, when $\f_+(T_1)=3\gamma(T_1)/2\l(T_1)$. Below $T_c$
this minimum becomes the global minimum and the minimum at
$\f=0$ becomes metastable.
Using Eqs.
(\ref{eq:BUB}) and (\ref{eq:POT}) in Eq. (\ref{eq:FREE}), we obtain for the
free energy $F({\bar \f})$,\re{GK1}
\beq
\label{eq:FREE1}
F\left ({\bar \f}_{0(+)}\right)=\alpha_{0(+)}R + \beta_{0(+)}R^3~~,
\eeq
where
\beq
\label{eq:ALPHA}
\alpha_0=\alpha_+={{3\sqrt{2}}\over 8}\pi^{3/2}\f_+^2~~,
\eeq

\ba
\label{eq:BETA0}
\beta_0 & = &\pi^{3/2}\f_+^2\left[ {{m^2(T)}\over 8}(\sqrt2-8)
+\gamma(T)\f_+\left(3-{{3\sqrt2}\over 4}+{{\sqrt3}\over 9}\right)\right.
   \nonumber\\
& & \left.
+\l(T)\f_+^2\left(-1+{{3\sqrt2}\over 8}-{{\sqrt3}\over 9}+{1\over {32}}
\right)\right]~~,
\ea
and
\beq
\label{eq:BETA+}
\beta_+=\pi^{3/2}\f_+^2\left [{{m^2(T)\sqrt2}\over 8}-
{{\sqrt{3}}\over 9}\gamma(T)\f_+~
+{{\l(T)}\over {32}}\f_+^2\right ]~~.
\eeq

\vspace{24pt}
\thesection{\bf 4. SOLVING THE KINETIC EQUATION}
\setcounter{section}{4}
\setcounter{equation}{0}
\vspace{18pt}

We will solve Eq.~(\ref{eq:KIN}) in different regimes assuming that
the dominant process for the disappearance of bubbles is: 1.) their
shrinking, 2.) thermal noise and 3.) the  nucleation of bubbles of the
 true vacuum inside them.
This will allow us to make a direct comparison
of the results for the relaxation time scale and equilibrium number
density obtained in these regimes, in the context of the electroweak
transition in the next Section.
\vspace{16pt}

\centerline{\bf 4.1 Kinetic Equation with Shrinking}

We include only the shrinking term, neglecting the last two terms
of Eq.~(\ref{eq:KIN}), and solve this equation with the approximation,
\beq
\label{eq:CONS}
\left({{V_0}\over V}\right)=1 - \int_{\xi}^{\infty}dR\left[-{4\over 3}\pi
R^3{{\partial\n}\over {\partial R}}\right]\equiv 1-|I|\simeq 1~~.
\eeq
In words, we will solve the kinetic equation in the regime in which
 the volume in the (+)--phase, given by the sum
over all bubbles with
radii from $\xi$ to $\infty$ (actually, to $R\sim V^{1/3}\gg \xi$), is
small, i.e. $|I|\ll 1$. We
will check our results for consistency after obtaining $n(R,t)$.
With this approximation the
kinetic equation becomes,
\beq
\label{eq:KINS}
{{\partial\n}\over {\partial t}} = {{\partial\n}\over {\partial R}}
\left[f(R)\right] + \Gamma_{0\rightarrow +}(R)~~,
\eeq
where we wrote $dR/dt=-f(R)<0$. The positive definite function $f(R)$
encompasses the physically interesting cases $dR/dt=v={\rm constant}$, and
$dR/dt\sim 1/R$. We enforced the shrinking explicitly by choosing the minus
sign in $dR/dt$. The rate $\Gamma_{0\rightarrow +}$ was defined in
Eq.~(\ref{eq:RATES}), with the free energy given by Eq.~(\ref{eq:FREE1}) with
$\alpha_+$ and $\beta_+$ given by Eqs.~(\ref{eq:ALPHA}) and (\ref{eq:BETA+})
respectively. In order to solve this equation analytically we make one further
approximation; we neglect the volume term in the expression for the free
energy, so that the nucleation rate can be written as
\beq
\Gamma_{0\rightarrow +}(R)\simeq AT^4{\rm exp}\left[-\alpha_+R/T\right]\equiv
g(R)~~.
\eeq
Here we have defined the function $g(R)$. Given that most bubbles have radii
$R\ga \xi$ this should be a good approximation
that
must be tested in each application. For the electroweak case, independently
of the parameters of the model, we obtain
$\alpha_+ \xi/\beta_+ \xi^3 \simeq 6.65$ for $T=T_1$. The ratio increases for
lower temperatures.

In order to solve the above equation, first note that the time
independent equilibrium
number density at the temperature chosen, ${\bar n}(R)$, is the solution of
\beq
\label{eq:EQ}
{{\partial {\bar n}(R)}\over {\partial R}}= -{{g(R)}\over {f(R)}}~~,
\eeq
which is easily obtained as
\beq
{\bar n}(R)={\bar n}(\xi) - \int_{\xi}^R{{g(R)}\over {f(R)}}dR~~.
\eeq
Choosing $f(R)=v$ and the definition of $g(R)$ above we obtain,
\beq
\label{eq:nEQ1}
{\bar n}(R)={{AT^5}\over {v\alpha_+}}{\rm exp}\left[-\alpha_+R/T\right] ~~.
\eeq
Using Eq.~(\ref{eq:EQ}), we can rewrite the kinetic equation as
\beq
\label{eq:Y}
{{\partial Y(R,t)}\over {\partial t}}={{\partial Y(R,t)}\over {\partial R}}
f(R),
\eeq
where we introduced the departure from equilibrium, $Y(R,t)\equiv \n - {\bar n}
(R)$. This equation is solved by writing
\beq
Y(R,t)=X(R){\rm exp}\left[-t/\tau_1\right]~~,
\eeq
so that $\tau_1$ is the relaxation time and the solution approaches the
equilibrium distribution as $t\rightarrow \infty$. Choosing again $f(R)=v$ we
obtain upon substitution in Eq.~(\ref{eq:Y}),
\beq
\label{eq:X}
X(R)=X_0{\rm exp}\left[-R/v\tau_1\right]~~,
\eeq
where $X_0$ is a constant, which, together with $\tau_1$, will
be fixed by the initial condition $Y(R,0)=-
{\bar n}(R)$. Using Eq.~(\ref{eq:nEQ1}) we find
\beq
\label{eq:TAU1}
X_0=-{{AT^5}\over {v\alpha_+}}~~~{\rm and}~~~\tau_1={T\over {v\alpha_+}}~~.
\eeq
Putting the results together we find for the solution of the kinetic equation,
\beq
\label{eq:SOL1}
\n={\bar n}(R)\left(1-e^{-t/\tau_1}\right)={{AT^5}\over {v\alpha_+}}
e^{-\alpha_+R/T}\left[1 - e^{-\alpha_+vt/T}\right]~~.
\eeq
Thus, the relaxation time to approach the equilibrium distribution
${\bar n}(R)$ is the
time for a bubble of characteristic radius $v\tau_1=T/\alpha_+$ to shrink with
constant velocity $v$. (The reason why $\tau_1$ is independent of $R$ is due to
our choice of constant shrinking speed for all bubbles.) Substituting this
solution into the consistency condition given in Eq.~ (\ref{eq:CONS}) we obtain
\beq
\label{eq:CONS1}
|I|={4\over 3}\pi \xi^3{\bar n}(\xi)\left[1+3\left({T\over {\alpha_+\xi}}
\right) + 6\left({T\over {\alpha_+\xi}}\right)^2 + 6\left({T\over {\alpha_+
\xi}}\right)^3\right]\ll 1~.
\eeq
The consistency condition is then an expression of the validity of the
semi-classical approximation, which requires that exp $ \left [- F\left ({\bar
\f}_+ \right )/T\right ]\simeq $
exp $ \left [- \alpha_+R/T \right ] \ll 1$; if the
smallest bubble has a large nucleation barrier ($=F_+/T$) its production is
exponentially suppressed and only a negligible fraction of the total volume
will be occupied by the (+)--phase.

\vspace{16pt}
\centerline{\bf 4.2 Kinetic Equation with Thermal Destruction}

In Ref.~\ref{CRITICS} Anderson writes the thermal destruction rate
per unit volume as
\begin{equation}
\Gamma{(R)}_{TN} \simeq T^4 ~.
\end{equation}
With this expression, the rate of disappearance of a bubble increases with its
 volume. As mentioned above, we think this is counter-intuitive, since larger
 bubbles should be less prone to be detroyed by thermal noise than smaller
ones,
  not the contrary. In lack of a better understood expression we will take this
 rate to be $a T$, on dimensional grounds, independently of the size of the
 bubble.
The rate per unit volume of the disappearance of bubbles
due to thermal noise is then,
\begin{equation}
\Gamma{(R)}_{TN} = \frac{aT}{{{4 \pi}\over 3} R^3}~~.
\end{equation}
 The constant $a$ is proportional to the coupling of
the bubble to the thermal bath to some power.
 This is a difficult quantity to obtain
microscopically, and will depend on how the field couples to itself and
to other fields in the model. There has been some progress recently
in the computation of the viscosity coefficient in hot field theories,
although the results are model dependent.\re{MORIK} However, it is by now
clear that
viscosity (which is related to the coupling to the bath by
the fluctuation-dissipation theorem) in field theories is at least
a two-loop effect.

The kinetic equation is now,
\begin{equation}
\frac{\partial n(R,t)}{\partial t}  = \left(\frac{V_0}{V}\right)
\Gamma_{0 \to +} (R) - \frac{4}{3} \pi R^3 n (R, t)~ \Gamma_{TN} (R)~~.
\end{equation}
We will again make the approximation of Eq. (4.1). Using  Eqs. (4.3)
 and (4.13), the kinetic equation becomes
\begin{equation}
\frac{\partial n(R,t)}{\partial t}  = g (R) - a T n(R,t)~~.
\end{equation}
Thus, the time independent equilibrium number density is now
\begin{equation}
\bar{n} (R) = \frac{g(R)}{aT}={{AT^3}\over {a}}
e^{-\alpha_+R/T}~~,
\end{equation}
and we solve the equation for ($n - \bar{n}$) with the ansatz
\begin{equation}
n (R, t) - \bar{n} (R) = X(R) e^{- t/\tau_2}~~,
\end{equation}
and the initial condition $n (R,0) = 0$, which yields $X (R) = \bar{n}
(R)$.  Thus, $\tau_2^{-1} = aT$ and
\begin{equation}
n(R,t) = \bar{n} (R) ( 1 -  e^{-a Tt})={{AT^3}\over {a}} e^{-\alpha_+R/T}
( 1 - e^{-a Tt})
\end{equation}
The relaxation time is thus $\tau_2 = (aT)^{-1}$ as
expected.  Comparing this value with the relaxation time when shrinking
alone is considered $\tau_1 \simeq T/\alpha_+ v$, as obtained in the
previous section, we see that, under the approximations we choosed,
thermal noise will be dominant, {\it i.e.}
$\tau_2 < \tau_1$, for
\begin{equation}
a > \frac{\alpha_+ v}{T^2} \simeq \frac{\phi_+^2 v}{T^2} .
\end{equation}
Here we have taken  $\alpha_+ \simeq \phi_+^2$ from Eq. (3.6).
This is an important condition, since, as we mentioned
above, $a$ is proportional to some
power  of the coupling of the field $\phi$ with the thermal bath,
and $\phi_+/T$ is a measure of the strength of the
transition. (For successful baryogenesis during the electroweak scale
one needs roughly $\phi_+/T\ga 1$.\re{REVBAR})
Thus, thermal noise only dominates the dynamics over shrinking for
sufficiently weak transitions, {\it and} for strong enough
coupling to the thermal
bath.
The consistency  condition  in Eq. (4.1) is  again given by
Eq.  (4.12), but in this case ${\bar n}(\xi)$ is given  by Eq. (4.17). Thus,
this condition  is again an expression of the  validity of  the semiclassical
approximation, as explained below Eq. (4.17).



\vspace{16pt}
\centerline{\bf 4.3 Kinetic Equation Without Shrinking and Thermal
Destruction}

Neglecting the shrinking of bubbles and their coupling to thermal noise,
the kinetic equation is
\beq
{{\partial \n}\over {\partial t}}=\left({{V_0}\over V}\right)\Gamma_{0
\rightarrow +}(R) - \left({{V_+}\over V}\right)\Gamma_{+\rightarrow 0}~~,
\eeq
where the nucleation rates have been defined before. In order to be
consistent with our previous approach, we will again take $V_0/V\simeq 1$.
Since $\left(V_+/V \right) \Gamma_{+\rightarrow 0}(R)$
is the rate at which bubbles of (+)--phase of radius $R$ disappear due to the
nucleation of a region of (0)--phase in its interior,
as mentioned before, $V_+$ is the total
volume of all bubbles of radius $R$ (and not the total volume of (+)--phase).
 Thus we
have $V_+/V=(4\pi/3)R^3\n $. Consistency  with the assumption $V_0/V\simeq 1$
as $t\rightarrow \infty$
requires that  $(4\pi/3)R^3{\bar n}(R)\ll 1$. Since
most bubbles of the (+)--phase will have $R\simeq \xi$, this condition is
essentially the same as that of Eq.~(\ref{eq:CONS1}), as it should.

In principle, to obtain $\Gamma_{+\rightarrow 0}$ we should sum over bubbles of
the (0)--phase  of different radii which can trigger the disappearance of
regions of the (+)--phase.  This sum should be dominated by the contribution of
bubbles of radius $\xi$. In this case the dominant process for wiping out
regions of (+)--phase is nucleation of correlation volume regions of the
(0)-phase, as was explicitly assumed in the work of GKW. However, whenever we
will need to write $\Gamma_{+\rightarrow 0}$ explicitly to obtain analytic
expressions, we will approximate it with the rate of
thermal nucleation of bubbles of radius $R$,  $\Gamma_{+\rightarrow 0} \simeq
\Gamma_{+\rightarrow 0} (R)$. We expect this approximation to be good since
most bubbles of (+)--phase have radii $R$ not much larger than $\xi$ anyway.
The kinetic equation is, therefore,
\beq
\label{eq:KIN2}
{{\partial \n}\over {\partial t}}=\Gamma_{0\rightarrow +}(R) -
{{4\pi}\over 3}R^3\n \Gamma_{+\rightarrow 0}~~.
\eeq
We can rewrite it as,
\beq
\label{eq:Z}
{{\partial z(R,t)}\over {\partial t}}= - q(R)z(R,t),~~~~
z(R,t)\equiv p(R)-q(R)\n ~,
\eeq
where we defined
\beq
p(R)\equiv \Gamma_{0\rightarrow +}(R)~~~{\rm and}~~~
q(R)\equiv {{4\pi}\over 3}R^3\Gamma_{+\rightarrow 0}~~~.
\eeq
The solution to Eq.~(\ref{eq:Z}) is simply
$z(R,t)=z_0{\rm exp}[-q(R)t]$, or, using the initial condition
$n(R,0)=0$,
\beq
\label{eq:SOL2}
\n = {\bar n}(R)\left[1 - e^{-q(R)t}\right]~~;~~{\bar n}(R)={{p(R)}\over
{q(R)}}~~.
\eeq
For a given radius $R$, the relaxation time is then
\beq
\label{eq:TAU2}
\tau_3(R) = \left[q(R)\right]^{-1} =
\left[{{4\pi}\over 3}R^3\Gamma_{+\rightarrow 0}\right]^{-1}~~,
\eeq
that is, the time scale for the nucleation of a bubble of the (0)--phase inside
a bubble of radius $R$ of the (+)--phase. Note that $\tau_3$ depends
exponentially on $R^3$; bubbles of larger radii will approach the equilibrium
distribution at a much slower rate than smaller bubbles. The fastest bubbles to
equilibrate are those with $R \simeq \xi$.
With the approximation $\Gamma_{+\rightarrow 0} \simeq
\Gamma_{+\rightarrow 0} (R)$ and
using the expressions of Section 2 for the nucleation rates,
the equilibrium distribution is given by
\beq
\label{eq:N2}
{{4\pi}\over 3}R^3{\bar n}(R)={\rm exp}\left[-{{\left(\beta_+-\beta_0\right)
R^3}\over T}\right]~~.
\eeq
The consistency condition then states that the volume occupied by the
(+)--phase is small,
\beq
\label{eq:CONS2}
{{4\pi}\over 3}\xi^3{\bar n}(\xi)={\rm exp}\left[-{{\left(\beta_+-\beta_0
\right)\xi^3}\over T}\right] \ll 1~~.
\eeq

\vspace{24pt}
\thesection{\bf 5. APPLICATION TO THE ELECTROWEAK TRANSITION}
\setcounter{section}{5}
\setcounter{equation}{0}
\vspace{18pt}

For a given model with a first order transition which of the approaches
above better describes the dynamics of thermal fluctuations? We are
limited to study the transition at $T\la T_1$ when only small sub-critical
fluctuations exist. However, even for this limited temperature range we
should be able to examine the importance of incorporating the shrinking of
the bubbles and their coupling to thermal noise into the description of the
kinetics. In this Section we will do this in the context of the standard
electroweak model using the 1-loop approximation to the effective potential.
Even though recent work has shown that the 1-loop approximation is not adequate
due to large infrared corrections at $T_c$,\re{IR} we will take the 1-loop
potential as an example of how to apply our methods. Application to other
potentials is quite straightforward.


