%Paper: 
%From: mshaposh@nxth04.cern.ch
%Date: Mon, 21 Jun 93 13:30:58 +0100


\documentstyle[12pt,epsfig]{article}

 \hoffset=-1cm
 \voffset=-2cm
 \textwidth=15.5cm
 \textheight=22.5cm

%\include{preamb}
\newcommand{\la}[1]{\label{#1}}

% allow a lot of figures and so on
\renewcommand{\topfraction}{1.0}
\renewcommand{\bottomfraction}{1.0}
\renewcommand{\textfraction}{0.0}
\setcounter{topnumber}{4}
\setcounter{bottomnumber}{4}
\setcounter{totalnumber}{6}
\parindent=1em
\baselineskip.4cm
% increase line spacing by small amount
% \renewcommand{\baselinestretch}{1.5}
%\newcommand{\defarraystretch}{1.5}
%	\renewcommand{\arraystretch}{\defarraystretch}
%\setlength{\tabcolsep}{7.5mm}

%
\newlength{\numlen}
\newcommand{\n}{\settowidth{\numlen}{0}\makebox[\numlen]{}}
\newcommand{\cen}[1]{\multicolumn{1}{c}{#1}}

\newlength{\indexlength}
\newcommand{\indlen}{
	\settowidth{\indexlength}{$^0$}
\makebox[\indexlength]{}}

\newcommand{\eq}{\begin{equation}}
\newcommand{\en}{\end{equation}}

\newcommand{\be}{\begin{equation}}
\newcommand{\ee}{\end{equation}}
\newcommand{\ba}{\begin{eqnarray}}
\newcommand{\ea}{\end{eqnarray}}

\newcommand{\eps}{\varepsilon}
\newcommand{\rmi}[1]{{\mbox{\scriptsize #1}}}

\newcommand{\ie}{{\em ie\ }}
\newcommand{\eg}{{\em e.\,g.\ }}
\newcommand{\cf}{cf.\ }
\newcommand{\etc}{etc.\ }
% \newcommand{\etal}{{\em et al\ }}
\newcommand{\etal}{{et al.\ }}
%\newcommand{\eq}{eq.~}
\newcommand{\eqs}{eqs.~}
\newcommand{\fig}{fig.~}
\newcommand{\figs}{figs.~}
\newcommand{\blank}{\ }
\newcommand{\OO}{\O}
\renewcommand{\O}{{\cal O}}

\newcommand{\nr}[1]{(\ref{#1})}

\newcommand{\h}{{\hspace{0.5 cm}}}

\newcommand{\x}[1]{{\h {\rm #1} \h}}

\newcommand{\dd}{\mbox{d}}
\newcommand{\tr}{\mbox{Tr\,}}
\newcommand{\mod}{{\rm\,mod\,}}

\newcommand{\bfk}{\mbox{\bf k}}
\newcommand{\bfp}{\mbox{\bf p}}
\newcommand{\bfx}{\mbox{\bf x}}
\newcommand{\eff}{{\rm eff}}
\newcommand{\half}{{\scriptstyle{1\over2}}}
\newcommand{\quarter}{{\scriptstyle{1\over4}}}

\newcommand{\fr}[2]{{\frac{#1}{#2}}}
\newcommand{\bfi}[1]{{\mbox{\bf#1}}}

\begin{document}
% Title

\begin{titlepage}

\hfill CERN-TH.6918/93\\

\begin{centering}
\vfill

{\bf ON NON-PERTURBATIVE EFFECTS AT THE HIGH-TEMPERATURE ELECTROWEAK PHASE
TRANSITION}
\vspace{1cm}


M. Shaposhnikov\footnote{On leave of absence from the Institute for
Nuclear Research of the Russian Academy of Sciences, Moscow 117312,
Russia.} \\


\vspace{1cm}
{\em Theory Division, CERN,\\ CH-1211 Geneva 23, Switzerland}\\
\vspace{0.3cm}
{\bf Abstract}\\
\vspace{1cm}
\end{centering}
It is argued that confining effects in 3-dimensional non-Abelian gauge theories
(high-temperature limit of 4-dimensional ones) imply the existence of the
condensates of the gauge and Higgs fields in 3-d vacuum. This non-perturbative
effect can decrease the energy of the phase with unbroken symmetry and may
result in the creation of a barrier separating the broken and unbroken phases.
Thus the high-temperature phase transitions in gauge theories can be  stronger
first order than is expected from perturbation theory. The applications of
these results to electroweak baryogenesis are briefly discussed.
\vspace{0.3cm}\noindent


\vfill \vfill
\noindent CERN-TH.6918/93\\
\noindent June 1993
\end{titlepage}


\section{Introduction}
The study of the high-temperature phase transitions in the gauge theories
\cite{kir}--\cite{weinberg} provides an interesting interplay between particle
physics and cosmology. Recently considerable progress has been achieved in the
understanding
of the perturbative expansion for the effective potential of the scalar field
at high temperatures \cite{linde}--\cite{buch}. One can summarize the present
understanding as follows. Let us take for definiteness the standard electroweak
theory with one scalar doublet. Then at zero temperatures the one-loop
effective potential has the form
\eq
V(\phi)_{T=0} = -(2\lambda + B) \sigma^2\phi^2 + \lambda \phi^4
+ B \phi^4 \log (\phi^2/\sigma^2),
\label{vt=0}
\en
where $\phi = \sigma = 250$ GeV corresponds to the minimum $V(\phi)$,
\eq
B=\frac{3}{64\pi^2} (2m_W^4 + m_Z^4 - 4m_t^4).
\en
Here all particle masses are given in terms of the vacuum expectation value of
the Higgs field. The Higgs mass is given by $M_H^2 = 4\sigma^2 (3B+ 2\lambda)$.
For $\lambda \ll g_W^2$ the main contribution to the finite-temperature
effective potential comes from the gauge loops; the
result of the standard calculation in the high-temperature limit ($T$ is much
larger than any mass scale) is \cite{linde,dolan}:
\eq
\Delta V_T = \frac{1}{8} T^2 \phi^2(2m_W^2 + m_Z^2 +2m_t^2) -
\frac{T\phi^3}{4\pi}(2m_W^3 + m_Z^3).
\label{dvt}
\en

The naive loop expansion of the effective potential works provided the mass of
the gauge bosons induced by the Higgs mechanism,  $M_W(\phi) = \frac{1}{2}g_W
\phi$, is larger than the Debye screening scale $M_D = C_D g_W T$ (for the
electroweak theory with three fermionic generations $C_D^2 = \frac{11}{6}$). In
order to go to the smaller values of $\phi$ one has to perform a resummation of
the perturbation theory. This can be done with the use of gap equations for
plasma masses taking into account the Debye screening \cite{eqz,ae,buch}.
Roughly speaking, the effect of the resummation reduces the coefficient in
front of the $\phi^3$ term by a factor $\frac{2}{3}$ \cite{lindeandson} (see
also \cite{ms,carrington}), so that the first-order phase transition is weaker
than one would expect from eq.(\ref{dvt}). The effective potential with this
effect taken into account is
\eq
V_T (\phi) =
\frac{1}{8} (T^2-T_0^2) \phi^2(2m_W^2 + m_Z^2 +2m_t^2) -\frac{2}{3}
\frac{T\phi^3}{4\pi}(2m_W^3 + m_Z^3)+ \lambda \phi^4,
\en
where
\eq
T_0^2 = \frac{8 \sigma^2(B + 2 \lambda)}{2m_W^2 + m_Z^2 +2m_t^2}.
\en
It is argued that for sufficiently small Higgs masses (say, $m_H < 70$ GeV) the
improved perturbative calculation of the effective potential is self-consistent
if $M_W(\phi)> M_M \sim \frac{1}{3\pi}g_W^2 T$ \cite{eqz,ae,buch}. Here $M_M$
is the so-called magnetic mass providing the screening of the static gauge
fields in the plasma, which cures the infrared problem in the thermodynamics of
Yang-Mills fields \cite{linde:pl80,gpy}. So, one expects that the first-order
electroweak phase transition is rather weak for those Higgs masses. For the
larger Higgs masses, the approximation breaks down, although there is an
indication that the phase transition is actually of the second order
\cite{eqz}.

Thus, the perturbative calculations of the effective potential seem to provide
a self-consistent picture of the phase transitions in gauge theories at
sufficiently small scalar self-coupling constants. According to perturbation
theory, the only requirement that has to be met is the smallness of the ratio
$M_M/M_W(\phi)\sim \frac{2 g_W T}{3 \pi \phi}$. This value is indeed small for
the interesting range of temperatures and fields $\phi$ for cosmological phase
transitions in Grand Unified Theories and the electroweak theory, so that one
might think that we achieved (an almost complete) understanding of those
phenomena.

The aim of the present paper is to argue that non-perturbative effects can
change the conclusions drawn from the study of the perturbative expansion of
the effective potential. The paper is organized as follows. In Section 2 we
show that 3-d non-perturbative effects are likely to {\em decrease} the free
energy of the system in the unbroken phase, thus decreasing the value of the
critical temperature. In Section 3 we discuss the contribution of some set of
non-perturbative fluctuations to $V(\phi)$. In Section 4 we analyse the
dynamics of the phase transition in cosmology and argue that the phase
transition can be  actually a very strongly of the first-order, contrary to the
result obtained with perturbative calculation. Some applications of these
results to cosmology and electroweak baryogenesis are discussed in  Section 5.
We summarize our results in the Conclusion.