We will compare the different relaxation time scales obtained above,
$\tau_1$, $\tau_2$ and
$\tau_3$, and investigate which mechanism for the suppression of regions of
broken-symmetric phase will dominate as the strength of the transition
changes. Our strategy is as follows. First we compare $\tau_1$ with $\tau_2$,
that is, we compare the relaxation time scale incorporating only shrinking
(Section 4.1) with the relaxation time scale incorporating only thermal
noise (Section 4.2). We have already shown under our assumptions
that thermal noise dominates
over shrinking if the parameter $a$ satisfies the inequality
$a > \alpha_+v/T^2$, Eq. (4.20). Since $a$ is a free parameter in our model
we have two possibilities, depending on the value of $a$. If $a$ does not
satisfy the inequality, shrinking dominates and thermal noise is a sub-dominant
mechanism during the approach to equilibrium. Otherwise, shrinking is
the sub-dominant mechanism. Since we then will know
the values of $a$ for which shrinking or thermal noise dominates as a function
of the strength of the transition, we can
proceed by comparing these two processes
with the inverse
thermal nucleation rate time scale, given by $\tau_3$ (Section 4.3). As a
result, we will be able to establish which mechanism dominates the dynamics as
the transition's strength varies for different values of $a$.


We take the Higgs mass to be the parameter that controls  the strength of the
transition,  while we fix the top mass at $m_T=130$ GeV.
For the 1-loop approximation to the electroweak potential, we can write\re{AH}
\beq
\label{eq:VEW}
V_{\rm EW}(\f,T)=D\left(T^2-T_2^2\right)\f^2-ET\f^3+{{\l_T}\over 4}\f^4~~,
\eeq
where the constants $D$ and $E$ are given by $D=\left[6(m_W/\s)^2+
3(m_Z/\s)^2+6(m_T/\s)^2\right]/24$, and $E=\left[6(m_W/\s)^3
+3(m_Z/\s)^3\right]/12\pi\simeq
10^{-2}$. $T_2$ is the temperature at which the origin becomes unstable,
given by
\beq
T_2=\sqrt{\left(m_H^2-8B\s^2\right)/4D}~~,
\eeq
where the physical Higgs mass is given in terms of the 1-loop corrected
$\l$ as $m_H^2=\left(2\l+12B\right)\s^2$, with $B=\left(6m_W^4+3m_Z^4-12m_T^4
\right)/64\pi^2\s^4$. We use $m_W=80.6$ GeV, $m_Z=91.2$ GeV, and $\s=246$ GeV.
The temperature corrected Higgs self-coupling is
\beq
\l_T=\l- {1\over {16\pi^2}}\left[\sum_Bg_B\left({{m_B}\over {\s}}\right)^4
{\rm ln}\left(m_B^2/c_BT^2\right)-\sum_Fg_F\left({{m_F}\over {\s}}\right)^4
{\rm ln}\left(m_F^2/c_FT^2\right)\right],
\eeq
where the sum is performed over bosons and fermions (in our case only the
top quark) with their respective degrees of freedom $g_{B(F)}$.
Also, ${\rm ln}~c_B=5.41$ and ${\rm ln}~c_F=2.64$.

This potential is equivalent to the potential of Eq.~(\ref
{eq:POT}), with the replacements $m^2(T)=2D(T^2-T_2^2)$, $\gamma(T)=ET$, and
$\l(T)=\l_T$. The temperatures $T_1$ and $T_c$ are given by
\beq
\label{eq:T}
T_1=T_2/\sqrt{1-9E^2/8\l_TD},~~{\rm and}~~ T_c=T_2/\sqrt{1-E^2/\l_TD}~~.
\eeq

${\rm From}$ these values for $T_1$ and $T_c$, it is clear that the
quantity $x\equiv E^2/\l_TD$ can be used as a measure of the strength of
the transition. For $x=0$, the transition is second order. As shown in
Ref.~\ref{GK2}, $x\simeq 0.027$ at $m_H=60$ GeV, becoming smaller for larger
Higgs masses. The transition is already quite weak at the experimental lower
bound of $m_H=57$ GeV.\re{H} In Fig. 1 we show
the quantity $x$ as a function of
the Higgs mass for $m_H\ge 35$ GeV.

With the potential above, we can easily compute the nucleation rates using the
expressions of Section 2, as done by Gleiser and Kolb.\re{GK1} We have then all
that is needed to compute the relaxation time scales $\tau_1$, $\tau_2$, and
$\tau_3(\xi)$ [since $\tau_3$ depends on $R$, we consider only the fastest
bubbles to equilibrate, those of radius $\sim \xi$],
and the equilibrium distributions ${\bar n}(R)$.

Let us start by comparing the relaxation time scales for the shrinking term
and the thermal destruction term, following Eq. (4.20). In Fig. 2 we plot
$\alpha_+(T_1)/T^2_1$ (we took $v=1$)
as a function of the Higgs mass. Thermal noise
dominates over shrinking
if $a$ lies above the curve, for a given Higgs mass. Notice that
for small Higgs masses, {\it i.e.} strong transitions, shrinking should be
the dominant process unless the coupling to the bath is unrealistically
large (or non-perturbative). However, since there are uncertainties in the
precise expression for the thermal destruction rate, we will consider both
possibilities, with shrinking and thermal noise dominating the dynamics,
respectively.
If shrinking dominates, we can neglect thermal noise and compare $\tau_1$
and $\tau_3(\xi)$ directly. This is done in the continuous lines of
Fig. 3 where
we show the ratio of $\tau_1/\tau_3(\xi)$ as a function of the
Higgs mass. The results are shown for two different shrinking velocities,
$v=1$ and $v=0.4$.
For both velocities, with Higgs masses below $52$ GeV we find that
$\tau_1 \ll \tau_3(\xi)$, so that the approach to equilibrium
is dominated by the shrinking.
In Fig. 4 we show the two consistency conditions
Eqs.~(\ref{eq:CONS1}) and (\ref{eq:CONS2}) as a
function of the Higgs mass. We see that  the fraction of the total
volume occupied by the (+)--phase increases rapidly as the
Higgs mass increases. That is, as the transition grows weaker a larger
fraction of the volume is occupied by the broken-symmetric phase.
Even though our results indicate
that we cannot trust our approximations for $m_H\ga 53$
GeV, where $V_+/V\ga 10\%$, it is quite clear that the reason our
approximations break down is precisely the large
fraction of the volume occupied
by sub-critical bubbles. These results suggest that pre-transitional
phenomena will be present for weak enough transitions and that we should
expect modifications of the vacuum decay picture in this case. A
precise description of the transition is beyond the scope of the present
formalism.

We now consider the case in which thermal noise dominates over shrinking.
By inspecting Fig. 2, we can find an appropriate value of $a$ which is large
enough for the inequality Eq. (4.20)
to be always satisfied. We will take $a=0.5$ as an
illustration, even though this value is probably unrealistically large.
In Fig. 3 the dashed line shows the ratio $\tau_2/\tau_3(\xi)$
as a function of the Higgs mass. Note that again thermal noise becomes
sub-dominant as the Higgs mass is increased, although it does so at a
slower rate than the shrinking term. However, the qualitative conclusion is
the same in both cases. For large enough Higgs masses, the fraction of the
total volume in the broken-symmetric phase becomes substantial due to the
increasing weakness of the transition. This weakness is characterized by
the fact that both the shrinking of sub-critical bubbles as well as their
destruction due to thermal noise become less important in the description
of the transition. Since the breakdown of our approximations is due to the
failure of the semi-classical, or dilute gas approach, we are confident that
as the Higgs mass increases beyond the limit of validity of our approximations
a regime will be reached in which a departure from the usual false vacuum decay
mechanism is to be expected, although at this point we cannot afford
to make a quantitative prediction. A rough estimate may be obtained by
comparing, at the nucleation temperature,
the typical distance between sub-critical bubbles to the radius
of a critical bubble obtained by the usual calculations.
If the distance between sub-critical bubbles is of the order of
the critical radius, the usual nucleation mechanism must be revised.
Work on this topic is currently in progress.



\vspace{24pt}
\thesection{\bf 6. CONCLUDING REMARKS}
\vspace{18pt}

We have obtained a kinetic equation describing the approach to equilibrium in
first-order transitions for temperatures above the critical temperature. For
sufficiently strong transitions
and making approximations that we consider reasonable,
 we were able to analytically solve the kinetic
equation for three
different regimes, determined by the dominant mechanism responsible for
the suppression of regions of the broken-symmetric phase within the
symmetric phase. The three processes are the shrinking of the sub-critical
bubbles, their destruction due to the thermal bath to which they couple, and
by thermal nucleation of regions of the symmetric phase in their interior.
By obtaining the relaxation time-scales in all regimes, we were able to study
the relative importance of each process in the early stages of the
transition.


We applied our approach to the standard electroweak transition, showing that
for Higgs masses below 55 GeV or so, the approach to
equilibrium is dominated by
either shrinking or thermal destruction, depending on the strength of the
coupling of bubbles to the thermal bath. In this case, the total volume
occupied by the equilibrium distribution of sub-critical bubbles of the
broken-symmetric phase is negligible, and the transition proceeds by the
usual vacuum decay mechanism.
As the Higgs mass increases and the transition
becomes progressively weaker, we found that a larger fraction of the total
volume becomes occupied by the broken-symmetric phase, forcing the breakdown
of our analytical approximations. However, it is clear from our results that
a regime will eventually be reached in which a substantial fraction of the
volume is in the broken-symmetric phase as the critical temperature is
reached. In this case we should expect a departure from the usual vacuum
decay mechanism. We cannot be quantitative about the
value of the Higgs
mass (for a given top mass)
where this occurs due to the limitations of our analytical approach.
Given that the lower bound on the Higgs mass is now above 60 GeV, we expect
very interesting physics to be lurking behind our present knowledge of the
dynamics of weak first-order transitions.


\vspace{36pt}

\centerline{ \bf ACKNOWLEDGEMENTS}
\vspace{18pt}

We thank E. W. Kolb and D. Seckel for useful discussions. We would like to
thank the Institute for Theoretical Physics at Santa Barbara for its
hospitality during the Cosmological Phase Transitions program, where this
work was initiated.
(GG) was supported in part by the Department of Energy under the contract
No. DE-FG03-91ER 40662, Task C.
(MG) was supported in part by National Science Foundation grants
No.  at Dartmouth and No.  at
the Institute for Theoretical
Physics at Santa Barbara.




\vspace{1.0in}
\centerline{{\bf References}}
\frenchspacing
\begin{enumerate}


\item\label{NUC} For reviews see, J. D. Gunton, M. San Miguel, and P. S. Sahni,
in {\it Phase Transitions and Critical Phenomena}, edited by C. Domb and J. L.
Lebowitz (Academic, London, 1983), Vol. 8; J. S. Langer, Lectures presented
at l'\'Ecole de Physique de la Mati\`ere Condens\'ee, Beg Rohu, France,
August 1989, ITP preprint NSF-ITP-90-221i.

\item\label{LAN} See the review by J. Langer in Ref. 1.

\item\label{A} E.W. Kolb and M.S. Turner, {\it The Early Universe},
(Addison-Wesley, 1990); A.D. Linde, {\it Particle Physics and Inflationary
Cosmology}, (Harwood Academic Publishers, 1990).



\item\label{LQ} T. Stinton III and J. Lister, {\it Phys. Rev. Lett.}
{\bf 25}, 503 (1970). H. Zink and W.H. de Jeu, {\it Mol. Cryst. Liq. Cryst.}
{\bf 124}, 287 (1985). For other condensed matter systems exhibiting
pre-transitional phenomena see, for example, L.A. F\'ernandez, J.J.
Ruiz-Lorenzo, M. Lombardo, and A. Taranc\'on, {\it Phys. Lett. B} {\bf  277},
485 (1992); A. Gonzalez-Arroyo, M. Okawa, and Y. Shimizu, {\it Phys. Rev.
Lett.} {\bf 60}, 487 (1988).

\item\label{LQ2} J.J. Stankus, R. Torre, C.D. Marshall, S.R. Greenfield,
A. Sengupta, A. Tokmakoff, and M.D. Fayer, {\it Chem. Phys. Lett.} {\bf 194},
213 (1992).

\item\label{GR} M. Gleiser and R.O. Ramos, {\it Phys. Lett. B} {\bf 300},
271 (1993).

\item\label{GKW} M. Gleiser, E. W. Kolb, and R. Watkins, {\it Nucl. Phys.}
{\bf B364}, 411 (1991); M. Gleiser, {\it Phys. Rev.} {\bf D42}, 3350 (1990).

\item\label{CRITICS} G. Anderson, {\it Phys. Lett. B} {\bf 295}, 32 (1992);
See also,
M. Dine, R. Leigh, P. Huet, A. Linde, and D. Linde,
{\it Phys. Rev. D} {\bf 46}, 550 (1992).

\item\label{NTS} J. Frieman, G. Gelmini, M. Gleiser, and E. W. Kolb,
{\it Phys. Rev. Lett.} {\bf 60}, 2101 (1988).


\item\label{PULSONS} M. Gleiser, Dartmouth College report No. DART-HEP-93/05,
August 1993; V.G. Makhankov, {\it Phys. Rep. C} {\bf 35}, 1 (1978).


\item\label{GK1} M. Gleiser and E. W. Kolb, {\it Phys. Rev. Lett.}
{\bf 69}, 1304 (1992).

\item\label{MORIK} A. Hosoya and M. Sakagami, {\it Phys. Rev. D} {\bf 29},
2228 (1984); A. Hosoya, M. Sakagami,and M. Takao, {\it Ann. Phys.} (NY)
{\bf 154}, 229 (1984); M. Morikawa, {\it Phys. Rev. D} {\bf 33}, 3607 (1986).

\item\label{REVBAR} A.G. Cohen, D.B. Kaplan, and A.E. Nelson, UC San Diego
report No. UCSD-PTH-93-02, to appear in
{\it Ann. Rev. Nucl. Part. Sci.}, {\bf 43}.

\item\label{IR} G. Boyd, D. Brahm and S.D.H. Hsu, Harvard preprint No.
HUTP-92-A027 (1992), in press {\it Phys. Rev. D};
M. E. Carrington, {\it Phys. Rev. D} {\bf 45},
2933 (1992); M. Dine {\it et. al.} in Ref.~\ref{CRITICS};
P. Arnold, {\it Phys. Rev.} {\bf D46}, 2628 (1992); M. Gleiser
and E. W. Kolb, {\it Phys. Rev. D} {\bf 48}, 1560 (1993).

\item\label{AH} G.W. Anderson and L.J. Hall, {\it Phys. Rev.} {\bf D45},
2685 (1992).

\item\label{H} ALEPH, DELPHI, L3 and OPAL Collaborations, as presented by
M. Davier, Proceedings of the International Lepton-Photon Symposium and
Europhysics Conference on High Energy Physics, eds. S. Hegerty, K. Potter and
E. Quercigh,  November 1991, to appear.

\item\label{GK2} M. Gleiser and E. W. Kolb, in Ref.~\ref{IR}.



\end{enumerate}

\newpage

FIG.~1. The parameter $x=E^2/\l_TD$ as a function of the Higgs mass for
several values of the top mass.


\vspace{1.0in}

FIG.~2 The ration of relaxation time-scales for shrinking and thermal
destruction processes as a function of the Higgs mass. The region above
the curve defines the domain for thermal destruction domination.

\vspace{1.0in}

FIG.~3. The continuous lines denote the
ratio between the shrinking and reverse nucleation time-scales,
as a function
of the Higgs mass for shrinking velocities $v=1$ and $v=0.4$.
The dashed line denotes the ratio between thermal destruction and reverse
nucleation time-scales with parameter $a=0.5$.
\vspace{1.0in}

FIG.~4. The consistency conditions of Eqs.~\ref{eq:CONS1} and \ref{eq:CONS2}
as a function of the Higgs mass.

\end{document}



%% FOLLOWING LINE CANNOT BE BROKEN BEFORE 80 CHAR
%% FOLLOWING LINE CANNOT BE BROKEN BEFORE 80 CHAR
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%FIGS 2,3, and 4%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





%!PS-Adobe-2.0 EPSF-2.0
%%Creator: SM
%%BoundingBox: 18 144 592 718
%%DocumentFonts: Helvetica
%%EndComments
 20 dict begin
72 300 div dup scale
1 setlinejoin 0 setlinecap
/Helvetica findfont 55 scalefont setfont
/B { stroke newpath } def /F { moveto 0 setlinecap} def
/C { CS M 1 1 3 { pop 3 1 roll 255 div } for SET_COLOUR } def
/CS { currentpoint stroke } def
/CF { currentpoint fill } def
/L { lineto } def /M { moveto } def
/P { moveto 0 1 rlineto stroke } def
/T { currentlinecap exch 1 setlinecap show setlinecap } def
errordict /nocurrentpoint { pop 0 0 M currentpoint } put
/SET_COLOUR { pop pop pop } def
 80 600 translate
gsave
CS [] 0 setdash M
CS M 3 100 mul 72 div dup setlinewidth
/P [ /moveto cvx 0 5 -1 roll .05 add /rlineto cvx /stroke cvx ] cvx def
 0 0 0 C
CS M 3 100 mul 72 div dup setlinewidth
/P [ /moveto cvx 0 5 -1 roll .05 add /rlineto cvx /stroke cvx ] cvx def
346 2169 M 352 2155 L
358 2142 L
364 2128 L
370 2114 L
376 2100 L
382 2087 L
389 2073 L
395 2060 L
401 2046 L
407 2033 L
413 2019 L
419 2006 L
425 1993 L
431 1979 L
437 1966 L
443 1953 L
450 1940 L
456 1927 L
462 1914 L
468 1901 L
474 1888 L
480 1876 L
486 1863 L
492 1850 L
498 1838 L
504 1825 L
511 1813 L
517 1800 L
523 1788 L
529 1776 L
535 1764 L
541 1752 L
547 1739 L
553 1727 L
559 1715 L
565 1704 L
572 1692 L
578 1680 L
584 1668 L
590 1657 L
596 1645 L
602 1634 L
608 1622 L
614 1611 L
620 1600 L
626 1588 L
633 1577 L
639 1566 L
645 1555 L
651 1544 L
657 1533 L
663 1523 L
669 1512 L
675 1501 L
681 1490 L
687 1480 L
693 1469 L
700 1459 L
706 1449 L
712 1438 L
718 1428 L
724 1418 L
730 1408 L
736 1398 L
742 1388 L
748 1378 L
755 1368 L
761 1359 L
767 1349 L
773 1339 L
779 1330 L
785 1320 L
791 1311 L
797 1301 L
803 1292 L
809 1283 L
816 1274 L
822 1265 L
828 1256 L
834 1247 L
840 1238 L
846 1229 L
852 1220 L
858 1212 L
864 1203 L
870 1194 L
876 1186 L
883 1177 L
889 1169 L
895 1161 L
901 1152 L
907 1144 L
913 1136 L
919 1128 L
925 1120 L
931 1112 L
937 1104 L
944 1096 L
950 1089 L
956 1081 L
962 1073 L
968 1066 L
974 1058 L
980 1051 L
986 1043 L
992 1036 L
998 1028 L
1005 1021 L
1011 1014 L
1017 1007 L
1023 1000 L
1029 993 L
1035 986 L
1041 979 L
1047 972 L
1053 965 L
1059 959 L
1066 952 L
1072 945 L
1078 939 L
1084 932 L
1090 926 L
1096 919 L
1102 913 L
1108 907 L
1114 900 L
1120 894 L
1127 888 L
1133 882 L
1139 876 L
1145 870 L
1151 864 L
1157 858 L
1163 852 L
1169 846 L
1175 841 L
1181 835 L
1187 829 L
1194 824 L
1200 818 L
1206 813 L
1212 807 L
1218 802 L
1224 796 L
1230 791 L
1236 786 L
1242 780 L
1248 775 L
1255 770 L
1261 765 L
1267 760 L
1273 755 L
1279 750 L
1285 745 L
1291 740 L
1297 735 L
1303 730 L
1309 726 L
1316 721 L
1322 716 L
1328 712 L
1334 707 L
1340 702 L
1346 698 L
1352 693 L
1358 689 L
1364 685 L
1370 680 L
1377 676 L
1383 672 L
1389 667 L
1395 663 L
1401 659 L
1407 655 L
1413 651 L
1419 647 L
1425 643 L
1431 639 L
1438 635 L
1444 631 L
1450 627 L
1456 623 L
1462 619 L
1468 615 L
1474 612 L
1480 608 L
1486 604 L
1492 601 L
1499 597 L
1505 593 L
1511 590 L
1517 586 L
1523 583 L
1529 579 L
1535 576 L
1541 572 L
1547 569 L
1553 566 L
1559 562 L
1566 559 L
1572 556 L
1578 553 L
1584 549 L
1590 546 L
1596 543 L
1602 540 L
1608 537 L
1614 534 L
1620 531 L
1627 528 L
1633 525 L
1639 522 L
1645 519 L
1651 516 L
1657 513 L
1663 510 L
1669 508 L
1675 505 L
1682 502 L
1688 499 L
1694 497 L
1700 494 L
1706 491 L
1712 489 L
1718 486 L
1724 483 L
1730 481 L
1736 478 L
1742 476 L
1749 473 L
1755 471 L
1761 468 L
1767 466 L
1773 464 L
1779 461 L
1785 459 L
1791 456 L
1797 454 L
1803 452 L
1810 450 L
1816 447 L
1822 445 L
1828 443 L
1834 441 L
1840 438 L
1846 436 L
1852 434 L
1858 432 L
1864 430 L
1871 428 L
1877 426 L
1883 424 L
1889 422 L
1895 420 L
1901 418 L
1907 416 L
1913 414 L
1919 412 L
1925 410 L
1932 408 L
1938 406 L
1944 404 L
1950 402 L
1956 401 L
1962 399 L
1968 397 L
1974 395 L
1980 393 L
1986 392 L
1993 390 L
1999 388 L
2005 387 L
2011 385 L
2017 383 L
2023 382 L
2029 380 L
2035 378 L
2041 377 L
2047 375 L
2053 373 L
2060 372 L
2066 370 L
2072 369 L
2078 367 L
2084 366 L
2090 364 L
2096 363 L
2102 361 L
2108 360 L
2114 358 L
2121 357 L
2127 356 L
2133 354 L
2139 353 L
2145 351 L
2151 350 L
2157 349 L
2163 347 L
2169 346 L
CS [] 0 setdash M
255 255 M 2261 255 L
CS M
279 255 M 279 289 L
401 255 M 401 289 L
523 255 M 523 289 L
645 255 M 645 323 L
767 255 M 767 289 L
889 255 M 889 289 L
1011 255 M 1011 289 L
1133 255 M 1133 289 L
1255 255 M 1255 323 L
1377 255 M 1377 289 L
1499 255 M 1499 289 L
1621 255 M 1621 289 L
1742 255 M 1742 289 L
1864 255 M 1864 323 L
1986 255 M 1986 289 L
2108 255 M 2108 289 L
2230 255 M 2230 289 L
581 129 M 619 190 M 619 129 L
622 196 M 622 129 L
622 196 M 587 148 L
638 148 L
609 129 M 632 129 L
674 196 M 664 193 L
658 184 L
654 168 L
654 158 L
658 142 L
664 132 L
674 129 L
680 129 L
690 132 L
696 142 L
699 158 L
699 168 L
696 184 L
690 193 L
680 196 L
674 196 L
667 193 L
664 190 L
661 184 L
658 168 L
658 158 L
661 142 L
664 135 L
667 132 L
674 129 L
680 129 M 686 132 L
690 135 L
693 142 L
696 158 L
696 168 L
693 184 L
690 190 L
686 193 L
680 196 L
1190 129 M 1206 196 M 1200 164 L
1206 171 L
1216 174 L
1226 174 L
1235 171 L
1242 164 L
1245 155 L
1245 148 L
1242 139 L
1235 132 L
1226 129 L
1216 129 L
1206 132 L
1203 135 L
1200 142 L
1200 145 L
1203 148 L
1206 145 L
1203 142 L
1226 174 M 1232 171 L
1239 164 L
1242 155 L
1242 148 L
1239 139 L
1232 132 L
1226 129 L
1206 196 M 1239 196 L
1206 193 M 1223 193 L
1239 196 L
1283 196 M 1274 193 L
1267 184 L
1264 168 L
1264 158 L
1267 142 L
1274 132 L
1283 129 L
1290 129 L
1300 132 L
1306 142 L
1309 158 L
1309 168 L
1306 184 L
1300 193 L
1290 196 L
1283 196 L
1277 193 L
1274 190 L
1271 184 L
1267 168 L
1267 158 L
1271 142 L
1274 135 L
1277 132 L
1283 129 L
1290 129 M 1296 132 L
1300 135 L
1303 142 L
1306 158 L
1306 168 L
1303 184 L
1300 190 L
1296 193 L
1290 196 L
1800 129 M 1848 187 M 1845 184 L
1848 180 L
1852 184 L
1852 187 L
1848 193 L
1842 196 L
1832 196 L
1823 193 L
1816 187 L
1813 180 L
1810 168 L
1810 148 L
1813 139 L
1819 132 L
1829 129 L
1836 129 L
1845 132 L
1852 139 L
1855 148 L
1855 152 L
1852 161 L
1845 168 L
1836 171 L
1832 171 L
1823 168 L
1816 161 L
1813 152 L
1832 196 M 1826 193 L
1819 187 L
1816 180 L
1813 168 L
1813 148 L
1816 139 L
1823 132 L
1829 129 L
1836 129 M 1842 132 L
1848 139 L
1852 148 L
1852 152 L
1848 161 L
1842 168 L
1836 171 L
1893 196 M 1884 193 L
1877 184 L
1874 168 L
1874 158 L
1877 142 L
1884 132 L
1893 129 L
1900 129 L
1909 132 L
1916 142 L
1919 158 L
1919 168 L
1916 184 L
1909 193 L
1900 196 L
1893 196 L
1887 193 L
1884 190 L
1880 184 L
1877 168 L
1877 158 L
1880 142 L
1884 135 L
1887 132 L
1893 129 L
1900 129 M 1906 132 L
1909 135 L
1913 142 L
1916 158 L
1916 168 L
1913 184 L
1909 190 L
1906 193 L
1900 196 L
255 2261 M 2261 2261 L
279 2261 M 279 2226 L
401 2261 M 401 2226 L
523 2261 M 523 2226 L
645 2261 M 645 2192 L
767 2261 M 767 2226 L
889 2261 M 889 2226 L
1011 2261 M 1011 2226 L
1133 2261 M 1133 2226 L
1255 2261 M 1255 2192 L
1377 2261 M 1377 2226 L
1499 2261 M 1499 2226 L
1621 2261 M 1621 2226 L
1742 2261 M 1742 2226 L
1864 2261 M 1864 2192 L
1986 2261 M 1986 2226 L
2108 2261 M 2108 2226 L
2230 2261 M 2230 2226 L
255 255 M 255 2261 L
255 346 M 289 346 L
255 506 M 289 506 L
255 666 M 289 666 L
255 826 M 323 826 L
255 986 M 289 986 L
255 1146 M 289 1146 L
255 1306 M 289 1306 L
255 1466 M 323 1466 L
255 1626 M 289 1626 L
255 1786 M 289 1786 L
255 1946 M 289 1946 L
255 2106 M 323 2106 L
36 792 M 65 860 M 55 856 L
49 847 L
46 831 L
46 821 L
49 805 L
55 795 L
65 792 L
71 792 L
81 795 L
87 805 L
91 821 L
91 831 L
87 847 L
81 856 L
71 860 L
65 860 L
58 856 L
55 853 L
52 847 L
49 831 L
49 821 L
52 805 L
55 799 L
58 795 L
65 792 L
71 792 M 78 795 L
81 799 L
84 805 L
87 821 L
87 831 L
84 847 L
81 853 L
78 856 L
71 860 L
116 799 M 113 795 L
116 792 L
119 795 L
116 799 L
145 847 M 148 844 L
145 840 L
142 844 L
142 847 L
145 853 L
148 856 L
158 860 L
171 860 L
180 856 L
184 853 L
187 847 L
187 840 L
184 834 L
174 828 L
158 821 L
152 818 L
145 812 L
142 802 L
142 792 L
171 860 M 177 856 L
180 853 L
184 847 L
184 840 L
180 834 L
171 828 L
158 821 L
142 799 M 145 802 L
152 802 L
168 795 L
177 795 L
184 799 L
187 802 L
152 802 M 168 792 L
180 792 L
184 795 L
187 802 L
CS M
187 808 L
36 1432 M 65 1500 M 55 1496 L
49 1487 L
46 1471 L
46 1461 L
49 1445 L
55 1435 L
65 1432 L
71 1432 L
81 1435 L
87 1445 L
91 1461 L
91 1471 L
87 1487 L
81 1496 L
71 1500 L
65 1500 L
58 1496 L
55 1493 L
52 1487 L
49 1471 L
49 1461 L
52 1445 L
55 1439 L
58 1435 L
65 1432 L
71 1432 M 78 1435 L
81 1439 L
84 1445 L
87 1461 L
87 1471 L
84 1487 L
81 1493 L
78 1496 L
71 1500 L
116 1439 M 113 1435 L
116 1432 L
119 1435 L
116 1439 L
171 1493 M 171 1432 L
174 1500 M 174 1432 L
174 1500 M 139 1451 L
190 1451 L
161 1432 M 184 1432 L
36 2072 M 65 2139 M 55 2136 L
49 2127 L
46 2111 L
46 2101 L
49 2085 L
55 2075 L
65 2072 L
71 2072 L
81 2075 L
87 2085 L
91 2101 L
91 2111 L
87 2127 L
81 2136 L
71 2139 L
65 2139 L
58 2136 L
55 2133 L
52 2127 L
49 2111 L
49 2101 L
52 2085 L
55 2078 L
58 2075 L
65 2072 L
71 2072 M 78 2075 L
81 2078 L
84 2085 L
87 2101 L
87 2111 L
84 2127 L
81 2133 L
78 2136 L
71 2139 L
116 2078 M 113 2075 L
116 2072 L
119 2075 L
116 2078 L
180 2130 M 177 2127 L
180 2123 L
184 2127 L
184 2130 L
180 2136 L
174 2139 L
164 2139 L
155 2136 L
148 2130 L
145 2123 L
142 2111 L
142 2091 L
145 2082 L
152 2075 L
161 2072 L
168 2072 L
177 2075 L
184 2082 L
187 2091 L
187 2095 L
184 2104 L
177 2111 L
168 2114 L
164 2114 L
155 2111 L
148 2104 L
145 2095 L
164 2139 M 158 2136 L
152 2130 L
148 2123 L
145 2111 L
145 2091 L
148 2082 L
155 2075 L
161 2072 L
168 2072 M 174 2075 L
180 2082 L
184 2091 L
184 2095 L
180 2104 L
174 2111 L
168 2114 L
2261 255 M 2261 2261 L
2261 346 M 2226 346 L
2261 506 M 2226 506 L
2261 666 M 2226 666 L
2261 826 M 2192 826 L
2261 986 M 2226 986 L
2261 1146 M 2226 1146 L
2261 1306 M 2226 1306 L
2261 1466 M 2192 1466 L
2261 1626 M 2226 1626 L
2261 1786 M 2226 1786 L
2261 1946 M 2226 1946 L
2261 2106 M 2192 2106 L
CS [] 0 setdash M
CS [] 0 setdash M
1060 38 M 1076 105 M 1076 38 L
1079 105 M 1098 47 L
1076 105 M 1098 38 L
1121 105 M 1098 38 L
1121 105 M 1121 38 L
1124 105 M 1124 38 L
1066 105 M 1079 105 L
1121 105 M 1134 105 L
1066 38 M 1085 38 L
1111 38 M 1134 38 L
1150 47 M 1150 7 L
1151 47 M 1151 7 L
1175 47 M 1175 7 L
1176 47 M 1176 7 L
1144 47 M 1157 47 L
1169 47 M 1182 47 L
1151 28 M 1175 28 L
1144 7 M 1157 7 L
1169 7 M 1182 7 L
1250 118 M 1193 15 L
1311 95 M 1314 86 L
1314 105 L
1311 95 L
1305 102 L
1295 105 L
1289 105 L
1279 102 L
1273 95 L
1270 89 L
1266 79 L
1266 63 L
1270 54 L
1273 47 L
1279 41 L
1289 38 L
1295 38 L
1305 41 L
1311 47 L
1289 105 M 1282 102 L
1276 95 L
1273 89 L
1270 79 L
1270 63 L
1273 54 L
1276 47 L
1282 41 L
1289 38 L
1311 63 M 1311 38 L
1314 63 M 1314 38 L
1302 63 M 1324 63 L
1343 63 M 1382 63 L
1382 70 L
1379 76 L
1375 79 L
1369 83 L
1359 83 L
1350 79 L
1343 73 L
1340 63 L
1340 57 L
1343 47 L
1350 41 L
1359 38 L
1366 38 L
1375 41 L
1382 47 L
1379 63 M 1379 73 L
1375 79 L
1359 83 M 1353 79 L
1347 73 L
1343 63 L
1343 57 L
1347 47 L
1353 41 L
1359 38 L
1401 105 M 1424 38 L
1404 105 M 1424 47 L
1446 105 M 1424 38 L
1395 105 M 1414 105 L
1433 105 M 1452 105 L
CS [] 0 setdash M
767 1466 M CS [] 0 setdash M
799 1511 M 789 1508 L
783 1501 L
780 1495 L
776 1485 L
776 1476 L
780 1469 L
789 1466 L
796 1466 L
802 1469 L
812 1479 L
818 1488 L
824 1501 L
828 1511 L
799 1511 M 792 1508 L
786 1501 L
783 1495 L
780 1485 L
780 1476 L
783 1469 L
789 1466 L
799 1511 M 805 1511 L