\section{Non-perturbative effects in non-Abelian gauge theories at high
temperatures}
In what follows we confine ourselves to the study of the phase transition in
SU(2) gauge theory with one Higgs doublet, without fermions. For numerical
presentations we  will use the electroweak gauge coupling, $g_W = 2/3$.  The
results can be easily extended to a more general case.

Our starting point is a dimensionally reduced gauge theory (see
\cite{jackiw}--\cite{landsman} and a recent discussion in \cite{kari}). The
finite-temperature field theory is equivalent (for static quantities such as
the effective potential we are interested in) to a Euclidean field theory, with
compact fourth dimension whose size is $\frac{1}{T}$. Bosonic (fermionic)
fields obey periodic (antiperiodic) boundary conditions in Euclidean time so
that `energies' of particles are discrete ($\omega_B = 2 \pi n T,~~\omega_F =
\pi(2n +1) T,~~n = 0, \pm 1, \pm 2,...$. If all mass scales of the theory are
smaller than the temperature (this is true for the theory with small coupling
constants in unbroken phase and for the system in the broken phase provided the
Higgs-induced mass $M_W$ is small with respect to the temperature) all
fermionic modes and non-zero bosonic modes can be integrated out. In this way
one gets the effective 3-d gauge theory with the action \cite{kari}:
\begin{eqnarray}
&&S_3
= \int d^3x \biggl\{{1\over4} F_{ij}^aF_{ij}^a +
\fr12 (D_iA_0)^a(D_iA_0)^a + (D_i\phi)^\dagger(D_i\phi)+ \nonumber
\\&&
+\fr12 \fr56 g_3^2T A_0^aA_0^a +{g_3^4\over12\pi^2}{17\over16}(A_0^aA_0^a)^2
+
\nonumber
\\&&
+\biggl[-\fr12 m_H^2 +({3\over16}g_3^2 +\fr12\lambda_3)T
\biggr]\phi^\dagger\phi
+\lambda_3(\phi^\dagger\phi)^2 + \nonumber \\&&
+\fr14 g_3^2 A_0^aA_0^a \phi^\dagger\phi \biggr\}+ counterterms,
\la{3daction}
\end{eqnarray}
containing, in addition to 3-d gauge fields and the Higgs doublet, a scalar
field in adjoint representation (former $A_0$ component of the 4-d gauge
field). There are also other higher polynomial contributions to this effective
Lagrangian; they are, however, suppressed by the powers of temperature. In this
equation $g_3^2 = g_W^2 T,~~\lambda_3 = 4 \lambda T$.

The 3-d effective Lagrangian contains four dimensionful parameters. The first
one is just the Debye screening mass $\sim g_W T$; the second scale is a
dimensionful coupling of the 3-d gauge theory $g_3^2 = g_W^2 T$; the third one
is the mass of the Higgs $m(T)^2 = \biggl[-\fr12 m_H^2 +({3\over16}g_3^2
+\fr12\lambda_3)T \biggr]$; and the fourth is the scalar self-coupling. The
phase transition is expected to happen near $m^2(T)=0$, so that at this point
there is a hierarchy of scales, $M_D \gg g_3^2,~M_D \gg m(T)$. Hence, one can
integrate out the $A_0$ field and study the action containing just the 3-d
gauge fields and the Higgs field. From this exercise it is obvious how the
expansion parameter $\frac{g_3}{2\pi M_W(\phi)}$ arises when one computes gauge
loops in the effective potential. Higher-order corrections generate some powers
of $g_3$; one has to compensate these powers in order to get a correct
dimension for the expression, and the only dimensionful quantity at hand is the
mass of the $W$, originated from the Higgs mechanism. As usually in a loop
expansion one gets a number of $2\pi$'s in the denominator from the integration
over momenta.

In some cases, however, the region of applicability of the perturbation theory
{\em cannot} be derived from the analysis of the perturbative expansion. The
well-known example is provided by fermionic number non-conservation in the
electroweak theory \cite{hooft}. Here the amplitudes for the processes with
B-violation are equal to zero in {\em any} order of perturbation theory while
these processes do occur because of instantons. Another example, which is very
close in spirit to the question we are discussing, is provided by QCD. Since we
will use this analogy quite intensively, let us discuss in some detail the
perturbation theory in QCD. As a classic example consider the ratio
$
R = \frac{\sigma(e^+e^- \rightarrow hadrons)}{\sigma(e^+e^- \rightarrow
\mu^+\mu^-)}
$
at some energy scale $s \sim 1$ GeV$^2$ for three fermionic flavours. A
first-order QCD correction to this ratio is known for a long time,
$
R = 2[ 1 + \frac{\alpha_s}{\pi}].
$
The scale at which one should take $\alpha_s$ is not determined at this level.
The computation of the three-loop corrections \cite{kataev} allow one to fix
the scale in $\alpha_s$ and one gets
\eq
R = 2 \left[1 + \frac{\alpha_s(s/\Lambda^2)}{\pi}+ 1.64
{(\frac{\alpha_s(s/\Lambda^2)}{\pi})}^2\right],
\en
where $\Lambda \sim 100-200$ MeV is the scale of the strong interactions in the
$\overline{MS}$ scheme. The convergence of the perturbation theory is pretty
good: at, say, $\sqrt{s} \sim 700$ MeV, one has numerically
$
R = 2[1 + (0.12-0.18) + (0.024 -0.05)]
$
where the first number in brackets refers to $\Lambda = 100$ MeV and the second
one to $\Lambda = 200$ MeV. The natural tendency would then be to conclude that
we know $R$ with  quite a good precision (say, 5\%) at this energy scale. This
conclusion is, however, evidently wrong as can be seen from the experimental
data, since precisely at this scale one has $\rho$-meson resonance and the
correct $R$-ratio has nothing in common with a perturbative expression.

The same story happens with other confining theories, such as  QCD$_2$($N_c$)
in two dimensions \cite{hooftqcd}. Here, at least in the limit of an infinite
number of colours $(N_c \rightarrow \infty)$ the spectrum of the states is
discrete and there is no continuum in the spectrum,  contrary to expectations
from any given order of perturbation theory.

One of the manifestations of confinement is the existence of the
non-perturbative condensates of the different composite operators. For example,
in QCD there are condensates of quark and gluonic fields,
$\langle(\bar{q}q)\rangle \sim -(250 MeV)^3 $ and $\langle \frac{\alpha_s}{\pi}
G^2\rangle \sim (330 MeV)^4$ \cite{vzs}, which appear also in QCD$_2$
\cite{zh}. In QCD in 4-d one can even relate the properties of resonances to
condensates via QCD sum rules \cite{nsvz}; the predictions are quite impressive
for a number of hadronic channels \cite{nsvz}. The analysis of the QCD sum
rules indicates that the actual range of applicability of the perturbation
theory comes not from the analysis of the perturbative expansion but from
non-perturbative corrections.

Now we come back to our 3-d theory. {\em Non-Abelian} gauge theory in three
dimensions has a lot in common with 4-d QCD. Namely, both theories are
confining (one has `logarithmic' confinement in perturbation theory and linear
confinement beyond it in 3d). Therefore, it is natural to assume that the
mechanism for the mass gap generation is the same in both theories \footnote{In
refs. \cite{kks:magn,kks} the $0^{++}$ glueball mass has been estimated in pure
gauge SU(2) theory in 3 dimensions on the lattice. The two papers give
consistent results for the glueball mass; according to \cite{kks:magn} $M_G =
(1.7 \pm 0.4) g_3 $ and according to \cite{kks} $M_G = (2.2 \pm 0.2)  g_3 $.
One can see that, in full analogy with QCD, the scale associated with
non-perturbative effects (3-d glueball mass) is numerically larger than the
perturbative scale $g_3/2\pi$, by a factor $4\pi \sim 10$ (of course, the
parametric dependence is the same). This means that the region of applicability
of the perturbation theory is actually smaller that can be expected from the
analysis of the perturbative expansion.}. In particular, one should expect the
existence of condensates of gauge and scalar fields in 3-d non-Abelian theory.
(The gauge field condensate in a pure 3-d  Yang-Mills theory has been discussed
also in a recent paper by J.M. Cornwall \cite{cornwall} in a different
context.) The lowest-order gauge-invariant operators are $F^2$ (we shall call
it gluonic condensate, in analogy with QCD) and $\phi^{\dagger}\phi$ (scalar
condensate). Just on dimensional grounds, near the point where $m^2(T) = 0$ one
gets
\eq
\langle F_{ij}^a F_{ij}^a\rangle = A_F g_3^6,~~\langle
\phi^{\dagger}\phi\rangle = A_S g_3,~~\langle (\phi^{\dagger}\phi)^2\rangle =
A_4 g_3^2,
\en
where $A_F$, $A_S$ and $A_4$ are some dimensionless numbers. In 4-d QCD, the
numerical values of condensates can be found from the analysis of the
experimental data; in QCD$_2$ from the exact 't Hooft solution \cite{zh}. Here
we do not have this possibility\footnote{One can try to extract the value of
the gluonic condensate from the analysis of QCD sum rules, given the lattice
value for glueball mass in 3d. However, since QCD sum rules do not work in QCD
\cite{nsvz1} and QCD$_2$ \cite{hooftqcd,zh1} for the channel with $0^{++}$
quantum numbers,  we do not attempt to do this here.  Unfortunately, we were
also unable  to extract any information concerning the magnitude of the scalar
condensate from the available lattice data.}.