812 1508 L
815 1501 L
821 1476 L
824 1469 L
828 1466 L
805 1511 M 808 1508 L
812 1501 L
818 1476 L
821 1469 L
828 1466 L
831 1466 L
866 1470 M 866 1435 L
848 1452 M 883 1452 L
926 1546 M 919 1540 L
913 1530 L
907 1517 L
903 1501 L
903 1488 L
907 1472 L
913 1459 L
919 1450 L
926 1443 L
919 1540 M 913 1527 L
910 1517 L
907 1501 L
907 1488 L
910 1472 L
913 1463 L
919 1450 L
964 1533 M 964 1466 L
968 1533 M 968 1466 L
945 1533 M 942 1514 L
942 1533 L
990 1533 L
990 1514 L
987 1533 L
955 1466 M 977 1466 L
1008 1468 M 1012 1470 L
1018 1476 L
1018 1435 L
1016 1474 M 1016 1435 L
1008 1435 M 1025 1435 L
1045 1546 M 1051 1540 L
1057 1530 L
1064 1517 L
1067 1501 L
1067 1488 L
1064 1472 L
1057 1459 L
1051 1450 L
1045 1443 L
1051 1540 M 1057 1527 L
1061 1517 L
1064 1501 L
1064 1488 L
1061 1472 L
1057 1463 L
1051 1450 L
1144 1546 M 1086 1443 L
1179 1533 M 1179 1466 L
1183 1533 M 1183 1466 L
1160 1533 M 1157 1514 L
CS M
1157 1533 L
1205 1533 L
1205 1514 L
1202 1533 L
1170 1466 M 1192 1466 L
1223 1468 M 1227 1470 L
1233 1476 L
1233 1435 L
1231 1474 M 1231 1435 L
1223 1435 M 1240 1435 L
1258 1550 M 1260 1548 L
1258 1546 L
1256 1548 L
1256 1550 L
1258 1554 L
1260 1556 L
1265 1558 L
1273 1558 L
1279 1556 L
1281 1554 L
1283 1550 L
1283 1546 L
1281 1542 L
1275 1538 L
1265 1535 L
1262 1533 L
1258 1529 L
1256 1523 L
1256 1517 L
1273 1558 M 1277 1556 L
1279 1554 L
1281 1550 L
1281 1546 L
1279 1542 L
1273 1538 L
1265 1535 L
1256 1521 M 1258 1523 L
1262 1523 L
1271 1519 L
1277 1519 L
1281 1521 L
1283 1523 L
1262 1523 M 1271 1517 L
1279 1517 L
1281 1519 L
1283 1523 L
1283 1527 L
CS [] 0 setdash M
CS [] 0 setdash M
783 2365 M 783 2298 L
786 2365 M 786 2298 L
805 2346 M 805 2320 L
773 2365 M 824 2365 L
824 2346 L
821 2365 L
786 2333 M 805 2333 L
773 2298 M 796 2298 L
847 2365 M 847 2298 L
850 2365 M 850 2298 L
837 2365 M 860 2365 L
837 2298 M 860 2298 L
921 2356 M 924 2346 L
924 2365 L
921 2356 L
914 2362 L
905 2365 L
898 2365 L
889 2362 L
882 2356 L
879 2349 L
876 2339 L
876 2323 L
879 2314 L
882 2307 L
889 2301 L
898 2298 L
905 2298 L
914 2301 L
921 2307 L
898 2365 M 892 2362 L
885 2356 L
882 2349 L
879 2339 L
879 2323 L
882 2314 L
885 2307 L
892 2301 L
898 2298 L
921 2323 M 921 2298 L
924 2323 M 924 2298 L
911 2323 M 934 2323 L
956 2365 M 956 2317 L
959 2307 L
966 2301 L
975 2298 L
982 2298 L
991 2301 L
998 2307 L
1001 2317 L
1001 2365 L
959 2365 M 959 2317 L
962 2307 L
969 2301 L
975 2298 L
946 2365 M 969 2365 L
991 2365 M 1011 2365 L
1033 2365 M 1033 2298 L
1036 2365 M 1036 2298 L
1023 2365 M 1062 2365 L
1072 2362 L
1075 2359 L
1078 2352 L
1078 2346 L
1075 2339 L
1072 2336 L
1062 2333 L
1036 2333 L
1062 2365 M 1068 2362 L
1072 2359 L
1075 2352 L
1075 2346 L
1072 2339 L
1068 2336 L
1062 2333 L
1023 2298 M 1046 2298 L
1052 2333 M 1059 2330 L
1062 2327 L
1072 2304 L
1075 2301 L
1078 2301 L
1081 2304 L
1059 2330 M 1062 2323 L
1068 2301 L
1072 2298 L
1078 2298 L
1081 2304 L
1081 2307 L
1104 2365 M 1104 2298 L
1107 2365 M 1107 2298 L
1126 2346 M 1126 2320 L
1094 2365 M 1145 2365 L
1145 2346 L
1142 2365 L
1107 2333 M 1126 2333 L
1094 2298 M 1145 2298 L
1145 2317 L
1142 2298 L
1219 2352 M 1222 2349 L
1219 2346 L
1216 2349 L
1216 2352 L
1219 2359 L
1222 2362 L
1232 2365 L
1245 2365 L
1255 2362 L
1258 2359 L
1261 2352 L
1261 2346 L
1258 2339 L
1248 2333 L
1232 2327 L
1226 2323 L
1219 2317 L
1216 2307 L
1216 2298 L
1245 2365 M 1251 2362 L
1255 2359 L
1258 2352 L
1258 2346 L
1255 2339 L
1245 2333 L
1232 2327 L
1216 2304 M 1219 2307 L
1226 2307 L
1242 2301 L
1251 2301 L
1258 2304 L
1261 2307 L
1226 2307 M 1242 2298 L
1255 2298 L
1258 2301 L
1261 2307 L
1261 2314 L
CS [] 0 setdash M
stroke
grestore
showpage
end
%!PS-Adobe-2.0 EPSF-2.0
%%Creator: SM
%%BoundingBox: 18 144 592 718
%%DocumentFonts: Helvetica
%%EndComments
 20 dict begin
72 300 div dup scale
1 setlinejoin 0 setlinecap
/Helvetica findfont 55 scalefont setfont
/B { stroke newpath } def /F { moveto 0 setlinecap} def
/C { CS M 1 1 3 { pop 3 1 roll 255 div } for SET_COLOUR } def
/CS { currentpoint stroke } def
/CF { currentpoint fill } def
/L { lineto } def /M { moveto } def
/P { moveto 0 1 rlineto stroke } def
/T { currentlinecap exch 1 setlinecap show setlinecap } def
errordict /nocurrentpoint { pop 0 0 M currentpoint } put
/SET_COLOUR { pop pop pop } def
 80 600 translate
gsave
CS [] 0 setdash M
CS M 3 100 mul 72 div dup setlinewidth
/P [ /moveto cvx 0 5 -1 roll .05 add /rlineto cvx /stroke cvx ] cvx def
 0 0 0 C
CS M 3 100 mul 72 div dup setlinewidth
/P [ /moveto cvx 0 5 -1 roll .05 add /rlineto cvx /stroke cvx ] cvx def
255 403 M 265 403 L
275 403 L
285 403 L
295 403 L
305 403 L
315 403 L
325 403 L
335 403 L
345 403 L
355 403 L
365 403 L
375 403 L
385 403 L
395 403 L
405 403 L
415 403 L
425 403 L
435 403 L
445 403 L
455 404 L
465 404 L
475 404 L
485 404 L
495 404 L
505 404 L
515 404 L
526 404 L
536 404 L
546 404 L
556 404 L
566 404 L
576 404 L
586 404 L
596 404 L
606 404 L
616 404 L
626 404 L
636 404 L
646 404 L
656 404 L
666 404 L
676 405 L
686 405 L
696 405 L
706 405 L
716 405 L
726 405 L
736 405 L
746 405 L
756 405 L
766 406 L
776 406 L
786 406 L
796 406 L
806 406 L
816 407 L
826 407 L
836 407 L
846 407 L
857 408 L
867 408 L
877 408 L
887 409 L
897 409 L
907 409 L
917 410 L
927 410 L
937 411 L
947 411 L
957 412 L
967 412 L
977 413 L
987 414 L
997 414 L
1007 415 L
1017 416 L
1027 417 L
1037 418 L
1047 419 L
1057 420 L
1067 421 L
1077 422 L
1087 423 L
1097 424 L
1107 426 L
1117 427 L
1127 429 L
1137 430 L
1147 432 L
1157 434 L
1167 436 L
1177 438 L
1187 440 L
1197 443 L
1207 445 L
1217 448 L
1228 450 L
1238 453 L
1248 456 L
1258 459 L
1268 463 L
1278 466 L
1288 470 L
1298 474 L
1308 478 L
1318 483 L
1328 488 L
1338 493 L
1348 498 L
1358 503 L
1368 509 L
1378 515 L
1388 522 L
1398 529 L
1408 536 L
1418 543 L
1428 551 L
1438 560 L
1448 569 L
1458 578 L
1468 588 L
1478 598 L
1488 609 L
1498 620 L
1508 632 L
1518 645 L
1528 658 L
1538 672 L
1548 686 L
1559 701 L
1569 717 L
1579 734 L
1589 752 L
1599 770 L
1609 790 L
1619 810 L
1629 831 L
1639 853 L
1649 877 L
1659 901 L
1669 927 L
1679 954 L
1689 982 L
1699 1012 L
1709 1042 L
1719 1075 L
1729 1108 L
1739 1144 L
1749 1180 L
1759 1219 L
1769 1259 L
1779 1302 L
1789 1346 L
1799 1392 L
1809 1440 L
1819 1490 L
1829 1543 L
1839 1597 L
1849 1655 L
1859 1714 L
1869 1776 L
1879 1841 L
1889 1909 L
1900 1980 L
1910 2053 L
1919 2130 L
1930 2210 L
1936 2261 L
255 403 M 265 403 L
275 403 L
285 403 L
295 403 L
305 403 L
315 403 L
325 403 L
335 403 L
345 404 L
355 404 L
365 404 L
375 404 L
385 404 L
395 404 L
405 404 L
415 404 L
425 404 L
435 404 L
445 404 L
455 404 L
465 404 L
475 404 L
485 404 L
495 404 L
505 404 L
515 404 L
526 404 L
536 404 L
546 404 L
556 405 L
566 405 L
576 405 L
586 405 L
596 405 L
606 405 L
616 405 L
626 405 L
636 406 L
646 406 L
656 406 L
666 406 L
676 406 L
686 407 L
696 407 L
706 407 L
716 407 L
726 408 L
736 408 L
746 408 L
756 409 L
766 409 L
776 410 L
786 410 L
796 411 L
806 411 L
816 412 L
826 412 L
836 413 L
846 413 L
857 414 L
867 415 L
877 416 L
887 417 L
897 418 L
907 419 L
917 420 L
927 421 L
937 422 L
947 423 L
957 425 L
967 426 L
977 428 L
987 429 L
997 431 L
1007 433 L
1017 435 L
1027 437 L
1037 439 L
1047 442 L
1057 444 L
1067 447 L
1077 450 L
1087 453 L
1097 456 L
1107 460 L
1117 463 L
1127 467 L
1137 471 L
1147 475 L
1157 480 L
1167 485 L
1177 490 L
1187 496 L
1197 501 L
1207 507 L
1217 514 L
1228 521 L
1238 528 L
1248 536 L
1258 544 L
1268 552 L
1278 561 L
1288 571 L
1298 581 L
1308 591 L
1318 602 L
1328 614 L
1338 627 L
1348 640 L
1358 654 L
1368 668 L
1378 683 L
1388 700 L
1398 717 L
1408 735 L
1418 754 L
1428 774 L
1438 795 L
1448 817 L
1458 840 L
1468 864 L
1478 890 L
1488 917 L
1498 945 L
1508 975 L
1518 1006 L
1528 1039 L
1538 1074 L
1548 1110 L
1559 1148 L
1569 1188 L
1579 1230 L
CS M
1589 1274 L
1599 1320 L
1609 1369 L
1619 1420 L
1629 1473 L
1639 1529 L
1649 1587 L
1659 1648 L
1669 1713 L
1679 1780 L
1689 1850 L
1699 1924 L
1709 2001 L
1719 2081 L
1729 2166 L
1739 2254 L
1740 2261 L
455 2038 M 857 2038 L
907 2038 M CS [] 0 setdash M
942 2079 M 932 2038 L
942 2079 M 936 2038 L
913 2073 M 919 2079 L
929 2083 L
964 2083 L
913 2073 M 919 2076 L
929 2079 L
964 2079 L
982 2040 M 986 2041 L
992 2047 L
992 2007 L
990 2045 M 990 2007 L
982 2007 M 1000 2007 L
1073 2118 M 1016 2015 L
1115 2079 M 1106 2038 L
1115 2079 M 1109 2038 L
1086 2073 M 1093 2079 L
1102 2083 L
1138 2083 L
1086 2073 M 1093 2076 L
1102 2079 L
1138 2079 L
1152 2040 M 1154 2038 L
1152 2036 L
1150 2038 L
1150 2040 L
1152 2043 L
1154 2045 L
1159 2047 L
1167 2047 L
1173 2045 L
1175 2041 L
1175 2036 L
1173 2032 L
1167 2030 L
1161 2030 L
1167 2047 M 1171 2045 L
1173 2041 L
1173 2036 L
1171 2032 L
1167 2030 L
1171 2028 L
1175 2024 L
1177 2020 L
1177 2015 L
1175 2011 L
1173 2009 L
1167 2007 L
1159 2007 L
1154 2009 L
1152 2011 L
1150 2015 L
1150 2016 L
1152 2018 L
1154 2016 L
1152 2015 L
1173 2026 M 1175 2020 L
1175 2015 L
1173 2011 L
1171 2009 L
1167 2007 L
1218 2118 M 1211 2111 L
1205 2102 L
1199 2089 L
1195 2073 L
1195 2060 L
1199 2044 L
1205 2031 L
1211 2022 L
1218 2015 L
1211 2111 M 1205 2099 L
1202 2089 L
1199 2073 L
1199 2060 L
1202 2044 L
1205 2034 L
1211 2022 L
1263 2105 M 1256 2102 L
1253 2099 L
1253 2095 L
1256 2092 L
1266 2089 L
1276 2089 L
1266 2089 M 1253 2086 L
1247 2083 L
1244 2076 L
1244 2070 L
1250 2063 L
1260 2060 L
1269 2060 L
1266 2089 M 1256 2086 L
1250 2083 L
1247 2076 L
1247 2070 L
1253 2063 L
1260 2060 L
1247 2057 L
1240 2054 L
1237 2047 L
1237 2041 L
1244 2034 L
1260 2028 L
1263 2025 L
1263 2018 L
1256 2015 L
1250 2015 L
1260 2060 M 1250 2057 L
1244 2054 L
1240 2047 L
1240 2041 L
1247 2034 L
1260 2028 L
1292 2118 M 1298 2111 L
1305 2102 L
1311 2089 L
1314 2073 L
1314 2060 L
1311 2044 L
1305 2031 L
1298 2022 L
1292 2015 L
1298 2111 M 1305 2099 L
1308 2089 L
1311 2073 L
1311 2060 L
1308 2044 L
1305 2034 L
1298 2022 L
CS [] 0 setdash M
CS [80 24] 0 setdash M
255 403 M 265 403 L
275 403 L
285 403 L
295 403 L
305 403 L
315 403 L
325 403 L
335 403 L
345 403 L
355 403 L
365 403 L
375 403 L
385 403 L
395 403 L
405 403 L
415 403 L
425 403 L
435 403 L
445 403 L
455 403 L
465 403 L
475 403 L
485 403 L
495 403 L
505 403 L
515 403 L
526 403 L
536 403 L
546 403 L
556 403 L
566 403 L
576 403 L
586 403 L
596 404 L
606 404 L
616 404 L
626 404 L
636 404 L
646 404 L
656 404 L
666 404 L
676 404 L
686 404 L
696 404 L
706 404 L
716 404 L
726 404 L
736 404 L
746 404 L
756 404 L
766 404 L
776 404 L
786 404 L
796 404 L
806 404 L
816 404 L
826 404 L
836 405 L
846 405 L
857 405 L
867 405 L
877 405 L
887 405 L
897 405 L
907 405 L
917 405 L
927 405 L
937 406 L
947 406 L
957 406 L
967 406 L
977 406 L
987 406 L
997 407 L
1007 407 L
1017 407 L
1027 407 L
1037 408 L
1047 408 L
1057 408 L
1067 408 L
1077 409 L
1087 409 L
1097 409 L
1107 410 L
1117 410 L
1127 411 L
1137 411 L
1147 412 L
1157 412 L
1167 413 L
1177 413 L
1187 414 L
1197 414 L
1207 415 L
1217 416 L
1228 416 L
1238 417 L
1248 418 L
1258 419 L
1268 420 L
1278 421 L
1288 422 L
1298 423 L
1308 424 L
1318 425 L
1328 426 L
1338 427 L
1348 429 L
1358 430 L
1368 432 L
1378 433 L
1388 435 L
1398 437 L
1408 439 L
1418 440 L
1428 442 L
1438 444 L
1448 447 L
1458 449 L
1468 451 L
1478 454 L
1488 457 L
1498 459 L
1508 462 L
1518 465 L
1528 469 L
1538 472 L
1548 475 L
1559 479 L
1569 483 L
1579 487 L
1589 491 L
1599 495 L
1609 500 L
1619 505 L
1629 510 L
1639 515 L
1649 520 L
1659 526 L
1669 532 L
1679 538 L
1689 545 L
1699 552 L
1709 559 L
1719 566 L
1729 574 L
1739 582 L
1749 590 L
1759 599 L
1769 608 L
1779 617 L
1789 627 L
1799 637 L
CS M
1809 648 L
1819 659 L
1829 671 L
1839 683 L
1849 695 L
1859 708 L
1869 722 L
1879 736 L
1889 751 L
1900 766 L
1910 782 L
1919 798 L
1930 815 L
1940 833 L
1950 851 L
1960 871 L
1970 890 L
1980 911 L
1990 933 L
2000 955 L
2010 978 L
2020 1002 L
2030 1027 L
2040 1052 L