The knowledge of these condensates allows one to estimate the influence of
non-perturbative effects on the critical temperature of the phase transition.
At critical temperature the free energies of the broken and unbroken phases
coincide; and now we have to take into account the non-perturbative shift of
the energy densities due to the existence of the condensates in the broken and
unbroken phases.  This shift can be easily derived with the scaling arguments.
Indeed, vacuum energy density $\epsilon_{vac}$ in the 3-dimensional theory
given by the functional integral
\eq
\exp(-\epsilon_{vac}V) = \int dA_i(x)\exp(-S_3),
\label{evac}
\en
where $V$ is the 3-d volume and $S_3$ is the action given by eq.
(\ref{3daction}).

Rescaling the fields as $A_i = \sqrt{g_3} \bar{A_i},~~ \phi = \sqrt{g_3}
\bar{\phi}$, and differentiating eq. (\ref{evac}) with respect to $g_3$,
$m(T)^2$ and $\lambda_3$ one gets for small $\lambda_3$ and for $m^2(T)$ close
to zero\footnote{For small $m^2(T)$ and $\lambda_3$ the contribution of the
scalar condensate is small with respect to the contribution of the gluonic
condensate.}:
\eq
\epsilon_{vac} = - \frac{1}{3}\langle \frac{1}{4} F_{ij}^a F_{ij}^a - 2 m^2(T)
\phi^{\dagger}\phi - \lambda_3 (\phi^{\dagger}\phi)^2 \rangle \simeq -
\frac{1}{12}\langle F_{ij}^a F_{ij}^a\rangle,
\label{epsvac}
\en
where we take into account the fact that $\epsilon_{vac} \sim g_3^3$ and used
the equations of motion for the scalar field.
So, again in full analogy with QCD one has an energy shift proportional (with
the minus sign) to gluonic condensate . This energy shift is an analogue of the
bag constant in QCD\footnote{Note that the contribution of the gluonic
condensate to the free energy is of the order of $g_W^6 T^4$, precisely the
term that is not computable by perturbation theory.}. Note that eq.
(\ref{epsvac}) is true in the broken phase minimum as well. The $\phi^3$ term
in the effective potential in this phase arises from the perturbative value of
$\langle F_{ij}^a F_{ij}^a\rangle$.

Clearly, non-perturbative contributions to the energy density should change the
dynamics of the phase transitions at high temperatures. If the gluonic
condensate is positive (as in Euclidean QCD$_4$ \cite{vzs} and QCD$_2$
\cite{zh}), then non-perturbative effects `dig' a `pit' near the origin,
therefore reducing the value of the critical temperature. For the negative
gluonic condensate\footnote{In principle, the gluonic condensate (as well as
the scalar condensate) can have either sign, since the positive-definiteness of
the operator $F^2$ can be spoiled by renormalization.} (this situation seems to
be quite improbable, though) the value of the critical temperature is larger
than that predicted by perturbation theory.

The change of the critical temperature can be estimated by using the value of
the free energy of the system in the broken phase. It is natural to expect that
in the broken phase, with non-zero vacuum expectation value of the Higgs field,
non-trivial fluctuations giving rise to the gluonic condensate are highly
suppressed (we will discuss this point in more detail in the next section), so
that one should take into account this shift in the unbroken phase only. The
critical temperature $T_c$ is  then determined by the equation
\eq
\epsilon_{vac} = V_T(\phi),
\en
where $\frac{dV_T(\phi)}{d\phi}=0$. The shift depends on the mass of the Higgs
boson and constant $A_F$. We present this dependence for positive $A_F$ in Fig.
1. One can see that at $M_H > 50$ GeV and, say, $A_F = 0.1$, the critical
temperature is even lower than the temperature $T_0$, which is thought to be
the temperature of absolute instability of the unbroken phase. Numerically this
shift is quite small for the light Higgs and gets larger for higher Higgs
masses. It is clear that the changing of the effective potential at the origin
generates also a barrier separating the broken and unbroken phases. In
cosmology this barrier will prevent the phase transition to occur at the
critical temperature and it happens at temperatures smaller than $T_c$. In the
next section an attempt is made to estimate this effect.

\section{Estimate of the gluonic condensate}
We are mainly interested  in the non-perturbative contributions to the
effective potential at small $\phi$. It is clear that there is no hope to
determine it in some regular way due to strong coupling and confinement in 3-d
gauge theory. In some models, however, one can study this question by
semi-classical methods in a small coupling regime. The example is provided by
the Georgi-Glashow model in 3-d (SU(2) gauge theory with a triplet of scalar
fields and spontaneous symmetry breaking). It has been shown \cite{polyakov}
that in this model confinement is due to instantons (coinciding with monopoles
in this case). The shift of the vacuum energy density is just
\eq
\epsilon_{vac} =
-\frac{M_W^{\fr72}}{g_3}\alpha(\lambda/g_W^2)\exp\left(-\frac{4\pi
M_W}{g_3^2}\beta(\lambda/g_W^2)\right),
\en
where $\alpha$ and $\beta$ are some functions that can be numerically
calculated, $\beta(0) = 1$, $M_W$ is the $W$-mass. The semi-classical
approximation does not work at small $M_W$, but one can see that this shift is
negative and exponentially small in the broken phase and gets larger with the
decrease of the vacuum expectation value.

The theory with the doublet of the scalar field is more complicated, since
there are no stable solutions to the classical equations of motion even in the
broken phase. So, one cannot perform the analysis in a semi-classical
approximation. To get some insight into the problem, let us study the
non-perturbative gauge field configurations, which may give rise to the gluonic
condensate. We start from a pure Yang-Mills theory. The gluonic condensate is
given by the functional integral
\eq
\langle F_{ij}^a F_{ij}^a\rangle = \int dA_i(x)F_{ij}^a F_{ij}^a\exp(-S).
\label{cond}
\en
According to a suggestion made in \cite{gpy} one can consider the contribution
to eq. (\ref{cond}) of unstable monopole configurations characterized by some
scale $\rho$. To be more specific, we choose as a trial configuration the 4-d
instanton at zero time (see also \cite{rubakov}),
\eq
A_i^a(x) = \frac{1}{g_3}\epsilon_{aij}\frac{x_j}{x^2 + \rho^2}.
\en
The action of this configuration is
\eq
S = \frac{3\pi^2}{g_3^2 \rho}.
\en

There is a number of zero modes associated with this configuration, namely
three translational zero modes and three rotational ones. The normalization
factors associated with them can be computed in  full analogy with the
sphaleron zero-mode problem \cite{armc}. For rotational zero modes we have
\eq
N_{rot} = 8\pi^2 \left[\frac{8 \pi \rho}{3g_3^2}\right]^{\frac{3}{2}}.
\en
Translational zero modes give the contribution
\eq
N_{tr} = \left[\frac{16}{3g_3^2 \rho}(15\pi/8 - \pi^3/12)\right]^{\frac{3}{2}}.
\en
In order to compute the functional integral in the vicinity of this
configuration, one should also introduce a normalization for a scale mode
associated with $\rho$. It is given by
\eq
N_{\rho} = \left[\frac{\pi}{2 g_3^2\rho}\right]^{\frac{1}{2}}.
\en
For dimensional reasons, the determinant of non-zero modes is just
\eq
D = \kappa \frac{1}{\rho^6},
\en
where $\kappa$ is some dimensionless number. From the experience with the
sphaleron \cite{det}, one would expect $\kappa \sim 1$.

Combining all factors together we obtain
\eq
\langle F_{ij}^a F_{ij}^a\rangle =  \int
\frac{d\rho}{\rho}N_{rot}N_{tr}N_{\rho}D\frac{12\pi^2}{g_3^2
\rho}\exp(-\frac{3\pi^2}{g_3 \rho})=0.36 \kappa g_3^6 \sim 0.4 g_3^6 .
\en
The integral over the scale converges at small $\rho$, owing  to an exponential
factor (the energy of the configuration diverges when $\rho \rightarrow
\infty$) and also converges at small $\rho$ due to a pre-exponential entropy
factor. The scale at which the integral is saturated is about $\rho^{-1} \sim 2
g_3^2/\pi^2$. Of course, this estimate of the condensate is rather crude and it
is impossible to compute corrections to it. For our future estimates, we
consider the factor $A_F$ as a parameter of order 1 \footnote{A very different
estimate of the gluonic condensate can be found in \cite{cornwall}, $A_F \sim 5
\cdot 10^{-3}$. Cornwall also concluded that non-perturbative effects introduce
a
negative energy shift in a pure Yang-Mills theory in 3-d.}

Now, we can turn to our theory with Higgs fields. The presence of the scalar
condensate due to the symmetry breaking suppresses the fluctuations of the
gauge field. Again, one can take  't Hooft solution \cite{hooft} for the scalar
field in the vicinity of the instanton with boundary conditions $\phi(x
\rightarrow \infty)= v$
\eq
\phi(x) = \frac{\sigma_i x_i}{(x^2 + \rho^2)^{\frac{1}{2}}}(0,v),
\en
and repeat the previous calculation. In the limit of $m^2(T) = 0$ and of a
small scalar self-coupling constant, one obtains
\eq
\langle F_{ij}^a F_{ij}^a\rangle(\phi) = A_F \frac{g_3^6}{\Gamma({15\over
2})2^{13 \over 2}}z^{15\over 2}K_{15\over 2}(z),
\en
where $K$ is a modified Bessel function and
\eq
z = \frac{3 \pi^2 v}{\sqrt{2}g_3}.
\label{z}
\en
As expected, the non-perturbative contribution decreases exponentially with the
field $\phi$, so that non-perturbative effects are frozen in the broken phase.
Again, it is difficult to estimate the corrections to this calculation;
however, the non-perturbative contribution coming from the gluon condensate has
the properties expected from the physical grounds, namely we are getting a
negative energy shift at the origin, and this shift exponentially decreases in
the broken phase.

To summarize, the effective potential for the scalar field, with the
contribution of the non-perturbative effects and for small $\lambda$ and
$m^2(T)$,  is likely to have an approximate form
\eq
V_{tot}= V_T(\phi) - \frac{T}{12}\langle F_{ij}^a F_{ij}^a\rangle(\phi).
\label{vtot}
\en
This potential is shown in Fig. 2 at different values of the temperature, for
$M_H = 90$ GeV and $A_F = 0.36$, as a function of $z$ and in Fig. 3 for $T=140$
GeV for small values of $z$. With this potential the temperature $T_a$ of the
absolute instability of the unbroken phase is given by
\eq
T_a^2 = \frac{T_0^2}{1 + \frac{16}{13}\pi^2g_W^2 A_F}
\en
and is smaller than $T_0$.

\section{Dynamics of the phase transition}
With  potential (\ref{vtot}) one can study the dynamics of the phase
transition. The crucial question here is the computation of the free energy of
the nucleating bubbles of the new phase. The standard procedure is to find an
extremum of the effective action for the scalar field \footnote{The
non-perturbative effects can also modify the kinetic term for the Higgs field
in addition to the modification of the potential. We do not attempt to estimate
the influence of this effect here.}
\eq
S_{eff} = \int d^3x (\frac{1}{2}\left(\partial_i \phi)^2 + V_{tot}\right)
\en
with boundary conditions $\phi(x) \rightarrow 0, x \rightarrow \infty$, and
$d\phi/dx = 0$ at $x=0$. The phase transition is complete at the temperature
$T_*$ at which the action for the bubble is about \cite{lindenp}
\eq
4 \log\left(\frac{M_{Pl}}{T}\right) \sim 160
\en
for the electroweak theory. As usual, $M_{Pl}$ is the Planck mass.
The problem can be solved numerically. The phase transition occurs at the
temperature $T_*$, smaller than the critical temperature $T_c$. For example, at
$A_F = 1~(0.36,~0.12)$ and $M_H = 130~(90,~60)$ GeV, the  actual temperature of
the phase transition is $T_* \simeq 145~(138,~120)$GeV. The corresponding
values of $T_0$ are equal to $320~(220,~150)$ GeV. The jump of the order
parameter is quite substantial. For all these examples  $\delta\phi \sim 1.6
T$.   So, non-perturbative effects seem to change the behaviour of the
effective potential at the origin and convert a weakly first-order phase
transition to a strongly first-order one, provided $A_F$ is not numerically
small.

Of course, there are many uncertainties in this computation. The main one is
associated with the fact that we are dealing with a confining theory and work
actually in a strong coupling regime. The accuracy of the dimensional reduction
with experimental $g_W$ is quite bad, since there is no hierarchy of scales
$M_M \ll M_D \ll T$, which allow  4-d dynamics to be separated from a 3-d one.
Numerically, all the scales are just the same and $\sim T$. It is not clear how
 this situation should be dealt with. Even inside our approach, at $T=T_*$,
$m^2(T)$ is not small (remember that we neglected it in a previous
computation), and the value of the scalar self-coupling is of the order of
$g_W^2$. We do not think, however that the accounting for the $m^2$ and
$\lambda$ can qualitatively change the conclusion that non-perturbative effects
can make the phase transition strongly first order\footnote{The phase
transition is stronger first order if $\epsilon_{vac}(T_0) <0$ in the unbroken
phase (see eq. (\ref{epsvac})). If $\langle (\phi^{\dagger}\phi)^2\rangle < 0$,
this is always true. If the scalar condensate $\langle
(\phi^{\dagger}\phi)^2\rangle >0$ and large enough, then the transition may be
more weakly first order than in perturbation theory for a sufficiently heavy
Higgs boson, $\lambda_3 > \frac{\langle F^2\rangle}{4\langle
(\phi^{\dagger}\phi)^2\rangle}$.}.

Some support for this observation comes from the 4-d \cite{bunk} and 3-d
\cite{kari} lattice simulation of the electroweak phase transition. In
particular, the data in \cite{kari} indicate that the actual temperature of the
electroweak phase transition is lower than the one predicted by perturbation
theory and that the actual region of metastability is larger. From \cite{bunk}
one sees that the actual jump of the order parameter is also larger than the
one from perturbation theory.

\section{Applications to the electroweak baryogenesis}
All electroweak baryogenesis mechanisms require a first-order phase transition.
Quantatively, the sphaleron mass in the broken phase must be sufficiently large
\cite{s:sm87},
\eq
M_{sph}(T)/T \simeq z_{vac}> 45
\en
in order for the baryonic asymmetry produced at the electroweak transition to
survive to the present time. Here $z_{vac}$ is the expectation value of the
variable $z$ defined by (\ref{z}). This requirement puts an upper bound on the
Higgs mass. The analysis of the one-loop perturbation theory  gives an upper
bound 45 GeV \cite{s:sm87}. As is argued above, non-perturbative effects change
the nature of the phase transition. With the form of the effective potential
advocated in this paper, the critical mass of the Higgs boson may be much
larger and depends on the unknown parameter $A_F$. For example, for $A_F =
1~(0.36,~0.12)$, $M_H^{crit} \simeq 130~(90,~60)$ GeV.  While the uncertainties
in these estimates may be  large, it seems clear that non-perturbative effects
may considerably increase $M_H^{crit}$. In other words, electroweak
baryogenesis can be possible with the experimentally allowed Higgs. At the same
time, the cosmological upper bound on the Higgs mass is still much stronger
than the one originating from triviality arguments. To establish the
cosmological bound with a high accuracy, the better understanding of the
non-perturbative effects in 3-d theories is required. The lattice simulations
can clarify the question. However, as shown in \cite{kari} the lattice size
should be huge in order to take into account all relevant effects.

Another important parameter for the electroweak baryogenesis is the thickness
of the domain wall $a$. With the effective potential derived with the use of
perturbation theory, one gets quite a thick wall. Say, with $M_H = 35$ GeV at
the transition point, $a \sim 40/T$. This value is larger than the mean free
path of the quarks in the plasma, which is estimated to be $l \sim 4/T$
\cite{lindeandson}. With our effective potential, the situation is different.
The domain-wall thickness is roughly the inverse mass of the Higgs boson in the
broken phase at $T=T_*$,
\eq
a \sim \frac{1}{g_w T}\sqrt{\frac{8 {T_*}^2}{3(T_0^2 - T_*^2)}}\sim
\frac{1-3}{T}
\en
for the critical value of the Higgs mass and $A_F = (1-0.1)$. This satisfies
the assumptions, made in the computation of the baryonic asymmetry of the
Universe in the standard electroweak theory \cite{ms,farrar}. To conclude, the
minimal standard model electroweak baryogenesis seems to be in good shape.

The non-perturbative effects in 3-d theory discussed in this paper may change
the dynamics of the grand unified phase transitions. In particular, the amount
of supercooling is expected to be larger than follows from the perturbation
theory. This may result in a prolongation of the inflation period. The study of
these questions is beyond the scope of this paper.

\section{Conclusion}
We have argued that the non-perturbative effects in 3d gauge theories
associated with confinement can change the dynamics of the high temperature
phase transitions in the gauge theories. These effects very likely generate the
condensates of different fields, like gluonic condensate, which decrease the
energy of the vacuum in the unbroken phase. This change results in the decrease
of the critical temperature of the phase transitions and create an additional
barrier separating the broken and unbroken phases. For the standard electroweak
model non-perturbative effects can make the phase transition to be strongly
first order and make an electroweak baryogenesis possible for the
experimentally allowed Higgs boson.

The author is deeply indebted to K. Kajantie, K. Rummukainen and A. Zhitnisky
for many valuable disscussions and suggestions. He is also grateful to K.
Farakos, G. Farrar, A. Kataev and I. Tkachev for helpful comments.
\begin{thebibliography}{99}

\bibitem{kir} D.A. Kirzhnitz, JETP Lett. 15 (1972) 529;\\
D.A. Kirzhnitz and A.D. Linde, Phys. Lett. 72B (1972) 471

\bibitem{dolan}L. Dolan and R. Jackiw, Phys.Rev. D9 (1974)3320

\bibitem{weinberg} S. Weinberg, Phys.Rev. D9 (1974) 3357

\bibitem{linde} D.A. Kirzhnitz and A.D. Linde, Ann. Phys. 101 (1976)
195;\\ A.D. Linde, Nucl. Phys. B216 (1983) 421, Rep. Prog. Phys. 47
(1984)925

\bibitem{takahashi} K. Takahashi, Phys. Rev. Lett. 56 (1986) 7

\bibitem{s:sm87} M.E. Shaposhnikov. Nucl. Phys. B287 (1987) 757; A.I. Bochkarev
and M.E. Shaposhnikov, Mod. Phys. Lett. 2A (1987) 417

\bibitem{anderson} G.W. Anderson and L.J. Hall, Phys. Rev. D45
(1992) 2685

\bibitem{ms} M.E. Shaposhnikov, Phys. Lett. B277 (1992)324; B282 (1992)
483(E);\\

\bibitem{carrington} M. Carrington, Phys. Rev. D45 (1992)
2933

\bibitem{lindeandson} M. Dine, R.G. Leigh, P. Huet, A. Linde and D.
Linde, Phys. Rev. D46 (1992) 550

\bibitem{enqvist} K. Enqvist, J. Ignatius, K. Kajantie and K.
Rummukainen, Phys. Rev. D45 (1992) 3415