2050 1079 L
2060 1107 L
2070 1135 L
2080 1165 L
2090 1196 L
2100 1228 L
2110 1261 L
2120 1295 L
2130 1330 L
2140 1367 L
2150 1405 L
2160 1444 L
2170 1485 L
2180 1527 L
2190 1570 L
2200 1615 L
2210 1662 L
2220 1710 L
2230 1760 L
2240 1811 L
2250 1864 L
2261 1919 L
455 1889 M 857 1889 L
907 1889 M CS [] 0 setdash M
942 1931 M 932 1889 L
942 1931 M 936 1889 L
913 1924 M 919 1931 L
929 1934 L
964 1934 L
913 1924 M 919 1928 L
929 1931 L
964 1931 L
978 1891 M 980 1889 L
978 1887 L
977 1889 L
977 1891 L
978 1895 L
980 1897 L
986 1899 L
994 1899 L
1000 1897 L
1002 1895 L
1003 1891 L
1003 1887 L
1002 1883 L
996 1879 L
986 1876 L
982 1874 L
978 1870 L
977 1864 L
977 1858 L
994 1899 M 998 1897 L
1000 1895 L
1002 1891 L
1002 1887 L
1000 1883 L
994 1879 L
986 1876 L
977 1862 M 978 1864 L
982 1864 L
992 1860 L
998 1860 L
1002 1862 L
1003 1864 L
982 1864 M 992 1858 L
1000 1858 L
1002 1860 L
1003 1864 L
1003 1868 L
1073 1969 M 1016 1867 L
1115 1931 M 1106 1889 L
1115 1931 M 1109 1889 L
1086 1924 M 1093 1931 L
1102 1934 L
1138 1934 L
1086 1924 M 1093 1928 L
1102 1931 L
1138 1931 L
1152 1891 M 1154 1889 L
1152 1887 L
1150 1889 L
1150 1891 L
1152 1895 L
1154 1897 L
1159 1899 L
1167 1899 L
1173 1897 L
1175 1893 L
1175 1887 L
1173 1883 L
1167 1881 L
1161 1881 L
1167 1899 M 1171 1897 L
1173 1893 L
1173 1887 L
1171 1883 L
1167 1881 L
1171 1879 L
1175 1876 L
1177 1872 L
1177 1866 L
1175 1862 L
1173 1860 L
1167 1858 L
1159 1858 L
1154 1860 L
1152 1862 L
1150 1866 L
1150 1868 L
1152 1870 L
1154 1868 L
1152 1866 L
1173 1877 M 1175 1872 L
1175 1866 L
1173 1862 L
1171 1860 L
1167 1858 L
1218 1969 M 1211 1963 L
1205 1953 L
1199 1940 L
1195 1924 L
1195 1912 L
1199 1895 L
1205 1883 L
1211 1873 L
1218 1867 L
1211 1963 M 1205 1950 L
1202 1940 L
1199 1924 L
1199 1912 L
1202 1895 L
1205 1886 L
1211 1873 L
1263 1956 M 1256 1953 L
1253 1950 L
1253 1947 L
1256 1944 L
1266 1940 L
1276 1940 L
1266 1940 M 1253 1937 L
1247 1934 L
1244 1928 L
1244 1921 L
1250 1915 L
1260 1912 L
1269 1912 L
1266 1940 M 1256 1937 L
1250 1934 L
1247 1928 L
1247 1921 L
1253 1915 L
1260 1912 L
1247 1908 L
1240 1905 L
1237 1899 L
1237 1892 L
1244 1886 L
1260 1879 L
1263 1876 L
1263 1870 L
1256 1867 L
1250 1867 L
1260 1912 M 1250 1908 L
1244 1905 L
1240 1899 L
1240 1892 L
1247 1886 L
1260 1879 L
1292 1969 M 1298 1963 L
1305 1953 L
1311 1940 L
1314 1924 L
1314 1912 L
1311 1895 L
1305 1883 L
1298 1873 L
1292 1867 L
1298 1963 M 1305 1950 L
1308 1940 L
1311 1924 L
1311 1912 L
1308 1895 L
1305 1886 L
1298 1873 L
CS [80 24] 0 setdash M
CS [] 0 setdash M
1060 38 M 1076 105 M 1076 38 L
1079 105 M 1098 47 L
1076 105 M 1098 38 L
1121 105 M 1098 38 L
1121 105 M 1121 38 L
1124 105 M 1124 38 L
1066 105 M 1079 105 L
1121 105 M 1134 105 L
1066 38 M 1085 38 L
1111 38 M 1134 38 L
1150 47 M 1150 7 L
1151 47 M 1151 7 L
1175 47 M 1175 7 L
1176 47 M 1176 7 L
1144 47 M 1157 47 L
1169 47 M 1182 47 L
1151 28 M 1175 28 L
1144 7 M 1157 7 L
1169 7 M 1182 7 L
1250 118 M 1193 15 L
1311 95 M 1314 86 L
1314 105 L
1311 95 L
1305 102 L
1295 105 L
1289 105 L
1279 102 L
1273 95 L
1270 89 L
1266 79 L
1266 63 L
1270 54 L
1273 47 L
1279 41 L
1289 38 L
1295 38 L
1305 41 L
1311 47 L
1289 105 M 1282 102 L
1276 95 L
1273 89 L
1270 79 L
1270 63 L
1273 54 L
1276 47 L
1282 41 L
1289 38 L
1311 63 M 1311 38 L
1314 63 M 1314 38 L
1302 63 M 1324 63 L
1343 63 M 1382 63 L
1382 70 L
1379 76 L
1375 79 L
1369 83 L
1359 83 L
1350 79 L
1343 73 L
1340 63 L
1340 57 L
1343 47 L
1350 41 L
1359 38 L
1366 38 L
1375 41 L
1382 47 L
1379 63 M 1379 73 L
1375 79 L
1359 83 M 1353 79 L
1347 73 L
1343 63 L
1343 57 L
1347 47 L
1353 41 L
1359 38 L
1401 105 M 1424 38 L
1404 105 M 1424 47 L
1446 105 M 1424 38 L
1395 105 M 1414 105 L
1433 105 M 1452 105 L
CS [80 24] 0 setdash M
1759 1072 M CS [] 0 setdash M
1769 1117 M 1788 1072 L
1772 1117 M 1788 1078 L
1807 1117 M 1788 1072 L
1762 1117 M 1782 1117 L
1794 1117 M 1814 1117 L
1830 1110 M 1887 1110 L
1830 1091 M 1887 1091 L
1920 1126 M 1926 1130 L
1936 1139 L
1936 1072 L
1932 1136 M 1932 1072 L
1920 1072 M 1948 1072 L
CS [80 24] 0 setdash M
1207 1146 M CS [] 0 setdash M
1217 1191 M 1236 1146 L
CS M
1220 1191 M 1236 1153 L
1256 1191 M 1236 1146 L
1211 1191 M 1230 1191 L
1243 1191 M 1262 1191 L
1278 1185 M 1336 1185 L
1278 1165 M 1336 1165 L
1378 1214 M 1368 1210 L
1362 1201 L
1358 1185 L
1358 1175 L
1362 1159 L
1368 1149 L
1378 1146 L
1384 1146 L
1394 1149 L
1400 1159 L
1403 1175 L
1403 1185 L
1400 1201 L
1394 1210 L
1384 1214 L
1378 1214 L
1371 1210 L
1368 1207 L
1365 1201 L
1362 1185 L
1362 1175 L
1365 1159 L
1368 1153 L
1371 1149 L
1378 1146 L
1384 1146 M 1390 1149 L
1394 1153 L
1397 1159 L
1400 1175 L
1400 1185 L
1397 1201 L
1394 1207 L
1390 1210 L
1384 1214 L
1429 1153 M 1426 1149 L
1429 1146 L
1432 1149 L
1429 1153 L
1483 1207 M 1483 1146 L
1487 1214 M 1487 1146 L
1487 1214 M 1451 1165 L
1503 1165 L
1474 1146 M 1496 1146 L
CS [80 24] 0 setdash M
CS [] 0 setdash M
873 2365 M 873 2298 L
876 2365 M 876 2298 L
895 2346 M 895 2320 L
863 2365 M 914 2365 L
914 2346 L
911 2365 L
876 2333 M 895 2333 L
863 2298 M 885 2298 L
937 2365 M 937 2298 L
940 2365 M 940 2298 L
927 2365 M 950 2365 L
927 2298 M 950 2298 L
1011 2355 M 1014 2346 L
1014 2365 L
1011 2355 L
1004 2362 L
995 2365 L
988 2365 L
978 2362 L
972 2355 L
969 2349 L
966 2339 L
966 2323 L
969 2314 L
972 2307 L
978 2301 L
988 2298 L
995 2298 L
1004 2301 L
1011 2307 L
988 2365 M 982 2362 L
975 2355 L
972 2349 L
969 2339 L
969 2323 L
972 2314 L
975 2307 L
982 2301 L
988 2298 L
1011 2323 M 1011 2298 L
1014 2323 M 1014 2298 L
1001 2323 M 1023 2323 L
1046 2365 M 1046 2317 L
1049 2307 L
1055 2301 L
1065 2298 L
1072 2298 L
1081 2301 L
1088 2307 L
1091 2317 L
1091 2365 L
1049 2365 M 1049 2317 L
1052 2307 L
1059 2301 L
1065 2298 L
1036 2365 M 1059 2365 L
1081 2365 M 1100 2365 L
1123 2365 M 1123 2298 L
1126 2365 M 1126 2298 L
1113 2365 M 1152 2365 L
1161 2362 L
1165 2359 L
1168 2352 L
1168 2346 L
1165 2339 L
1161 2336 L
1152 2333 L
1126 2333 L
1152 2365 M 1158 2362 L
1161 2359 L
1165 2352 L
1165 2346 L
1161 2339 L
1158 2336 L
1152 2333 L
1113 2298 M 1136 2298 L
1142 2333 M 1149 2330 L
1152 2327 L
1161 2304 L
1165 2301 L
1168 2301 L
1171 2304 L
1149 2330 M 1152 2323 L
1158 2301 L
1161 2298 L
1168 2298 L
1171 2304 L
1171 2307 L
1193 2365 M 1193 2298 L
1197 2365 M 1197 2298 L
1216 2346 M 1216 2320 L
1184 2365 M 1235 2365 L
1235 2346 L
1232 2365 L
1197 2333 M 1216 2333 L
1184 2298 M 1235 2298 L
1235 2317 L
1232 2298 L
1309 2352 M 1312 2349 L
1309 2346 L
1306 2349 L
1306 2352 L
1309 2359 L
1312 2362 L
1322 2365 L
1335 2365 L
1344 2362 L
1348 2355 L
1348 2346 L
1344 2339 L
1335 2336 L
1325 2336 L
1335 2365 M 1341 2362 L
1344 2355 L
1344 2346 L
1341 2339 L
1335 2336 L
1341 2333 L
1348 2327 L
1351 2320 L
1351 2311 L
1348 2304 L
1344 2301 L
1335 2298 L
1322 2298 L
1312 2301 L
1309 2304 L
1306 2311 L
1306 2314 L
1309 2317 L
1312 2314 L
1309 2311 L
1344 2330 M 1348 2320 L
1348 2311 L
1344 2304 L
1341 2301 L
1335 2298 L
CS [80 24] 0 setdash M
1759 478 M CS [] 0 setdash M
1775 516 M 1775 513 L
1772 513 L
1772 516 L
1775 519 L
1782 523 L
1794 523 L
1801 519 L
1804 516 L
1807 510 L
1807 487 L
1810 481 L
1814 478 L
1804 516 M 1804 487 L
1807 481 L
1814 478 L
1817 478 L
1804 510 M 1801 506 L
1782 503 L
1772 500 L
1769 494 L
1769 487 L
1772 481 L
1782 478 L
1791 478 L
1798 481 L
1804 487 L
1782 503 M 1775 500 L
1772 494 L
1772 487 L
1775 481 L
1782 478 L
1836 516 M 1894 516 L
1836 497 M 1894 497 L
1936 545 M 1926 542 L
1920 532 L
1916 516 L
1916 506 L
1920 490 L
1926 481 L
1936 478 L
1942 478 L
1952 481 L
1958 490 L
1961 506 L
1961 516 L
1958 532 L
1952 542 L
1942 545 L
1936 545 L
1929 542 L
1926 539 L
1923 532 L
1920 516 L
1920 506 L
1923 490 L
1926 484 L
1929 481 L
1936 478 L
1942 478 M 1948 481 L
1952 484 L
1955 490 L
1958 506 L
1958 516 L
1955 532 L
1952 539 L
1948 542 L
1942 545 L
1987 484 M 1984 481 L
1987 478 L
1990 481 L
1987 484 L
2019 545 M 2013 513 L
2019 519 L
2029 523 L
2038 523 L
2048 519 L
2054 513 L
2058 503 L
2058 497 L
2054 487 L
2048 481 L
2038 478 L
2029 478 L
2019 481 L
2016 484 L
2013 490 L
2013 494 L
2016 497 L
2019 494 L
2016 490 L
2038 523 M 2045 519 L
2051 513 L
2054 503 L
2054 497 L
2051 487 L
2045 481 L
2038 478 L
2019 545 M 2051 545 L
2019 542 M 2035 542 L
2051 545 L
CS [80 24] 0 setdash M
CS [] 0 setdash M
255 255 M 2261 255 L
255 255 M 255 289 L
355 255 M 355 289 L
455 255 M 455 289 L
556 255 M 556 323 L
656 255 M 656 289 L
756 255 M 756 289 L
857 255 M 857 289 L
957 255 M 957 289 L
1057 255 M 1057 323 L
1157 255 M 1157 289 L
1258 255 M 1258 289 L
1358 255 M 1358 289 L
1458 255 M 1458 289 L
CS M
1559 255 M 1559 323 L
1659 255 M 1659 289 L
1759 255 M 1759 289 L
1859 255 M 1859 289 L
1960 255 M 1960 289 L
2060 255 M 2060 323 L
2160 255 M 2160 289 L
2261 255 M 2261 289 L
491 129 M 530 190 M 530 129 L
533 196 M 533 129 L
533 196 M 498 148 L
549 148 L
520 129 M 543 129 L
572 196 M 565 164 L
572 171 L
581 174 L
591 174 L
601 171 L
607 164 L
610 155 L
610 148 L
607 139 L
601 132 L
591 129 L
581 129 L
572 132 L
568 135 L
565 142 L
565 145 L
568 148 L
572 145 L
568 142 L
591 174 M 597 171 L
604 164 L
607 155 L
607 148 L
604 139 L
597 132 L
591 129 L
572 196 M 604 196 L
572 193 M 588 193 L
604 196 L
993 129 M 1009 196 M 1003 164 L
1009 171 L
1019 174 L
1028 174 L
1038 171 L
1044 164 L
1047 155 L
1047 148 L
1044 139 L
1038 132 L
1028 129 L
1019 129 L
1009 132 L
1006 135 L
1003 142 L
1003 145 L
1006 148 L
1009 145 L
1006 142 L
1028 174 M 1035 171 L
1041 164 L
1044 155 L
1044 148 L
1041 139 L
1035 132 L
1028 129 L
1009 196 M 1041 196 L
1009 193 M 1025 193 L
1041 196 L
1086 196 M 1076 193 L
1070 184 L
1067 168 L
1067 158 L
1070 142 L
1076 132 L
1086 129 L
1092 129 L
1102 132 L
1108 142 L
1112 158 L
1112 168 L
1108 184 L
1102 193 L
1092 196 L
1086 196 L
1080 193 L
1076 190 L
1073 184 L
1070 168 L
1070 158 L
1073 142 L
1076 135 L
1080 132 L
1086 129 L
1092 129 M 1099 132 L
1102 135 L
1105 142 L
1108 158 L
1108 168 L
1105 184 L
1102 190 L
1099 193 L
1092 196 L
1494 129 M 1510 196 M 1504 164 L
1510 171 L
1520 174 L
1530 174 L
1539 171 L
1546 164 L
1549 155 L
1549 148 L
1546 139 L
1539 132 L
1530 129 L
1520 129 L
1510 132 L
1507 135 L
1504 142 L
1504 145 L
1507 148 L
1510 145 L
1507 142 L
1530 174 M 1536 171 L
1542 164 L
1546 155 L
1546 148 L
1542 139 L
1536 132 L
1530 129 L
1510 196 M 1542 196 L
1510 193 M 1526 193 L
1542 196 L
1575 196 M 1568 164 L
1575 171 L
1584 174 L
1594 174 L
1603 171 L
1610 164 L
1613 155 L
1613 148 L
1610 139 L
1603 132 L
1594 129 L
1584 129 L
1575 132 L
1571 135 L
1568 142 L
1568 145 L
1571 148 L
1575 145 L
1571 142 L
1594 174 M 1600 171 L
1607 164 L
1610 155 L
1610 148 L
1607 139 L
1600 132 L
1594 129 L
1575 196 M 1607 196 L
1575 193 M 1591 193 L
1607 196 L
1996 129 M 2044 187 M 2041 184 L
2044 180 L
2047 184 L
2047 187 L
2044 193 L
2037 196 L
2028 196 L
2018 193 L
2012 187 L
2009 180 L
2005 168 L
2005 148 L
2009 139 L
2015 132 L
2025 129 L
2031 129 L
2041 132 L
2047 139 L
2050 148 L
2050 152 L
2047 161 L
2041 168 L
2031 171 L
2028 171 L
2018 168 L
2012 161 L
2009 152 L
2028 196 M 2021 193 L
2015 187 L
2012 180 L
2009 168 L
2009 148 L
2012 139 L
2018 132 L
2025 129 L
2031 129 M 2037 132 L
2044 139 L
2047 148 L
2047 152 L
2044 161 L
2037 168 L
2031 171 L
2089 196 M 2079 193 L
2073 184 L
2070 168 L
2070 158 L
2073 142 L
2079 132 L
2089 129 L
2095 129 L
2105 132 L
2111 142 L
2114 158 L
2114 168 L
2111 184 L
2105 193 L
2095 196 L
2089 196 L
2082 193 L
2079 190 L
2076 184 L
2073 168 L
2073 158 L
2076 142 L
2079 135 L
2082 132 L
2089 129 L
2095 129 M 2102 132 L
2105 135 L
2108 142 L
2111 158 L
2111 168 L
2108 184 L
2105 190 L
2102 193 L
2095 196 L
255 2261 M 2261 2261 L
255 2261 M 255 2226 L
355 2261 M 355 2226 L
455 2261 M 455 2226 L
556 2261 M 556 2192 L
656 2261 M 656 2226 L
756 2261 M 756 2226 L
857 2261 M 857 2226 L