\bibitem{brahm}
D.E. Brahm, C.G. Boyd and S.D.H Hsu, Preprint  EFI-92-22, 1992

\bibitem{ae} P. Arnold and E. Espinosa, Preprint UW/PT-92-18, 1992

\bibitem{eqz} M. Quiros, J.R. Espinosa and F. Zwirner, Preprint
CERN-TH.6577/92, 1992

\bibitem{buch} W. Buchm\"uller, Z. Fodor, T. Helbig and D. Walliser,
Preprint DESY 93-021, 1993

\bibitem{linde:pl80} A.D. Linde, Phys. Lett. 96B (1980) 289;

\bibitem{gpy} D.~Gross, R.~Pisarski and L.~Yaffe, Rev. Mod. Phys. 53 (1981) 43

\bibitem{jackiw} R. Jackiw and S. Templeton, Phys. Rev. D23 (1981) 2291

\bibitem{pis} T. Appelquist and R.D. Pisarski, Phys. Rev. D23 (1981) 2305

\bibitem{nadkarni} S. Nadkarni, Phys. Rev. D27 (1983) 917 and
D38 (1988) 3287

\bibitem{ginsparg} P. Ginsparg, Nucl. Phys. B170 (1980) 388

\bibitem{landsman} N.P. Landsman, Nucl. Phys. B322 (1989) 498

\bibitem{kari} K. Kajantie, K. Rummukainen and M. Shaposhnikov, CERN preprint
CERN-TH.6901/93, 1993

\bibitem{hooft}G. 't Hooft, Phys. Rev. Lett.  37 (1976) 8; Phys.Rev.
D14 (1976)3432.

\bibitem{kataev} K.G. Chetyrkin, A.L. Kataev and F.V. Tkachov, Phys. Lett. B85
(1979) 277;\\
M. Dine and J. Sapirstein, Phys. Rev. Lett. 43 (1979) 668;\\
S.G. Gorishny, A.L. Kataev and S.A. Larin, Phys. Lett. 212B (1988) 238

\bibitem{hooftqcd}G.'t Hooft, Nucl. Phys. B75 (1974) 461

\bibitem{vzs} A. Vainshtein, V. Zakharov and M. Shifman, JETP Lett. 27 (1978)
55.

\bibitem{zh} A.R. Zhitnitski, Sov. J. Nucl. Phys. 43 (1986) 999; Phys. Lett.
B165 (1985) 405

\bibitem{nsvz} V. Novikov, M. Shifman, A. Vainshtein and V. Zakharov, Nucl.
Phys. B147 (1979) 385, 448, 519

\bibitem{kks:magn}A.~Irb\"ack and C.~Peterson, Phys. Lett. 174B (1986)
99

\bibitem{kks}G.~Koutsoumbas, K.~Farakos and S.~Sarantakos, Phys. Lett. 189B
(1986) 173

\bibitem{cornwall} J.M. Cornwall, Preprint UCLA/92/TEP/51, 1992

\bibitem{nsvz1}V. Novikov, M. Shifman, A. Vainshtein and V. Zakharov, Nucl.
Phys. B191 (1981) 301

\bibitem{zh1} A.R. Zhitnitski, Sov. J. Nucl. Phys. 44 (1986) 139

\bibitem{polyakov} A.M. Polyakov, Nucl. Phys. B120 (1977) 429

\bibitem{rubakov}V.A. Rubakov, Nucl. Phys. B256 (1985) 434.

\bibitem{armc} P. Arnold  and  L. McLerran, Phys.Rev. D36 (1987) 581

\bibitem{det}L.Carson, Xu Li, L. McLerran and R.T. Wang,
Phys. Rev. D42 (1990) 2127

\bibitem{lindenp} A.D. Linde, Nucl.Phys. B216 (1983) 421.

\bibitem{bunk} B. Bunk, E.-M. Ilgenfritz, J. Kripfganz, A. Schiller,
Phys.  Lett. B284 (1992) 371; Bielefeld Preprint BI-TP 92/46

\bibitem{farrar} G.R.~Farrar and M.E.~Shaposhnikov, Phys. Rev. Lett. 70 (1993)
2833;
 Preprint CERN-TH.6734/RU-93-11, 1993

\end{thebibliography}
\newpage
\begin{figure}%[h]
\vspace{-1cm}
\hspace{2cm}
\epsfig{file=fig1.ps,height=8cm}
\vspace{-3.5cm}
\caption[0]{The dependence of the quantity $\frac{T_c - T_0}{T_0}$ on the mass
of the Higgs boson for different values of the gluonic condensate. Curves 1,2,3
correspond to $A_F = 0,~0.12,~0.36$.}
\end{figure}
\begin{figure}%[h]
\vspace{-2cm}
\hspace{2.2cm}
\epsfig{file=fig2.ps,height=8cm}
\vspace{-1cm}
\caption[0]{Effective potential as a function of $z$ for $M_H = 90$ GeV and
$A_F = 0.36$ for different temperatures. Curve 1 - $T=220$ GeV, 2 - $199$ GeV,
3 - $190$ Gev,
4 - $150$ GeV. }
\end{figure}

\begin{figure}%[h]
%\vspace{-2cm}
\hspace{1.7cm}
\epsfig{file=fig3.ps,height=8cm}
\vspace{-3cm}
\caption[0]{Effective potential as a function of $z$ for $M_H = 90$ GeV and
$A_F = 0.36$ for $T=140$ GeV at small $z$.}
\end{figure}
\end{document}


%%%%fig1.ps


%!PS-Adobe-2.0
%%Title: UNTITLED
%%Creator: Draw
%%CreationDate: Fri Jun 11 10:47:50 1993
%%For: mshaposh
%%DocumentFonts: (atend)
%%Pages: (atend) 1
%%BoundingBox: (atend)
%%DocumentPaperSizes: Letter
%%Orientation: Portrait
%%NXNextStepVersion: 3.0
%%EndComments

%%BeginProcSet: /usr/lib/NextStep/printPackage.ps 3.0
%!
% NeXT Printing Package
% Version: 3.0
% Copyright: 1988, NeXT, Inc.

/__NXdef{1 index where{pop pop pop}{def}ifelse}bind def
/__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def
/UserObjects 10 array __NXdef
/defineuserobject{
	exch dup 1 add dup UserObjects length gt{
		array dup 0 UserObjects putinterval
		/UserObjects exch def
	}{pop}ifelse UserObjects exch 3 -1 roll put
}__NXbdef
/undefineuserobject{UserObjects exch null put}__NXbdef
/execuserobject{UserObjects exch get exec}__NXbdef
/__NXRectPath{4 2 roll moveto 1 index 0 rlineto
0 exch rlineto neg 0 rlineto closepath}__NXbdef
/__NXProcessRectArgs{
	1 index type /arraytype eq{
		exch 0 4 2 index length 1 sub{
			dup 3 add 1 exch{1 index exch get exch}for
			5 1 roll 5 index exec
		}for pop pop
	}{exec}ifelse
}__NXbdef
/rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs
grestore}__NXbdef
/rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef
/rectstroke{
	gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{
		{gsave __NXRectPath null concat stroke grestore}
		dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs
	}{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore
}__NXbdef
/_NXLevel2 systemdict /languagelevel known {languagelevel 2 ge}{false}ifelse
__NXdef
/xyshow{
	0 1 3 index length 1 sub{
		currentpoint 4 index 3 index 1 getinterval show
		3 index 3 index 2 mul 1 add get add exch
		3 index	3 index 2 mul get add exch moveto pop
	}for pop pop
}__NXbdef
/xshow{
	0 1 3 index length 1 sub{
		currentpoint 4 index 3 index 1 getinterval show
		exch 3 index 3 index get add exch moveto pop
	}for pop pop
}__NXbdef
/yshow{
	0 1 3 index length 1 sub{
		currentpoint 4 index 3 index 1 getinterval show
		3 index 3 index get add moveto pop
	}for pop pop
}__NXbdef
/arct{arcto pop pop pop pop}__NXbdef
/setbbox{pop pop pop pop}__NXbdef
/ucache{}__NXbdef
/ucachestatus{mark 0 0 0 0 0}__NXbdef
/setucacheparams{cleartomark}__NXbdef
/uappend{systemdict begin cvx exec end}__NXbdef
/ueofill{gsave newpath uappend eofill grestore}__NXbdef
/ufill{gsave newpath uappend fill grestore}__NXbdef
/ustroke{
	gsave newpath dup length 6 eq
	{exch uappend concat}{uappend}ifelse
	stroke grestore
}__NXbdef
/__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse
/ustrokepath{
	newpath dup length 6 eq{
		exch uappend __NXustrokepathMatrix currentmatrix exch concat
		strokepath setmatrix
	}{uappend strokepath}ifelse
} __NXbdef
/upath{
	[exch {/ucache cvx}if pathbbox /setbbox cvx
	 {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx
} __NXbdef
/setstrokeadjust{pop}__NXbdef
/currentstrokeadjust{false}__NXbdef
/selectfont{exch findfont exch
dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef
/_NXCombineArrays{
	counttomark dup 2 add index dup length 3 -1 roll {
		2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch
	}repeat pop pop pop
}__NXbdef
/flushgraphics{}def
/setwindowtype{pop pop}def
/currentwindowtype{pop 0}def
/setalpha{pop}def
/currentalpha{1.0}def
/hidecursor{}def
/obscurecursor{}def
/revealcursor{}def
/setcursor{4 {pop}repeat}bind def
/showcursor{}def
/NextStepEncoding where not{
/NextStepEncoding StandardEncoding 256 array copy def
0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave
/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis
/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute
/Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright
176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior
204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave
/aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute
/ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth
/ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute
/ucircumflex 246/udieresis/yacute 252/thorn/ydieresis]
{dup type /nametype eq
 {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse
}forall pop
/NextStepEncoding NextStepEncoding readonly def
/_NXfstr 128 string dup 0 (_NX) putinterval def
/_NXfindfont /findfont load def
/findfont{
 % Because we can never let NextStepEncoding get into
 % SharedFontDirectory, we cannot reencode a font to NextStepEncoding
 % if we are in shared mode.  So if currentshared is true,
 % we call the normal findfont and return that
 /currentshared where {pop currentshared} {false} ifelse
 {_NXfindfont}
 {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll
  getinterval cvn exch FontDirectory 2 index known
  {pop FontDirectory exch get}
  {_NXfindfont dup /Encoding get StandardEncoding eq
   {	dup length dict exch
	{1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall
	 dup /Encoding NextStepEncoding put definefont
	}{exch pop} ifelse
   }ifelse
 }ifelse
}bind def
}{pop}ifelse
/_NXImageString {/__NXImageString where{pop}{/__NXImageString 4000 string
__NXdef}ifelse __NXImageString}__NXbdef
/_NXDoImageOp{
	3 dict begin /parr 5 array def 1 index{dup}{1}ifelse /chans exch def
	chans 2 add 2 roll parr 0 chans getinterval astore pop
	5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1
add}ifelse
	4 index mul /totbytes exch def pop exch pop
	gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore
	{0 1 chans 1 sub{parr exch get exec length totbytes exch sub /totbytes exch
def}for totbytes 0 le{exit}if}loop end
}__NXbdef
/alphaimage{1 add _NXDoImageOp}def
_NXLevel2{
	/NXCalibratedRGBColorSpace where{pop}{
		/NXCalibratedRGBColorSpace
		{mark /NXCalibratedRGB /ColorSpace findresource exch pop}stopped
		{cleartomark /NXCalibratedRGB[/CIEBasedABC 2 dict dup begin
		/MatrixLMN[.4124 .2126 .0193 .3576 .7152 .1192 .1805 .0722 .9505]def
		/WhitePoint[.9505 1 1.089] def end] /ColorSpace defineresource}if def}ifelse
	/nxsetrgbcolor{NXCalibratedRGBColorSpace setcolorspace setcolor}__NXbdef
	/nxsetgray{dup dup nxsetrgbcolor}__NXbdef
	/_NXCalibratedImage{exch{array astore dup length true}{false}ifelse
		8 -1 roll{NXCalibratedRGBColorSpace setcolorspace}if
		8 dict dup 9 1 roll begin /ImageType 1 def /MultipleDataSources exch def
		currentcolorspace 0 get /Indexed eq{pop /Decode[0 2 6 index exp 1 sub]def}
		{2 mul dup array /Decode exch def 1 sub 0 1 3 -1 roll{Decode exch dup 2 mod
put}for}ifelse
		/DataSource exch def /ImageMatrix exch def
		/BitsPerComponent exch def /Height exch def /Width exch def end
image}__NXbdef
} {
	/setcmykcolor{
		1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll
		4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if
setrgbcolor}__NXbdef
	/currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef
	/colorimage{_NXDoImageOp}__NXbdef
	/nxsetrgbcolor{setrgbcolor}__NXbdef /nxsetgray{setgray}__NXbdef
	/setpattern{pop .5 setgray}__NXbdef
	/_NXCalibratedImage{dup 1 eq {pop pop image}{colorimage}ifelse pop}__NXbdef
} ifelse
/_NXSetCMYKOrRGB where{pop}{
	mark{systemdict /currentwindow get exec}stopped
	{{pop pop pop setcmykcolor}}{{nxsetrgbcolor pop pop pop pop}}ifelse
/_NXSetCMYKOrRGB exch def cleartomark
}ifelse
%%EndProcSet

gsave
-20 -28 translate
 /__NXbasematrix matrix currentmatrix def
grestore
%%EndProlog
%%BeginSetup
%%PaperSize: Letter
/oval {
    translate scale newpath 0.5 0.5 0.5 0 360 arc closepath
} def /line {
    moveto rlineto stroke
} def /setup {
    setlinewidth setlinecap setlinejoin gsave
} def /arrow {
    newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto
closepath gsave 0 setlinejoin stroke grestore fill neg rotate
} def
%%EndSetup

%%Page: 1 1
%%PageBoundingBox: 156 307 487 633
%%PageFonts: (atend)
%%BeginPageSetup
%%PaperSize: Letter
/__NXsheetsavetoken save def
36 36 translate
gsave
-20 -28 translate
 /__NXbasematrix matrix currentmatrix def
grestore
gsave
0 0 translate
%%EndPageSetup
gsave
0 0 540 720 rectclip
0 0 540 720 rectclip
0 0 0 setup
-15.000000 -55.000000 transform
gsave __NXbasematrix setmatrix itransform translate
0 0 612 792 rectclip

/__NXEPSSave save def /showpage {} def
_NXLevel2{/_NXsethsb where{pop}{/_NXsethsb /sethsbcolor load def}ifelse
/sethsbcolor{_NXsethsb currentrgbcolor nxsetrgbcolor}def
/setrgbcolor{nxsetrgbcolor}bind def /setgray{nxsetgray}bind def
/_NXcimage where{pop}{/_NXcimage /colorimage load def}ifelse /colorimage{dup 3
eq{true 2 index{1 index}{1}ifelse 7 add 1 roll
_NXCalibratedImage}{_NXcimage}ifelse}def}if
0 setgray 0 setlinecap 1 setlinewidth
0 setlinejoin 10 setmiterlimit [] 0 setdash newpath count /__NXEPSOpCount exch
def /__NXEPSDictCount countdictstack def
%%BeginDocument:
%!PS-Adobe-2.0
%%Title: crittemp.ma  -  /Net/nxth06/Users/mshaposh
%%Creator: Mathematica
%%CreationDate: Fri Jun 11 09:57:59 1993
%%For: mshaposh
%%DocumentFonts: (atend)
%%Pages: (atend) 1
%%BoundingBox: (atend)
%%DocumentPaperSizes: Letter
%%Orientation: Portrait
%%NXNextStepVersion: 3.0
%%EndComments

%%BeginProcSet: /usr/lib/NextStep/printPackage.ps 3.0
%!
% NeXT Printing Package
% Version: 3.0
% Copyright: 1988, NeXT, Inc.