957 2261 M 957 2226 L
1057 2261 M 1057 2192 L
1157 2261 M 1157 2226 L
1258 2261 M 1258 2226 L
1358 2261 M 1358 2226 L
1458 2261 M 1458 2226 L
1559 2261 M 1559 2192 L
1659 2261 M 1659 2226 L
1759 2261 M 1759 2226 L
1859 2261 M 1859 2226 L
1960 2261 M 1960 2226 L
2060 2261 M 2060 2192 L
2160 2261 M 2160 2226 L
2261 2261 M 2261 2226 L
255 255 M 255 2261 L
255 255 M 289 255 L
255 329 M 289 329 L
255 403 M 323 403 L
255 478 M 289 478 L
255 552 M 289 552 L
255 626 M 289 626 L
255 700 M 289 700 L
255 775 M 323 775 L
255 849 M 289 849 L
255 923 M 289 923 L
255 998 M 289 998 L
255 1072 M 289 1072 L
255 1146 M 323 1146 L
255 1221 M 289 1221 L
255 1295 M 289 1295 L
255 1369 M 289 1369 L
255 1443 M 289 1443 L
255 1518 M 323 1518 L
255 1592 M 289 1592 L
255 1666 M 289 1666 L
255 1741 M 289 1741 L
255 1815 M 289 1815 L
255 1889 M 323 1889 L
255 1963 M 289 1963 L
255 2038 M 289 2038 L
255 2112 M 289 2112 L
255 2186 M 289 2186 L
255 2261 M 323 2261 L
132 370 M 161 437 M 152 434 L
145 424 L
142 408 L
142 399 L
145 382 L
152 373 L
161 370 L
168 370 L
177 373 L
184 382 L
CS M
187 399 L
187 408 L
184 424 L
177 434 L
168 437 L
161 437 L
155 434 L
152 431 L
148 424 L
145 408 L
145 399 L
148 382 L
152 376 L
155 373 L
161 370 L
168 370 M 174 373 L
177 376 L
180 382 L
184 399 L
184 408 L
180 424 L
177 431 L
174 434 L
168 437 L
36 741 M 65 808 M 55 805 L
49 796 L
46 780 L
46 770 L
49 754 L
55 744 L
65 741 L
71 741 L
81 744 L
87 754 L
91 770 L
91 780 L
87 796 L
81 805 L
71 808 L
65 808 L
58 805 L
55 802 L
52 796 L
49 780 L
49 770 L
52 754 L
55 747 L
58 744 L
65 741 L
71 741 M 78 744 L
81 747 L
84 754 L
87 770 L
87 780 L
84 796 L
81 802 L
78 805 L
71 808 L
116 747 M 113 744 L
116 741 L
119 744 L
116 747 L
148 808 M 142 776 L
148 783 L
158 786 L
168 786 L
177 783 L
184 776 L
187 767 L
187 760 L
184 751 L
177 744 L
168 741 L
158 741 L
148 744 L
145 747 L
142 754 L
142 757 L
145 760 L
148 757 L
145 754 L
168 786 M 174 783 L
180 776 L
184 767 L
184 760 L
180 751 L
174 744 L
168 741 L
148 808 M 180 808 L
148 805 M 164 805 L
180 808 L
132 1113 M 152 1167 M 158 1170 L
168 1180 L
168 1113 L
164 1177 M 164 1113 L
152 1113 M 180 1113 L
36 1484 M 55 1538 M 62 1542 L
71 1551 L
71 1484 L
68 1548 M 68 1484 L
55 1484 M 84 1484 L
116 1490 M 113 1487 L
116 1484 L
119 1487 L
116 1490 L
148 1551 M 142 1519 L
148 1526 L
158 1529 L
168 1529 L
177 1526 L
184 1519 L
187 1510 L
187 1503 L
184 1494 L
177 1487 L
168 1484 L
158 1484 L
148 1487 L
145 1490 L
142 1497 L
142 1500 L
145 1503 L
148 1500 L
145 1497 L
168 1529 M 174 1526 L
180 1519 L
184 1510 L
184 1503 L
180 1494 L
174 1487 L
168 1484 L
148 1551 M 180 1551 L
148 1548 M 164 1548 L
180 1551 L
132 1855 M 145 1910 M 148 1907 L
145 1904 L
142 1907 L
142 1910 L
145 1916 L
148 1920 L
158 1923 L
171 1923 L
180 1920 L
184 1916 L
187 1910 L
187 1904 L
184 1897 L
174 1891 L
158 1884 L
152 1881 L
145 1875 L
142 1865 L
142 1855 L
171 1923 M 177 1920 L
180 1916 L
184 1910 L
184 1904 L
180 1897 L
171 1891 L
158 1884 L
142 1862 M 145 1865 L
152 1865 L
168 1859 L
177 1859 L
184 1862 L
187 1865 L
152 1865 M 168 1855 L
180 1855 L
184 1859 L
187 1865 L
187 1871 L
36 2227 M 49 2281 M 52 2278 L
49 2275 L
46 2278 L
46 2281 L
49 2288 L
52 2291 L
62 2294 L
74 2294 L
84 2291 L
87 2288 L
91 2281 L
91 2275 L
87 2268 L
78 2262 L
62 2256 L
55 2252 L
49 2246 L
46 2236 L
46 2227 L
74 2294 M 81 2291 L
84 2288 L
87 2281 L
87 2275 L
84 2268 L
74 2262 L
62 2256 L
46 2233 M 49 2236 L
55 2236 L
71 2230 L
81 2230 L
87 2233 L
91 2236 L
55 2236 M 71 2227 L
84 2227 L
87 2230 L
91 2236 L
91 2243 L
116 2233 M 113 2230 L
116 2227 L
119 2230 L
116 2233 L
148 2294 M 142 2262 L
148 2268 L
158 2272 L
168 2272 L
177 2268 L
184 2262 L
187 2252 L
187 2246 L
184 2236 L
177 2230 L
168 2227 L
158 2227 L
148 2230 L
145 2233 L
142 2240 L
142 2243 L
145 2246 L
148 2243 L
145 2240 L
168 2272 M 174 2268 L
180 2262 L
184 2252 L
184 2246 L
180 2236 L
174 2230 L
168 2227 L
148 2294 M 180 2294 L
148 2291 M 164 2291 L
180 2294 L
2261 255 M 2261 2261 L
2261 255 M 2226 255 L
2261 329 M 2226 329 L
2261 403 M 2192 403 L
2261 478 M 2226 478 L
2261 552 M 2226 552 L
2261 626 M 2226 626 L
2261 700 M 2226 700 L
2261 775 M 2192 775 L
2261 849 M 2226 849 L
2261 923 M 2226 923 L
2261 998 M 2226 998 L
2261 1072 M 2226 1072 L
2261 1146 M 2192 1146 L
2261 1221 M 2226 1221 L
2261 1295 M 2226 1295 L
2261 1369 M 2226 1369 L
2261 1443 M 2226 1443 L
2261 1518 M 2192 1518 L
2261 1592 M 2226 1592 L
2261 1666 M 2226 1666 L
2261 1741 M 2226 1741 L
2261 1815 M 2226 1815 L
2261 1889 M 2192 1889 L
2261 1963 M 2226 1963 L
2261 2038 M 2226 2038 L
2261 2112 M 2226 2112 L
2261 2186 M 2226 2186 L
2261 2261 M 2192 2261 L
CS [80 24] 0 setdash M
stroke
grestore
showpage
end
%!PS-Adobe-2.0 EPSF-2.0
%%Creator: SM
%%BoundingBox: 18 144 592 718
%%DocumentFonts: Helvetica
%%EndComments
 20 dict begin
72 300 div dup scale
1 setlinejoin 0 setlinecap
/Helvetica findfont 55 scalefont setfont
/B { stroke newpath } def /F { moveto 0 setlinecap} def
/C { CS M 1 1 3 { pop 3 1 roll 255 div } for SET_COLOUR } def
/CS { currentpoint stroke } def
/CF { currentpoint fill } def
/L { lineto } def /M { moveto } def
/P { moveto 0 1 rlineto stroke } def
/T { currentlinecap exch 1 setlinecap show setlinecap } def
errordict /nocurrentpoint { pop 0 0 M currentpoint } put
/SET_COLOUR { pop pop pop } def
 80 600 translate
gsave
CS [80 24] 0 setdash M
CS M 3 100 mul 72 div dup setlinewidth
/P [ /moveto cvx 0 5 -1 roll .05 add /rlineto cvx /stroke cvx ] cvx def
 0 0 0 C
CS M 3 100 mul 72 div dup setlinewidth
/P [ /moveto cvx 0 5 -1 roll .05 add /rlineto cvx /stroke cvx ] cvx def
262 403 M 270 404 L
277 406 L
284 407 L
292 408 L
299 409 L
307 410 L
314 412 L
322 413 L
329 414 L
336 415 L
344 417 L
351 418 L
359 419 L
366 421 L
374 422 L
381 424 L
388 425 L
396 427 L
403 428 L
411 430 L
418 431 L
426 433 L
433 435 L
440 436 L
448 438 L
455 440 L
463 442 L
470 443 L
478 445 L
485 447 L
492 449 L
500 451 L
507 453 L
515 455 L
522 457 L
530 459 L
537 461 L
544 463 L
552 465 L
559 467 L
567 470 L
574 472 L
582 474 L
589 476 L
596 479 L
604 481 L
611 484 L
619 486 L
626 488 L
634 491 L
641 494 L
648 496 L
656 499 L
663 502 L
671 504 L
678 507 L
686 510 L
693 513 L
700 516 L
708 519 L
715 522 L
723 525 L
730 528 L
738 531 L
745 534 L
753 537 L
760 540 L
767 543 L
775 547 L
782 550 L
790 554 L
797 557 L
805 560 L
812 564 L
819 568 L
827 571 L
834 575 L
842 579 L
849 582 L
856 586 L
864 590 L
871 594 L
879 598 L
886 602 L
894 606 L
901 610 L
908 614 L
916 619 L
923 623 L
931 627 L
938 631 L
946 636 L
953 640 L
960 645 L
968 649 L
975 654 L
983 659 L
990 663 L
998 668 L
1005 673 L
1012 678 L
1020 683 L
1027 688 L
1035 693 L
1042 698 L
1050 703 L
1057 708 L
1064 714 L
1072 719 L
1079 724 L
1087 730 L
1094 735 L
1102 741 L
1109 746 L
1116 752 L
1124 758 L
1131 763 L
1139 769 L
1146 775 L
1154 781 L
1161 787 L
1168 793 L
1176 799 L
1183 805 L
1191 811 L
1198 818 L
1206 824 L
1213 830 L
1220 837 L
1228 843 L
1235 850 L
1243 856 L
1250 863 L
1258 870 L
1265 876 L
1272 883 L
1280 890 L
1287 897 L
1295 904 L
1302 911 L
1310 918 L
1317 925 L
1324 933 L
1332 940 L
1339 947 L
1347 955 L
1354 962 L
1362 970 L
1369 977 L
1376 985 L
1384 993 L
1391 1000 L
1399 1008 L
1406 1016 L
1414 1024 L
1421 1032 L
1428 1040 L
1436 1048 L
1443 1056 L
1451 1064 L
1458 1072 L
1466 1081 L
1473 1089 L
1480 1098 L
1488 1106 L
1495 1114 L
1503 1123 L
1510 1132 L
1518 1140 L
1525 1149 L
1532 1158 L
1540 1167 L
1547 1176 L
1555 1185 L
1562 1194 L
1570 1203 L
1577 1212 L
1584 1221 L
1592 1230 L
1599 1240 L
1607 1249 L
1614 1258 L
1622 1268 L
1629 1277 L
1636 1287 L
1644 1296 L
1651 1306 L
1659 1316 L
1666 1325 L
1674 1335 L
1681 1345 L
1689 1355 L
1696 1365 L
1703 1375 L
1711 1385 L
1718 1395 L
1726 1405 L
1733 1416 L
1741 1426 L
1748 1436 L
1755 1446 L
1763 1457 L
1770 1467 L
1778 1478 L
1785 1488 L
1793 1499 L
1800 1510 L
1807 1520 L
1815 1531 L
1822 1542 L
1830 1552 L
1837 1563 L
1845 1574 L
1852 1585 L
1859 1596 L
1867 1607 L
1874 1618 L
1882 1629 L
1889 1640 L
1897 1652 L
1904 1663 L
1911 1674 L
1919 1686 L
1926 1697 L
1934 1708 L
1941 1720 L
1949 1731 L
1956 1743 L
1963 1754 L
1971 1766 L
1978 1778 L
1986 1789 L
1993 1801 L
2001 1813 L
2008 1825 L
2015 1836 L
2023 1848 L
2030 1860 L
2038 1872 L
2045 1884 L
2053 1896 L
2060 1908 L
2067 1920 L
2075 1932 L
2082 1945 L
2090 1957 L
2097 1969 L
2105 1981 L
2112 1993 L
2119 2006 L
2127 2018 L
2134 2030 L
2142 2043 L
2149 2055 L
2157 2068 L
2164 2080 L
2171 2093 L
2179 2105 L
2186 2118 L
2194 2130 L
2201 2143 L
2209 2156 L
2216 2168 L
2223 2181 L
2231 2194 L
2238 2206 L
2246 2219 L
2253 2232 L
2261 2245 L
262 350 M 270 350 L
277 350 L
284 350 L
292 350 L
299 350 L
307 350 L
314 350 L
322 350 L
329 350 L
336 350 L
344 350 L
351 350 L
359 350 L
366 350 L
374 350 L
381 350 L
388 350 L
396 350 L
403 350 L
411 350 L
418 350 L
426 350 L
433 350 L
440 350 L
448 350 L
455 350 L
463 350 L
470 350 L
478 350 L
485 350 L
492 350 L
CS M
500 350 L
507 350 L
515 350 L
522 350 L
530 350 L
537 350 L
544 350 L
552 350 L
559 350 L
567 350 L
574 350 L
582 350 L
589 350 L
596 350 L
604 350 L
611 350 L
619 350 L
626 350 L
634 350 L
641 350 L
648 350 L
656 350 L
663 350 L
671 350 L
678 350 L
686 350 L
693 350 L
700 350 L
708 350 L
715 350 L
723 350 L
730 350 L
738 350 L
745 350 L
753 350 L
760 350 L
767 350 L
775 350 L
782 350 L
790 350 L
797 351 L
805 351 L
812 351 L
819 351 L
827 351 L
834 351 L
842 351 L
849 351 L
856 351 L
864 351 L
871 351 L
879 351 L
886 351 L
894 351 L
901 351 L
908 351 L
916 351 L
923 351 L
931 352 L
938 352 L
946 352 L
953 352 L
960 352 L
968 352 L
975 352 L
983 353 L
990 353 L
998 353 L
1005 353 L
1012 354 L
1020 354 L
1027 354 L
1035 354 L
1042 355 L
1050 355 L
1057 356 L
1064 356 L
1072 357 L
1079 357 L
1087 358 L
1094 358 L
1102 359 L
1109 360 L
1116 360 L
1124 361 L
1131 362 L
1139 363 L
1146 364 L
1154 365 L
1161 366 L
1168 368 L
1176 369 L
1183 370 L
1191 372 L
1198 374 L
1206 375 L
1213 377 L
1220 379 L
1228 382 L
1235 384 L
1243 387 L
1250 389 L
1258 392 L
1265 396 L
1272 399 L
1280 403 L
1287 406 L
1295 411 L
1302 415 L
1310 420 L
1317 425 L
1324 430 L
1332 436 L
1339 442 L
1347 449 L
1354 456 L
1362 463 L
1369 471 L
1376 480 L
1384 489 L
1391 499 L
1399 509 L
1406 520 L
1414 532 L
1421 545 L
1428 558 L
1436 573 L
1443 588 L
1451 604 L
1458 621 L
1466 639 L
1473 659 L
1480 680 L
1488 702 L
1495 725 L
1503 750 L
1510 776 L
1518 804 L
1525 834 L
1532 865 L
1540 899 L
1547 934 L
1555 972 L
1562 1011 L
1570 1054 L
1577 1098 L
1584 1146 L
1592 1196 L
1599 1249 L
1607 1306 L
1614 1365 L
1622 1428 L
1629 1495 L
1636 1565 L
1644 1640 L
1651 1719 L
1659 1802 L
1666 1890 L
1674 1983 L
1681 2081 L
1689 2185 L
1694 2261 L
403 1974 M CS [] 0 setdash M
451 2025 M 454 2016 L
454 2033 L
451 2025 L
445 2030 L
437 2033 L
431 2033 L
423 2030 L
417 2025 L
415 2019 L
412 2010 L
412 1996 L
415 1988 L
417 1982 L
423 1977 L
431 1974 L
437 1974 L
445 1977 L
451 1982 L
454 1988 L
431 2033 M 426 2030 L
420 2025 L
417 2019 L
415 2010 L
415 1996 L
417 1988 L
420 1982 L
426 1977 L
431 1974 L
488 2013 M 479 2010 L
474 2005 L
471 1996 L
471 1991 L
474 1982 L
479 1977 L
488 1974 L
493 1974 L
502 1977 L
507 1982 L
510 1991 L
510 1996 L
507 2005 L
502 2010 L
493 2013 L
488 2013 L
482 2010 L
476 2005 L
474 1996 L
474 1991 L
476 1982 L
482 1977 L
488 1974 L
493 1974 M 499 1977 L
504 1982 L
507 1991 L
507 1996 L
504 2005 L
499 2010 L
493 2013 L
532 2013 M 532 1974 L
535 2013 M 535 1974 L
535 2005 M 541 2010 L
549 2013 L
555 2013 L
563 2010 L
566 2005 L
566 1974 L
555 2013 M 561 2010 L
563 2005 L
563 1974 L
524 2013 M 535 2013 L
524 1974 M 544 1974 L
555 1974 M 575 1974 L
617 2008 M 620 2013 L
620 2002 L
617 2008 L
614 2010 L
608 2013 L
597 2013 L
591 2010 L
589 2008 L
589 2002 L
591 1999 L
597 1996 L
611 1991 L
617 1988 L
620 1985 L
589 2005 M 591 2002 L
597 1999 L
611 1994 L
617 1991 L
620 1988 L
620 1980 L
617 1977 L
611 1974 L
600 1974 L
594 1977 L
591 1980 L
589 1985 L
589 1974 L
591 1980 L
642 2033 M 639 2030 L
642 2027 L
645 2030 L
642 2033 L
642 2013 M 642 1974 L
645 2013 M 645 1974 L
634 2013 M 645 2013 L
634 1974 M 653 1974 L
695 2008 M 698 2013 L
698 2002 L
695 2008 L
692 2010 L
687 2013 L
676 2013 L
670 2010 L
667 2008 L
667 2002 L
670 1999 L
676 1996 L
690 1991 L
695 1988 L
698 1985 L
667 2005 M 670 2002 L
676 1999 L
690 1994 L
695 1991 L
698 1988 L
698 1980 L
695 1977 L
690 1974 L
678 1974 L
673 1977 L
670 1980 L
667 1985 L
667 1974 L
670 1980 L
720 2033 M 720 1985 L
723 1977 L
CS M
729 1974 L
735 1974 L
740 1977 L
743 1982 L
723 2033 M 723 1985 L
726 1977 L
729 1974 L
712 2013 M 735 2013 L
760 1996 M 793 1996 L
793 2002 L
791 2008 L
788 2010 L
782 2013 L
774 2013 L
765 2010 L
760 2005 L
757 1996 L
757 1991 L
760 1982 L
765 1977 L
774 1974 L
779 1974 L
788 1977 L
793 1982 L
791 1996 M 791 2005 L
788 2010 L
774 2013 M 768 2010 L
763 2005 L
760 1996 L
760 1991 L
763 1982 L
768 1977 L
774 1974 L
816 2013 M 816 1974 L
819 2013 M 819 1974 L
819 2005 M 824 2010 L
833 2013 L
838 2013 L
847 2010 L
850 2005 L
850 1974 L
838 2013 M 844 2010 L
847 2005 L
847 1974 L
807 2013 M 819 2013 L
807 1974 M 827 1974 L
838 1974 M 858 1974 L
906 2005 M 903 2002 L
906 1999 L
909 2002 L
909 2005 L
903 2010 L
897 2013 L
889 2013 L
881 2010 L
875 2005 L
872 1996 L
872 1991 L
875 1982 L
881 1977 L
889 1974 L
895 1974 L
903 1977 L
909 1982 L
889 2013 M 883 2010 L
878 2005 L
875 1996 L
875 1991 L
878 1982 L
883 1977 L
889 1974 L
928 2013 M 945 1974 L
931 2013 M 945 1980 L
962 2013 M 945 1974 L
939 1963 L
934 1957 L
928 1954 L
925 1954 L
923 1957 L
925 1960 L
928 1957 L
923 2013 M 939 2013 L
951 2013 M 968 2013 L
1063 2025 M 1066 2016 L
1066 2033 L
1063 2025 L
1057 2030 L
1049 2033 L
1043 2033 L
1035 2030 L
1029 2025 L
1026 2019 L
1024 2010 L
1024 1996 L
1026 1988 L
1029 1982 L
1035 1977 L
1043 1974 L
1049 1974 L
1057 1977 L
1063 1982 L
1066 1988 L
1043 2033 M 1038 2030 L
1032 2025 L
1029 2019 L
1026 2010 L
1026 1996 L
1029 1988 L
1032 1982 L
1038 1977 L
1043 1974 L
1099 2013 M 1091 2010 L
1085 2005 L
1083 1996 L
1083 1991 L
1085 1982 L
1091 1977 L
1099 1974 L
1105 1974 L
1113 1977 L
1119 1982 L
1122 1991 L
1122 1996 L
1119 2005 L
1113 2010 L
1105 2013 L
1099 2013 L
1094 2010 L
1088 2005 L
1085 1996 L
1085 1991 L
1088 1982 L
1094 1977 L
1099 1974 L
1105 1974 M 1111 1977 L
1116 1982 L
1119 1991 L
1119 1996 L
1116 2005 L
1111 2010 L
1105 2013 L
1144 2013 M 1144 1974 L
1147 2013 M 1147 1974 L
1147 2005 M 1153 2010 L
1161 2013 L
1167 2013 L
1175 2010 L
1178 2005 L
1178 1974 L
1167 2013 M 1172 2010 L
1175 2005 L
1175 1974 L
1136 2013 M 1147 2013 L
1136 1974 M 1156 1974 L
1167 1974 M 1186 1974 L
1234 2033 M 1234 1974 L
1237 2033 M 1237 1974 L
1234 2005 M 1229 2010 L
1223 2013 L
1217 2013 L
1209 2010 L
1203 2005 L
1200 1996 L
1200 1991 L
1203 1982 L
1209 1977 L
1217 1974 L
1223 1974 L
1229 1977 L
1234 1982 L
1217 2013 M 1212 2010 L
1206 2005 L
1203 1996 L
1203 1991 L
1206 1982 L
1212 1977 L
1217 1974 L
1226 2033 M 1237 2033 L
1234 1974 M 1245 1974 L
1265 2033 M 1262 2030 L
1265 2027 L
1268 2030 L
1265 2033 L
1265 2013 M 1265 1974 L
1268 2013 M 1268 1974 L
1257 2013 M 1268 2013 L
1257 1974 M 1276 1974 L
1296 2033 M 1296 1985 L
1299 1977 L
1304 1974 L
1310 1974 L
1316 1977 L
1318 1982 L
1299 2033 M 1299 1985 L
1301 1977 L
1304 1974 L
1287 2013 M 1310 2013 L
1338 2033 M 1335 2030 L
1338 2027 L
1341 2030 L
1338 2033 L
1338 2013 M 1338 1974 L
1341 2013 M 1341 1974 L
1330 2013 M 1341 2013 L
1330 1974 M 1349 1974 L
1380 2013 M 1372 2010 L
1366 2005 L
1363 1996 L
1363 1991 L
1366 1982 L
1372 1977 L
1380 1974 L
1386 1974 L
1394 1977 L
1400 1982 L
1403 1991 L
1403 1996 L
1400 2005 L
1394 2010 L
1386 2013 L
1380 2013 L
1374 2010 L
1369 2005 L
1366 1996 L
1366 1991 L
1369 1982 L
1374 1977 L
1380 1974 L
1386 1974 M 1391 1977 L
1397 1982 L
1400 1991 L
1400 1996 L
1397 2005 L
1391 2010 L
1386 2013 L
1425 2013 M 1425 1974 L
1428 2013 M 1428 1974 L
1428 2005 M 1433 2010 L
1442 2013 L
1447 2013 L
1456 2010 L
1459 2005 L
1459 1974 L
1447 2013 M 1453 2010 L
1456 2005 L
1456 1974 L
1417 2013 M 1428 2013 L
1417 1974 M 1436 1974 L
1447 1974 M 1467 1974 L
1509 2008 M 1512 2013 L
1512 2002 L
1509 2008 L
1506 2010 L
1501 2013 L
1490 2013 L
1484 2010 L
1481 2008 L
1481 2002 L
1484 1999 L
1490 1996 L
1504 1991 L
1509 1988 L
1512 1985 L
1481 2005 M 1484 2002 L
1490 1999 L
1504 1994 L
1509 1991 L
1512 1988 L
1512 1980 L
1509 1977 L
1504 1974 L
1492 1974 L
1487 1977 L
1484 1980 L
1481 1985 L
1481 1974 L
1484 1980 L
CS [80 24] 0 setdash M
626 923 M CS [] 0 setdash M
640 982 M 640 923 L
643 982 M 677 929 L
643 977 M 677 923 L
677 982 M 677 923 L
632 982 M 643 982 L
668 982 M 685 982 L
632 923 M 649 923 L
716 963 M 708 960 L
702 954 L
699 946 L
699 940 L
702 932 L
708 926 L
716 923 L
722 923 L
730 926 L
736 932 L
738 940 L
738 946 L
736 954 L
730 960 L
722 963 L
716 963 L
CS M
710 960 L
705 954 L
702 946 L
702 940 L
705 932 L
710 926 L
716 923 L
722 923 M 727 926 L
733 932 L
736 940 L
736 946 L
733 954 L
727 960 L
722 963 L
837 974 M 840 982 L
840 965 L
837 974 L
831 979 L
823 982 L
814 982 L
806 979 L
800 974 L
800 968 L
803 963 L
806 960 L
811 957 L
828 951 L
834 949 L
840 943 L
800 968 M 806 963 L
811 960 L
828 954 L
834 951 L
837 949 L
840 943 L
840 932 L
834 926 L
826 923 L
817 923 L
809 926 L
803 932 L
800 940 L
800 923 L
803 932 L
862 982 M 862 923 L
865 982 M 865 923 L
865 954 M 870 960 L
879 963 L
884 963 L
893 960 L
896 954 L
896 923 L
884 963 M 890 960 L
893 954 L
893 923 L
854 982 M 865 982 L
854 923 M 873 923 L
884 923 M 904 923 L
924 963 M 924 923 L
927 963 M 927 923 L
927 946 M 929 954 L
935 960 L
941 963 L
949 963 L
952 960 L
952 957 L
949 954 L
946 957 L
949 960 L
915 963 M 927 963 L
915 923 M 935 923 L
971 982 M 969 979 L
971 977 L
974 979 L
971 982 L
971 963 M 971 923 L
974 963 M 974 923 L
963 963 M 974 963 L
963 923 M 983 923 L
1002 963 M 1002 923 L
1005 963 M 1005 923 L
1005 954 M 1011 960 L
1019 963 L
1025 963 L
1033 960 L
1036 954 L
1036 923 L
1025 963 M 1030 960 L
1033 954 L
1033 923 L
994 963 M 1005 963 L
994 923 M 1014 923 L
1025 923 M 1044 923 L
1064 982 M 1064 923 L
1067 982 M 1067 923 L
1095 963 M 1067 935 L
1081 946 M 1098 923 L
1078 946 M 1095 923 L
1056 982 M 1067 982 L
1087 963 M 1103 963 L
1056 923 M 1075 923 L
1087 923 M 1103 923 L
1123 982 M 1120 979 L
1123 977 L
1126 979 L
1123 982 L
1123 963 M 1123 923 L
1126 963 M 1126 923 L
1115 963 M 1126 963 L
1115 923 M 1134 923 L
1154 963 M 1154 923 L
1157 963 M 1157 923 L
1157 954 M 1162 960 L
1171 963 L
1176 963 L
1185 960 L
1188 954 L
1188 923 L
1176 963 M 1182 960 L
1185 954 L
1185 923 L
1145 963 M 1157 963 L
1145 923 M 1165 923 L
1176 923 M 1196 923 L
1224 963 M 1218 960 L
1216 957 L
1213 951 L
1213 946 L
1216 940 L
1218 937 L
1224 935 L
1230 935 L
1235 937 L
1238 940 L
1241 946 L
1241 951 L
1238 957 L
1235 960 L
1230 963 L
1224 963 L
1218 960 M 1216 954 L
1216 943 L
1218 937 L
1235 937 M 1238 943 L
1238 954 L
1235 960 L
1238 957 M 1241 960 L
1247 963 L
1247 960 L
1241 960 L
1216 940 M 1213 937 L
1210 932 L
1210 929 L
1213 923 L
1221 920 L
1235 920 L
1244 918 L
1247 915 L
1210 929 M 1213 926 L
1221 923 L
1235 923 L
1244 920 L
1247 915 L
1247 912 L
1244 906 L
1235 904 L
1218 904 L
1210 906 L
1207 912 L
1207 915 L
1210 920 L
1218 923 L
CS [80 24] 0 setdash M
1458 541 M CS [] 0 setdash M
1503 592 M 1506 600 L
1506 583 L
1503 592 L
1498 597 L
1489 600 L
1481 600 L
1472 597 L
1467 592 L
1467 586 L
1469 581 L
1472 578 L
1478 575 L
1495 569 L
1500 567 L
1506 561 L
1467 586 M 1472 581 L
1478 578 L
1495 572 L
1500 569 L
1503 567 L
1506 561 L
1506 550 L
1500 544 L
1492 541 L
1483 541 L
1475 544 L
1469 550 L
1467 558 L
1467 541 L
1469 550 L
1528 600 M 1528 541 L
1531 600 M 1531 541 L
1531 572 M 1537 578 L
1545 581 L
1551 581 L
1559 578 L
1562 572 L
1562 541 L
1551 581 M 1556 578 L
1559 572 L
1559 541 L
1520 600 M 1531 600 L
1520 541 M 1540 541 L
1551 541 M 1571 541 L
1590 581 M 1590 541 L
1593 581 M 1593 541 L
1593 564 M 1596 572 L
1601 578 L
1607 581 L
1615 581 L
1618 578 L
1618 575 L
1615 572 L
1613 575 L
1615 578 L
1582 581 M 1593 581 L
1582 541 M 1601 541 L
1638 600 M 1635 597 L
1638 595 L
1641 597 L
1638 600 L
1638 581 M 1638 541 L
1641 581 M 1641 541 L
1629 581 M 1641 581 L
1629 541 M 1649 541 L
1669 581 M 1669 541 L
1672 581 M 1672 541 L
1672 572 M 1677 578 L
1686 581 L
1691 581 L
1700 578 L
1702 572 L
1702 541 L
1691 581 M 1697 578 L
1700 572 L
1700 541 L
1660 581 M 1672 581 L
1660 541 M 1680 541 L
1691 541 M 1711 541 L
1731 600 M 1731 541 L
1733 600 M 1733 541 L
1761 581 M 1733 553 L
1747 564 M 1764 541 L
1745 564 M 1761 541 L
1722 600 M 1733 600 L
1753 581 M 1770 581 L
1722 541 M 1742 541 L
1753 541 M 1770 541 L
1789 600 M 1787 597 L
1789 595 L
1792 597 L
1789 600 L
1789 581 M 1789 541 L
1792 581 M 1792 541 L
1781 581 M 1792 581 L
1781 541 M 1801 541 L
1820 581 M 1820 541 L
1823 581 M 1823 541 L
1823 572 M 1829 578 L
1837 581 L
1843 581 L
1851 578 L
1854 572 L
1854 541 L
1843 581 M 1848 578 L
1851 572 L
1851 541 L
1812 581 M 1823 581 L
1812 541 M 1832 541 L
1843 541 M 1862 541 L
1891 581 M 1885 578 L
1882 575 L
1879 569 L
1879 564 L
1882 558 L
1885 555 L
1891 553 L
1896 553 L
1902 555 L
1905 558 L
1907 564 L
1907 569 L
1905 575 L
1902 578 L
1896 581 L
1891 581 L
1885 578 M 1882 572 L
1882 561 L
CS M
1885 555 L
1902 555 M 1905 561 L
1905 572 L
1902 578 L
1905 575 M 1907 578 L
1913 581 L
1913 578 L
1907 578 L
1882 558 M 1879 555 L
1876 550 L
1876 547 L
1879 541 L
1888 538 L
1902 538 L
1910 536 L
1913 533 L
1876 547 M 1879 544 L
1888 541 L
1902 541 L
1910 538 L
1913 533 L
1913 530 L
1910 524 L
1902 522 L
1885 522 L
1876 524 L
1874 530 L
1874 533 L
1876 538 L
1885 541 L
1997 611 M 1992 606 L
1986 597 L
1980 586 L
1978 572 L
1978 561 L
1980 547 L
1986 536 L
1992 527 L
1997 522 L
1992 606 M 1986 595 L
1983 586 L
1980 572 L
1980 561 L
1983 547 L
1986 538 L
1992 527 L
2014 581 M 2031 541 L
2017 581 M 2031 547 L
2048 581 M 2031 541 L
2008 581 M 2025 581 L
2036 581 M 2053 581 L
2067 575 M 2118 575 L
2067 558 M 2118 558 L
2146 589 M 2152 592 L
2160 600 L
2160 541 L
2157 597 M 2157 541 L
2146 541 M 2171 541 L
2194 611 M 2199 606 L
2205 597 L
2211 586 L
2213 572 L
2213 561 L
2211 547 L
2205 536 L
2199 527 L
2194 522 L
2199 606 M 2205 595 L
2208 586 L
2211 572 L
2211 561 L
2208 547 L
2205 538 L
2199 527 L
CS [80 24] 0 setdash M
CS [] 0 setdash M
1060 38 M 1076 105 M 1076 38 L
1079 105 M 1098 47 L
1076 105 M 1098 38 L
1121 105 M 1098 38 L
1121 105 M 1121 38 L
1124 105 M 1124 38 L
1066 105 M 1079 105 L
1121 105 M 1134 105 L
1066 38 M 1085 38 L
1111 38 M 1134 38 L
1150 47 M 1150 7 L
1151 47 M 1151 7 L
1175 47 M 1175 7 L
1176 47 M 1176 7 L
1144 47 M 1157 47 L
1169 47 M 1182 47 L
1151 28 M 1175 28 L
1144 7 M 1157 7 L
1169 7 M 1182 7 L
1250 118 M 1193 15 L
1311 95 M 1314 86 L
1314 105 L
1311 95 L
1305 102 L
1295 105 L
1289 105 L
1279 102 L
1273 95 L
1270 89 L
1266 79 L
1266 63 L
1270 54 L
1273 47 L
1279 41 L
1289 38 L
1295 38 L
1305 41 L
1311 47 L
1289 105 M 1282 102 L
1276 95 L
1273 89 L
1270 79 L
1270 63 L
1273 54 L
1276 47 L
1282 41 L
1289 38 L
1311 63 M 1311 38 L
1314 63 M 1314 38 L
1302 63 M 1324 63 L
1343 63 M 1382 63 L
1382 70 L
1379 76 L
1375 79 L
1369 83 L
1359 83 L
1350 79 L
1343 73 L
1340 63 L
1340 57 L
1343 47 L
1350 41 L
1359 38 L
1366 38 L
1375 41 L
1382 47 L
1379 63 M 1379 73 L
1375 79 L
1359 83 M 1353 79 L
1347 73 L
1343 63 L
1343 57 L
1347 47 L
1353 41 L
1359 38 L
1401 105 M 1424 38 L
1404 105 M 1424 47 L
1446 105 M 1424 38 L
1395 105 M 1414 105 L
1433 105 M 1452 105 L
CS [80 24] 0 setdash M
CS [] 0 setdash M
865 2357 M 865 2289 L
868 2357 M 868 2289 L
888 2337 M 888 2312 L
855 2357 M 907 2357 L
907 2337 L
904 2357 L