/__NXdef{1 index where{pop pop pop}{def}ifelse}bind def
/__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def
/UserObjects 10 array __NXdef
/defineuserobject{
	exch dup 1 add dup UserObjects length gt{
		array dup 0 UserObjects putinterval
		/UserObjects exch def
	}{pop}ifelse UserObjects exch 3 -1 roll put
}__NXbdef
/undefineuserobject{UserObjects exch null put}__NXbdef
/execuserobject{UserObjects exch get exec}__NXbdef
/__NXRectPath{4 2 roll moveto 1 index 0 rlineto
0 exch rlineto neg 0 rlineto closepath}__NXbdef
/__NXProcessRectArgs{
	1 index type /arraytype eq{
		exch 0 4 2 index length 1 sub{
			dup 3 add 1 exch{1 index exch get exch}for
			5 1 roll 5 index exec
		}for pop pop
	}{exec}ifelse
}__NXbdef
/rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs
grestore}__NXbdef
/rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef
/rectstroke{
	gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{
		{gsave __NXRectPath null concat stroke grestore}
		dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs
	}{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore
}__NXbdef
/_NXLevel2 systemdict /languagelevel known {languagelevel 2 ge}{false}ifelse
__NXdef
/xyshow{
	0 1 3 index length 1 sub{
		currentpoint 4 index 3 index 1 getinterval show
		3 index 3 index 2 mul 1 add get add exch
		3 index	3 index 2 mul get add exch moveto pop
	}for pop pop
}__NXbdef
/xshow{
	0 1 3 index length 1 sub{
		currentpoint 4 index 3 index 1 getinterval show
		exch 3 index 3 index get add exch moveto pop
	}for pop pop
}__NXbdef
/yshow{
	0 1 3 index length 1 sub{
		currentpoint 4 index 3 index 1 getinterval show
		3 index 3 index get add moveto pop
	}for pop pop
}__NXbdef
/arct{arcto pop pop pop pop}__NXbdef
/setbbox{pop pop pop pop}__NXbdef
/ucache{}__NXbdef
/ucachestatus{mark 0 0 0 0 0}__NXbdef
/setucacheparams{cleartomark}__NXbdef
/uappend{systemdict begin cvx exec end}__NXbdef
/ueofill{gsave newpath uappend eofill grestore}__NXbdef
/ufill{gsave newpath uappend fill grestore}__NXbdef
/ustroke{
	gsave newpath dup length 6 eq
	{exch uappend concat}{uappend}ifelse
	stroke grestore
}__NXbdef
/__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse
/ustrokepath{
	newpath dup length 6 eq{
		exch uappend __NXustrokepathMatrix currentmatrix exch concat
		strokepath setmatrix
	}{uappend strokepath}ifelse
} __NXbdef
/upath{
	[exch {/ucache cvx}if pathbbox /setbbox cvx
	 {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx
} __NXbdef
/setstrokeadjust{pop}__NXbdef
/currentstrokeadjust{false}__NXbdef
/selectfont{exch findfont exch
dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef
/_NXCombineArrays{
	counttomark dup 2 add index dup length 3 -1 roll {
		2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch
	}repeat pop pop pop
}__NXbdef
/flushgraphics{}def
/setwindowtype{pop pop}def
/currentwindowtype{pop 0}def
/setalpha{pop}def
/currentalpha{1.0}def
/hidecursor{}def
/obscurecursor{}def
/revealcursor{}def
/setcursor{4 {pop}repeat}bind def
/showcursor{}def
/NextStepEncoding where not{
/NextStepEncoding StandardEncoding 256 array copy def
0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave
/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis
/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute
/Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright
176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior
204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave
/aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute
/ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth
/ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute
/ucircumflex 246/udieresis/yacute 252/thorn/ydieresis]
{dup type /nametype eq
 {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse
}forall pop
/NextStepEncoding NextStepEncoding readonly def
/_NXfstr 128 string dup 0 (_NX) putinterval def
/_NXfindfont /findfont load def
/findfont{
 % Because we can never let NextStepEncoding get into
 % SharedFontDirectory, we cannot reencode a font to NextStepEncoding
 % if we are in shared mode.  So if currentshared is true,
 % we call the normal findfont and return that
 /currentshared where {pop currentshared} {false} ifelse
 {_NXfindfont}
 {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll
  getinterval cvn exch FontDirectory 2 index known
  {pop FontDirectory exch get}
  {_NXfindfont dup /Encoding get StandardEncoding eq
   {	dup length dict exch
	{1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall
	 dup /Encoding NextStepEncoding put definefont
	}{exch pop} ifelse
   }ifelse
 }ifelse
}bind def
}{pop}ifelse
/_NXImageString {/__NXImageString where{pop}{/__NXImageString 4000 string
__NXdef}ifelse __NXImageString}__NXbdef
/_NXDoImageOp{
	3 dict begin /parr 5 array def 1 index{dup}{1}ifelse /chans exch def
	chans 2 add 2 roll parr 0 chans getinterval astore pop
	5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1
add}ifelse
	4 index mul /totbytes exch def pop exch pop
	gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore
	{0 1 chans 1 sub{parr exch get exec length totbytes exch sub /totbytes exch
def}for totbytes 0 le{exit}if}loop end
}__NXbdef
/alphaimage{1 add _NXDoImageOp}def
_NXLevel2{
	/NXCalibratedRGBColorSpace where{pop}{
		/NXCalibratedRGBColorSpace
		{mark /NXCalibratedRGB /ColorSpace findresource exch pop}stopped
		{cleartomark /NXCalibratedRGB[/CIEBasedABC 2 dict dup begin
		/MatrixLMN[.4124 .2126 .0193 .3576 .7152 .1192 .1805 .0722 .9505]def
		/WhitePoint[.9505 1 1.089] def end] /ColorSpace defineresource}if def}ifelse
	/nxsetrgbcolor{NXCalibratedRGBColorSpace setcolorspace setcolor}__NXbdef
	/nxsetgray{dup dup nxsetrgbcolor}__NXbdef
	/_NXCalibratedImage{exch{array astore dup length true}{false}ifelse
		8 -1 roll{NXCalibratedRGBColorSpace setcolorspace}if
		8 dict dup 9 1 roll begin /ImageType 1 def /MultipleDataSources exch def
		currentcolorspace 0 get /Indexed eq{pop /Decode[0 2 6 index exp 1 sub]def}
		{2 mul dup array /Decode exch def 1 sub 0 1 3 -1 roll{Decode exch dup 2 mod
put}for}ifelse
		/DataSource exch def /ImageMatrix exch def
		/BitsPerComponent exch def /Height exch def /Width exch def end
image}__NXbdef
} {
	/setcmykcolor{
		1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll
		4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if
setrgbcolor}__NXbdef
	/currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef
	/colorimage{_NXDoImageOp}__NXbdef
	/nxsetrgbcolor{setrgbcolor}__NXbdef /nxsetgray{setgray}__NXbdef
	/setpattern{pop .5 setgray}__NXbdef
	/_NXCalibratedImage{dup 1 eq {pop pop image}{colorimage}ifelse pop}__NXbdef
} ifelse
/_NXSetCMYKOrRGB where{pop}{
	mark{systemdict /currentwindow get exec}stopped
	{{pop pop pop setcmykcolor}}{{nxsetrgbcolor pop pop pop pop}}ifelse
/_NXSetCMYKOrRGB exch def cleartomark
}ifelse
%%EndProcSet

_NXLevel2{/_NXsethsb where{pop}{/_NXsethsb /sethsbcolor load def}ifelse
/sethsbcolor{_NXsethsb currentrgbcolor nxsetrgbcolor}def
/setrgbcolor{nxsetrgbcolor}bind def /setgray{nxsetgray}bind def
}if
gsave
-20 9972 translate
 /__NXbasematrix matrix currentmatrix def
grestore
%%EndProlog
%%BeginSetup
%%PaperSize: Letter
%%EndSetup