868 2324 M 888 2324 L
855 2289 M 878 2289 L
929 2357 M 929 2289 L
933 2357 M 933 2289 L
920 2357 M 942 2357 L
920 2289 M 942 2289 L
1003 2347 M 1006 2337 L
1006 2357 L
1003 2347 L
997 2353 L
987 2357 L
981 2357 L
971 2353 L
965 2347 L
961 2340 L
958 2331 L
958 2315 L
961 2305 L
965 2299 L
971 2292 L
981 2289 L
987 2289 L
997 2292 L
1003 2299 L
981 2357 M 974 2353 L
968 2347 L
965 2340 L
961 2331 L
961 2315 L
965 2305 L
968 2299 L
974 2292 L
981 2289 L
1003 2315 M 1003 2289 L
1006 2315 M 1006 2289 L
993 2315 M 1016 2315 L
1038 2357 M 1038 2308 L
1042 2299 L
1048 2292 L
1058 2289 L
1064 2289 L
1074 2292 L
1080 2299 L
1083 2308 L
1083 2357 L
1042 2357 M 1042 2308 L
1045 2299 L
1051 2292 L
1058 2289 L
1029 2357 M 1051 2357 L
1074 2357 M 1093 2357 L
1115 2357 M 1115 2289 L
1119 2357 M 1119 2289 L
1106 2357 M 1144 2357 L
1154 2353 L
1157 2350 L
1160 2344 L
1160 2337 L
1157 2331 L
1154 2328 L
1144 2324 L
1119 2324 L
1144 2357 M 1151 2353 L
1154 2350 L
1157 2344 L
1157 2337 L
1154 2331 L
1151 2328 L
1144 2324 L
1106 2289 M 1128 2289 L
1135 2324 M 1141 2321 L
1144 2318 L
1154 2296 L
1157 2292 L
1160 2292 L
1164 2296 L
1141 2321 M 1144 2315 L
1151 2292 L
1154 2289 L
1160 2289 L
1164 2296 L
1164 2299 L
1186 2357 M 1186 2289 L
1189 2357 M 1189 2289 L
1209 2337 M 1209 2312 L
1176 2357 M 1228 2357 L
1228 2337 L
1225 2357 L
1189 2324 M 1209 2324 L
1176 2289 M 1228 2289 L
1228 2308 L
1225 2289 L
1327 2350 M 1327 2289 L
1330 2357 M 1330 2289 L
1330 2357 M 1295 2308 L
1347 2308 L
1318 2289 M 1340 2289 L
CS [80 24] 0 setdash M
CS [] 0 setdash M
255 255 M 2261 255 L
255 255 M 255 316 L
329 255 M 329 286 L
403 255 M 403 286 L
478 255 M 478 286 L
552 255 M 552 286 L
626 255 M 626 316 L
700 255 M 700 286 L
775 255 M 775 286 L
849 255 M 849 286 L
923 255 M 923 286 L
998 255 M 998 316 L
1072 255 M 1072 286 L
1146 255 M 1146 286 L
1221 255 M 1221 286 L
1295 255 M 1295 286 L
1369 255 M 1369 316 L
1443 255 M 1443 286 L
1518 255 M 1518 286 L
1592 255 M 1592 286 L
1666 255 M 1666 286 L
1741 255 M 1741 316 L
1815 255 M 1815 286 L
1889 255 M 1889 286 L
1963 255 M 1963 286 L
2038 255 M 2038 286 L
2112 255 M 2112 316 L
2186 255 M 2186 286 L
2261 255 M 2261 286 L
197 142 M 209 191 M 211 188 L
209 185 L
206 188 L
206 191 L
209 197 L
211 199 L
220 202 L
232 202 L
240 199 L
243 194 L
243 185 L
240 179 L
232 176 L
223 176 L
CS M
232 202 M 237 199 L
240 194 L
240 185 L
237 179 L
232 176 L
237 173 L
243 168 L
246 162 L
246 153 L
243 147 L
240 144 L
232 142 L
220 142 L
211 144 L
209 147 L
206 153 L
206 156 L
209 159 L
211 156 L
209 153 L
240 170 M 243 162 L
243 153 L
240 147 L
237 144 L
232 142 L
269 202 M 263 173 L
269 179 L
278 182 L
286 182 L
295 179 L
301 173 L
304 165 L
304 159 L
301 150 L
295 144 L
286 142 L
278 142 L
269 144 L
266 147 L
263 153 L
263 156 L
266 159 L
269 156 L
266 153 L
286 182 M 292 179 L
298 173 L
301 165 L
301 159 L
298 150 L
292 144 L
286 142 L
269 202 M 298 202 L
269 199 M 284 199 L
298 202 L
568 142 M 603 197 M 603 142 L
606 202 M 606 142 L
606 202 M 574 159 L
620 159 L
594 142 M 615 142 L
652 202 M 643 199 L
638 191 L
635 176 L
635 168 L
638 153 L
643 144 L
652 142 L
658 142 L
667 144 L
672 153 L
675 168 L
675 176 L
672 191 L
667 199 L
658 202 L
652 202 L
646 199 L
643 197 L
641 191 L
638 176 L
638 168 L
641 153 L
643 147 L
646 144 L
652 142 L
658 142 M 664 144 L
667 147 L
669 153 L
672 168 L
672 176 L
669 191 L
667 197 L
664 199 L
658 202 L
940 142 M 975 197 M 975 142 L
977 202 M 977 142 L
977 202 M 946 159 L
992 159 L
966 142 M 986 142 L
1012 202 M 1006 173 L
1012 179 L
1021 182 L
1029 182 L
1038 179 L
1044 173 L
1047 165 L
1047 159 L
1044 150 L
1038 144 L
1029 142 L
1021 142 L
1012 144 L
1009 147 L
1006 153 L
1006 156 L
1009 159 L
1012 156 L
1009 153 L
1029 182 M 1035 179 L
1041 173 L
1044 165 L
1044 159 L
1041 150 L
1035 144 L
1029 142 L
1012 202 M 1041 202 L
1012 199 M 1026 199 L
1041 202 L
1311 142 M 1326 202 M 1320 173 L
1326 179 L
1334 182 L
1343 182 L
1352 179 L
1358 173 L
1360 165 L
1360 159 L
1358 150 L
1352 144 L
1343 142 L
1334 142 L
1326 144 L
1323 147 L
1320 153 L
1320 156 L
1323 159 L
1326 156 L
1323 153 L
1343 182 M 1349 179 L
1355 173 L
1358 165 L
1358 159 L
1355 150 L
1349 144 L
1343 142 L
1326 202 M 1355 202 L
1326 199 M 1340 199 L
1355 202 L
1395 202 M 1386 199 L
1381 191 L
1378 176 L
1378 168 L
1381 153 L
1386 144 L
1395 142 L
1401 142 L
1409 144 L
1415 153 L
1418 168 L
1418 176 L
1415 191 L
1409 199 L
1401 202 L
1395 202 L
1389 199 L
1386 197 L
1383 191 L
1381 176 L
1381 168 L
1383 153 L
1386 147 L
1389 144 L
1395 142 L
1401 142 M 1407 144 L
1409 147 L
1412 153 L
1415 168 L
1415 176 L
1412 191 L
1409 197 L
1407 199 L
1401 202 L
1683 142 M 1697 202 M 1691 173 L
1697 179 L
1706 182 L
1714 182 L
1723 179 L
1729 173 L
1732 165 L
1732 159 L
1729 150 L
1723 144 L
1714 142 L
1706 142 L
1697 144 L
1694 147 L
1691 153 L
1691 156 L
1694 159 L
1697 156 L
1694 153 L
1714 182 M 1720 179 L
1726 173 L
1729 165 L
1729 159 L
1726 150 L
1720 144 L
1714 142 L
1697 202 M 1726 202 L
1697 199 M 1712 199 L
1726 202 L
1755 202 M 1749 173 L
1755 179 L
1763 182 L
1772 182 L
1781 179 L
1787 173 L
1790 165 L
1790 159 L
1787 150 L
1781 144 L
1772 142 L
1763 142 L
1755 144 L
1752 147 L
1749 153 L
1749 156 L
1752 159 L
1755 156 L
1752 153 L
1772 182 M 1778 179 L
1784 173 L
1787 165 L
1787 159 L
1784 150 L
1778 144 L
1772 142 L
1755 202 M 1784 202 L
1755 199 M 1769 199 L
1784 202 L
2054 142 M 2097 194 M 2095 191 L
2097 188 L
2100 191 L
2100 194 L
2097 199 L
2092 202 L
2083 202 L
2074 199 L
2069 194 L
2066 188 L
2063 176 L
2063 159 L
2066 150 L
2071 144 L
2080 142 L
2086 142 L
2095 144 L
2100 150 L
2103 159 L
2103 162 L
2100 170 L
2095 176 L
2086 179 L
2083 179 L
2074 176 L
2069 170 L
2066 162 L
2083 202 M 2077 199 L
2071 194 L
2069 188 L
2066 176 L
2066 159 L
2069 150 L
2074 144 L
2080 142 L
2086 142 M 2092 144 L
2097 150 L
2100 159 L
2100 162 L
2097 170 L
2092 176 L
2086 179 L
2138 202 M 2129 199 L
2123 191 L
2121 176 L
2121 168 L
2123 153 L
2129 144 L
2138 142 L
2144 142 L
2152 144 L
2158 153 L
CS M
2161 168 L
2161 176 L
2158 191 L
2152 199 L
2144 202 L
2138 202 L
2132 199 L
2129 197 L
2126 191 L
2123 176 L
2123 168 L
2126 153 L
2129 147 L
2132 144 L
2138 142 L
2144 142 M 2149 144 L
2152 147 L
2155 153 L
2158 168 L
2158 176 L
2155 191 L
2152 197 L
2149 199 L
2144 202 L
255 2261 M 2261 2261 L
255 2261 M 255 2199 L
329 2261 M 329 2230 L
403 2261 M 403 2230 L
478 2261 M 478 2230 L
552 2261 M 552 2230 L
626 2261 M 626 2199 L
700 2261 M 700 2230 L
775 2261 M 775 2230 L
849 2261 M 849 2230 L
923 2261 M 923 2230 L
998 2261 M 998 2199 L
1072 2261 M 1072 2230 L
1146 2261 M 1146 2230 L
1221 2261 M 1221 2230 L
1295 2261 M 1295 2230 L
1369 2261 M 1369 2199 L
1443 2261 M 1443 2230 L
1518 2261 M 1518 2230 L
1592 2261 M 1592 2230 L
1666 2261 M 1666 2230 L
1741 2261 M 1741 2199 L
1815 2261 M 1815 2230 L
1889 2261 M 1889 2230 L
1963 2261 M 1963 2230 L
2038 2261 M 2038 2230 L
2112 2261 M 2112 2199 L
2186 2261 M 2186 2230 L
2261 2261 M 2261 2230 L
255 255 M 255 2261 L
255 255 M 286 255 L
255 350 M 316 350 L
255 446 M 286 446 L
255 541 M 286 541 L
255 637 M 286 637 L
255 732 M 286 732 L
255 828 M 316 828 L
255 923 M 286 923 L
255 1019 M 286 1019 L
255 1114 M 286 1114 L
255 1210 M 286 1210 L
255 1305 M 316 1305 L
255 1401 M 286 1401 L
255 1496 M 286 1496 L
255 1592 M 286 1592 L
255 1687 M 286 1687 L
255 1783 M 316 1783 L
255 1879 M 286 1879 L
255 1974 M 286 1974 L
255 2070 M 286 2070 L
255 2165 M 286 2165 L
255 2261 M 316 2261 L
145 320 M 171 381 M 162 378 L
156 369 L
153 355 L
153 346 L
156 332 L
162 323 L
171 320 L
176 320 L
185 323 L
191 332 L
194 346 L
194 355 L
191 369 L
185 378 L
176 381 L
171 381 L
165 378 L
162 375 L
159 369 L
156 355 L
156 346 L
159 332 L
162 326 L
165 323 L
171 320 L
176 320 M 182 323 L
185 326 L
188 332 L
191 346 L
191 355 L
188 369 L
185 375 L
182 378 L
176 381 L
0 798 M 26 858 M 17 855 L
12 847 L
9 832 L
9 823 L
12 809 L
17 800 L
26 798 L
32 798 L
41 800 L
46 809 L
49 823 L
49 832 L
46 847 L
41 855 L
32 858 L
26 858 L
20 855 L
17 852 L
15 847 L
12 832 L
12 823 L
15 809 L
17 803 L
20 800 L
26 798 L
32 798 M 38 800 L
41 803 L
43 809 L
46 823 L
46 832 L
43 847 L
41 852 L
38 855 L
32 858 L
72 803 M 69 800 L
72 798 L
75 800 L
72 803 L
113 858 M 104 855 L
98 847 L
95 832 L
95 823 L
98 809 L
104 800 L
113 798 L
118 798 L
127 800 L
133 809 L
136 823 L
136 832 L
133 847 L
127 855 L
118 858 L
113 858 L
107 855 L
104 852 L
101 847 L
98 832 L
98 823 L
101 809 L
104 803 L
107 800 L
113 798 L
118 798 M 124 800 L
127 803 L
130 809 L
133 823 L
133 832 L
130 847 L
127 852 L
124 855 L
118 858 L
159 858 M 153 829 L
159 835 L
167 838 L
176 838 L
185 835 L
191 829 L
193 821 L
193 815 L
191 806 L
185 800 L
176 798 L
167 798 L
159 800 L
156 803 L
153 809 L
153 812 L
156 815 L
159 812 L
156 809 L
176 838 M 182 835 L
188 829 L
191 821 L
191 815 L
188 806 L
182 800 L
176 798 L
159 858 M 188 858 L
159 855 M 173 855 L
188 858 L
58 1275 M 84 1336 M 75 1333 L
69 1324 L
67 1310 L
67 1301 L
69 1287 L
75 1278 L
84 1275 L
90 1275 L
98 1278 L
104 1287 L
107 1301 L
107 1310 L
104 1324 L
98 1333 L
90 1336 L
84 1336 L
78 1333 L
75 1330 L
72 1324 L
69 1310 L
69 1301 L
72 1287 L
75 1281 L
78 1278 L
84 1275 L
90 1275 M 95 1278 L
98 1281 L
101 1287 L
104 1301 L
104 1310 L
101 1324 L
98 1330 L
95 1333 L
90 1336 L
130 1281 M 127 1278 L
130 1275 L
133 1278 L
130 1281 L
162 1324 M 167 1327 L
176 1336 L
176 1275 L
173 1333 M 173 1275 L
162 1275 M 188 1275 L
0 1753 M 26 1813 M 17 1810 L
12 1802 L
9 1787 L
9 1779 L
12 1764 L
17 1755 L
26 1753 L
32 1753 L
41 1755 L
46 1764 L
49 1779 L
49 1787 L
46 1802 L
41 1810 L
32 1813 L
26 1813 L
20 1810 L
17 1807 L
15 1802 L
12 1787 L
12 1779 L
15 1764 L
17 1758 L
20 1755 L
26 1753 L
32 1753 M 38 1755 L
41 1758 L
43 1764 L
46 1779 L
46 1787 L
43 1802 L
41 1807 L
38 1810 L
32 1813 L
72 1758 M 69 1755 L
72 1753 L
75 1755 L
72 1758 L
104 1802 M 110 1805 L
118 1813 L
118 1753 L
115 1810 M 115 1753 L
104 1753 M 130 1753 L
159 1813 M 153 1784 L
159 1790 L
167 1793 L
CS M
176 1793 L
185 1790 L
191 1784 L
193 1776 L
193 1770 L
191 1761 L
185 1755 L
176 1753 L
167 1753 L
159 1755 L
156 1758 L
153 1764 L
153 1767 L
156 1770 L
159 1767 L
156 1764 L
176 1793 M 182 1790 L
188 1784 L
191 1776 L
191 1770 L
188 1761 L
182 1755 L
176 1753 L
159 1813 M 188 1813 L
159 1810 M 173 1810 L
188 1813 L
58 2230 M 84 2291 M 75 2288 L
69 2279 L
67 2265 L
67 2256 L
69 2242 L
75 2233 L
84 2230 L
90 2230 L
98 2233 L
104 2242 L
107 2256 L
107 2265 L
104 2279 L
98 2288 L
90 2291 L
84 2291 L
78 2288 L
75 2285 L
72 2279 L
69 2265 L
69 2256 L
72 2242 L
75 2236 L
78 2233 L
84 2230 L
90 2230 M 95 2233 L
98 2236 L
101 2242 L
104 2256 L
104 2265 L
101 2279 L
98 2285 L
95 2288 L
90 2291 L
130 2236 M 127 2233 L
130 2230 L
133 2233 L
130 2236 L
156 2279 M 159 2276 L
156 2273 L
153 2276 L
153 2279 L
156 2285 L
159 2288 L
167 2291 L
179 2291 L
188 2288 L
191 2285 L
194 2279 L
194 2273 L
191 2268 L
182 2262 L
167 2256 L
162 2253 L
156 2247 L
153 2239 L
153 2230 L
179 2291 M 185 2288 L
188 2285 L
191 2279 L
191 2273 L
188 2268 L
179 2262 L
167 2256 L
153 2236 M 156 2239 L
162 2239 L
176 2233 L
185 2233 L
191 2236 L
194 2239 L
162 2239 M 176 2230 L
188 2230 L
191 2233 L
194 2239 L
194 2245 L
2261 255 M 2261 2261 L
2261 255 M 2230 255 L
2261 350 M 2199 350 L
2261 446 M 2230 446 L
2261 541 M 2230 541 L
2261 637 M 2230 637 L
2261 732 M 2230 732 L
2261 828 M 2199 828 L
2261 923 M 2230 923 L
2261 1019 M 2230 1019 L
2261 1114 M 2230 1114 L
2261 1210 M 2230 1210 L
2261 1305 M 2199 1305 L
2261 1401 M 2230 1401 L
2261 1496 M 2230 1496 L
2261 1592 M 2230 1592 L
2261 1687 M 2230 1687 L
2261 1783 M 2199 1783 L
2261 1879 M 2230 1879 L
2261 1974 M 2230 1974 L
2261 2070 M 2230 2070 L
2261 2165 M 2230 2165 L
2261 2261 M 2199 2261 L
CS [80 24] 0 setdash M
stroke
grestore
showpage
end