%%Page: 1 1
%%PageBoundingBox: 156 307 487 633
%%PageFonts: (atend)
%%BeginPageSetup
%%PaperSize: Letter
/__NXsheetsavetoken save def
0 0 translate
gsave
-20 9972 translate
 /__NXbasematrix matrix currentmatrix def
grestore
gsave
[1 0 0 -1 -19 10581] concat
19 9789 translate
%%EndPageSetup
gsave
0 0 612 792 rectclip
gsave
54 72 467 648 rectclip
1 setlinewidth 0 setgray
gsave
95 76 371.769226 230 rectclip
/Mnodistort true def
100 dict begin
/Mfixwid true def
/Mrot 0 def
/Mpstart {
    MathPictureStart
} bind def
/Mpend {
    MathPictureEnd
} bind def
/Mscale {
    0 1 0 1
    5 -1 roll
    MathScale
} bind def
/Plain	/Courier findfont def
/Bold	/Courier-Bold findfont def
/Italic /Courier-Oblique findfont def
/MathPictureStart {
	/Mimatrix
	 matrix currentmatrix
	def
	gsave
	newpath
	Mleft
	Mbottom
	translate
	1 -1 scale
	/Mtmatrix
	matrix currentmatrix
	def
	Plain
	Mfontsize scalefont
	setfont
	0 setgray
	0 setlinewidth
} bind def
/MathPictureEnd {
	grestore
} bind def
/MathSubStart {
        Mgmatrix Mtmatrix
        Mleft Mbottom
        Mwidth Mheight
        8 -2 roll
        moveto
        Mtmatrix setmatrix
        currentpoint
        Mgmatrix setmatrix
        10 -2 roll
        moveto
        Mtmatrix setmatrix
        currentpoint
        2 copy translate
        /Mtmatrix matrix currentmatrix def
        /Mleft 0 def
        /Mbottom 0 def
        3 -1 roll
        exch sub
        /Mheight exch def
        sub
        /Mwidth exch def
} bind def
/MathSubEnd {
        /Mheight exch def
        /Mwidth exch def
        /Mbottom exch def
        /Mleft exch def
        /Mtmatrix exch def
        dup setmatrix
        /Mgmatrix exch def
} bind def
/Mdot {
	moveto
	0 0 rlineto
	stroke
} bind def
/Mtetra {
	moveto
	lineto
	lineto
	lineto
	fill
} bind def
/Metetra {
	moveto
	lineto
	lineto
	lineto
	closepath
	gsave
	fill
	grestore
	0 setgray
	stroke
} bind def
/Mistroke {
	flattenpath
	0 0 0
	{
	4 2 roll
	pop pop
	}
	{
	4 -1 roll
	2 index
	sub dup mul
	4 -1 roll
	2 index
	sub dup mul
	add sqrt
	4 -1 roll
	add
	3 1 roll
	}
	{
	stop
	}
	{
	stop
	}
	pathforall
	pop pop
	currentpoint
	stroke
	moveto
	currentdash
	3 -1 roll
	add
	setdash
} bind def
/Mfstroke {
	stroke
	currentdash
	pop 0
	setdash
} bind def
/Mrotsboxa {
	gsave
	dup
	/Mrot
	exch def
	Mrotcheck
	Mtmatrix
	dup
	setmatrix
	7 1 roll
	4 index
	4 index
	translate
	rotate
	3 index
	-1 mul
	3 index
	-1 mul
	translate
	/Mtmatrix
	matrix
	currentmatrix
	def
	grestore
	Msboxa
	3  -1 roll
	/Mtmatrix
	exch def
	/Mrot
	0 def
} bind def
/Msboxa {
	newpath
	5 -1 roll
	Mvboxa
	pop
	Mboxout
	6 -1 roll
	5 -1 roll
	4 -1 roll
	Msboxa1
	5 -3 roll
	Msboxa1
	Mboxrot
	[
	7 -2 roll
	2 copy
	[
	3 1 roll
	10 -1 roll
	9 -1 roll
	]
	6 1 roll
	5 -2 roll
	]
} bind def
/Msboxa1 {
	sub
	2 div
	dup
	2 index
	1 add
	mul
	3 -1 roll
	-1 add
	3 -1 roll
	mul
} bind def
/Mvboxa	{
	Mfixwid
	{
	Mvboxa1
	}
	{
	dup
	Mwidthcal
	0 exch
	{
	add
	}
	forall
	exch
	Mvboxa1
	4 index
	7 -1 roll
	add
	4 -1 roll
	pop
	3 1 roll
	}
	ifelse
} bind def
/Mvboxa1 {
	gsave
	newpath
	[ true
	3 -1 roll
	{
	Mbbox
	5 -1 roll
	{
	0
	5 1 roll
	}
	{
	7 -1 roll
	exch sub
	(m) stringwidth pop
	.3 mul
	sub
	7 1 roll
	6 -1 roll
	4 -1 roll
	Mmin
	3 -1 roll
	5 index
	add
	5 -1 roll
	4 -1 roll
	Mmax
	4 -1 roll
	}
	ifelse
	false
	}
	forall
	{ stop } if
	counttomark
	1 add
	4 roll
	]
	grestore
} bind def
/Mbbox {
	0 0 moveto
	false charpath
	flattenpath
	pathbbox
	newpath
} bind def
/Mmin {
	2 copy
	gt
	{ exch } if
	pop
} bind def
/Mmax {
	2 copy
	lt
	{ exch } if
	pop
} bind def
/Mrotshowa {
	dup
	/Mrot
	exch def
	Mrotcheck
	Mtmatrix
	dup
	setmatrix
	7 1 roll
	4 index
	4 index
	translate
	rotate
	3 index
	-1 mul
	3 index
	-1 mul
	translate
	/Mtmatrix
	matrix
	currentmatrix
	def
	Mgmatrix setmatrix
	Mshowa
	/Mtmatrix
	exch def
	/Mrot 0 def
} bind def
/Mshowa {
	4 -2 roll
	moveto
	2 index
	Mtmatrix setmatrix
	Mvboxa
	7 1 roll
	Mboxout
	6 -1 roll
	5 -1 roll
	4 -1 roll
	Mshowa1
	4 1 roll
	Mshowa1
	rmoveto
	currentpoint
	Mfixwid
	{
	Mshowax
	}
	{
	Mshoway
	}
	ifelse
	pop pop pop pop
	Mgmatrix setmatrix
} bind def
/Mshowax {
	0 1
        4 index length
        -1 add
        {
        2 index
        4 index
        2 index
        get
        3 index
        add
        moveto
        4 index
        exch get
        show
        } for
} bind def
/Mshoway {
        3 index
        Mwidthcal
        5 1 roll
	0 1
	4 index length
	-1 add
	{
	2 index
	4 index
	2 index
	get
	3 index
	add
	moveto
	4 index
	exch get
	[
	6 index
	aload
	length
	2 add
	-1 roll
	{
	pop
	Strform
	stringwidth
	pop
	neg
	exch
	add
	0 rmoveto
	}
	exch
	kshow
	cleartomark
	} for
	pop
} bind def
/Mwidthcal {
	[
	exch
	{
	Mwidthcal1
	}
	forall
	]
	[
	exch
	dup
	Maxlen
	-1 add
	0 1
	3 -1 roll
	{
	[
	exch
	2 index
	{
	1 index
	Mget
	exch
	}
	forall
	pop
	Maxget
	exch
	}
	for
	pop
	]
	Mreva
} bind def
/Mreva	{
	[
	exch
	aload
	length
	-1 1
	{1 roll}
	for
	]
} bind def
/Mget	{
	1 index
	length
	-1 add
	1 index
	ge
	{
	get
	}
	{
	pop pop
	0
	}
	ifelse
} bind def
/Maxlen	{
	[
	exch
	{
	length
	}
	forall
	Maxget
} bind def
/Maxget	{
	counttomark
	-1 add
	1 1
	3 -1 roll
	{
	pop
	Mmax
	}
	for
	exch
	pop
} bind def
/Mwidthcal1 {
	[
	exch
	{
	Strform
	stringwidth
	pop
	}
	forall
	]
} bind def
/Strform {
	/tem (x) def
	tem 0
	3 -1 roll
	put
	tem
} bind def
/Mshowa1 {
	2 copy
	add
	4 1 roll
	sub
	mul
	sub
	-2 div
} bind def
/MathScale {
	Mwidth
	Mheight
	Mlp
	translate
	scale
	/Msaveaa exch def
	/Msavebb exch def
	/Msavecc exch def
	/Msavedd exch def
	/Mgmatrix
	matrix currentmatrix
	def
} bind def
/Mlp {
	3 copy
	Mlpfirst
	{
	Mnodistort
	{
	Mmin
	dup
	} if
	4 index
	2 index
	2 index
	Mlprun
	11 index
	11 -1 roll
	10 -4 roll
	Mlp1
	8 index
	9 -5 roll
	Mlp1
	4 -1 roll
	and
	{ exit } if
	3 -1 roll
	pop pop
	} loop
	exch
	3 1 roll
	7 -3 roll
	pop pop pop
} bind def
/Mlpfirst {
	3 -1 roll
	dup length
	2 copy
	-2 add
	get
	aload
	pop pop pop
	4 -2 roll
	-1 add
	get
	aload
	pop pop pop
	6 -1 roll
	3 -1 roll
	5 -1 roll
	sub
	dup /MsaveAx exch def
	div
	4 1 roll
	exch sub
	dup /MsaveAy exch def
	div
} bind def
/Mlprun {
	2 copy
	4 index
	0 get
	dup
	4 1 roll
	Mlprun1
	3 copy
	8 -2 roll
	9 -1 roll
	{
	3 copy
	Mlprun1
	3 copy
	11 -3 roll
	/gt Mlpminmax
	8 3 roll
	11 -3 roll
	/lt Mlpminmax
	8 3 roll
	} forall
	pop pop pop pop
	3 1 roll
	pop pop
	aload pop
	5 -1 roll
	aload pop
	exch
	6 -1 roll
	Mlprun2
	8 2 roll
	4 -1 roll
	Mlprun2
	6 2 roll
	3 -1 roll
	Mlprun2
	4 2 roll
	exch
	Mlprun2
	6 2 roll
} bind def
/Mlprun1 {
	aload pop
	exch
	6 -1 roll
	5 -1 roll
	mul add
	4 -2 roll
	mul
	3 -1 roll
	add
} bind def
/Mlprun2 {
	2 copy
	add 2 div
	3 1 roll
	exch sub
} bind def
/Mlpminmax {
	cvx
	2 index
	6 index
	2 index
	exec
	{
	7 -3 roll
	4 -1 roll
	} if
	1 index
	5 index
	3 -1 roll
	exec
	{
	4 1 roll
	pop
	5 -1 roll
	aload
	pop pop
	4 -1 roll
	aload pop
	[
	8 -2 roll
	pop
	5 -2 roll
	pop
	6 -2 roll
	pop
	5 -1 roll
	]
	4 1 roll
	pop
	}
	{
	pop pop pop
	} ifelse
} bind def
/Mlp1 {
	5 index
	3 index	sub
	5 index
	2 index mul
	1 index
	le
	1 index
	0 le
	or
	dup
	not
	{
	1 index
	3 index	div
	.99999 mul
	8 -1 roll
	pop
	7 1 roll
	}
	if
	8 -1 roll
	2 div
	7 -2 roll
	pop sub
	5 index
	6 -3 roll
	pop pop
	mul sub
	exch
} bind def
/intop 0 def
/inrht 0 def
/inflag 0 def
/outflag 0 def
/xadrht 0 def
/xadlft 0 def
/yadtop 0 def
/yadbot 0 def
/Minner {
	outflag
	1
	eq
	{
	/outflag 0 def
	/intop 0 def
	/inrht 0 def
	} if
	5 index
	gsave
	Mtmatrix setmatrix
	Mvboxa pop
	grestore
	3 -1 roll
	pop
	dup
	intop
	gt
	{
	/intop
	exch def
	}
	{ pop }
	ifelse
	dup
	inrht
	gt
	{
	/inrht
	exch def
	}
	{ pop }
	ifelse
	pop
	/inflag
	1 def
} bind def
/Mouter {
	/xadrht 0 def
	/xadlft 0 def
	/yadtop 0 def
	/yadbot 0 def
	inflag
	1 eq
	{
	dup
	0 lt
	{
	dup
	intop
	mul
	neg
	/yadtop
	exch def
	} if
	dup
	0 gt
	{
	dup
	intop
	mul
	/yadbot
	exch def
	}
	if
	pop
	dup
	0 lt
	{
	dup
	inrht
	mul
	neg
	/xadrht
	exch def
	} if
	dup
	0 gt
	{
	dup
	inrht
	mul
	/xadlft
	exch def
	} if
	pop
	/outflag 1 def
	}
	{ pop pop}
	ifelse
	/inflag 0 def
	/inrht 0 def
	/intop 0 def
} bind def
/Mboxout {
	outflag
	1
	eq
	{
	4 -1
	roll
	xadlft
	leadjust
	add
	sub
	4 1 roll
	3 -1
	roll
	yadbot
	leadjust
	add
	sub
	3 1
	roll
	exch
	xadrht
	leadjust
	add
	add
	exch
	yadtop
	leadjust
	add
	add
	/outflag 0 def
	/xadlft 0 def
	/yadbot 0 def
	/xadrht 0 def
	/yadtop 0 def
	} if
} bind def
/leadjust {
	(m) stringwidth pop
	.5 mul
} bind def
/Mrotcheck {
	dup
	90
	eq
	{
	yadbot
	/yadbot
	xadrht
	def
	/xadrht
	yadtop
	def
	/yadtop
	xadlft
	def
	/xadlft
	exch
	def
	}
	if
	dup
	cos
	1 index
	sin
	Checkaux
	dup
	cos
	1 index
	sin neg
	exch
	Checkaux
	3 1 roll
	pop pop
} bind def
/Checkaux {
	4 index
	exch
	4 index
	mul
	3 1 roll
	mul add
	4 1 roll
} bind def
/Mboxrot {
	Mrot
	90 eq
	{
	brotaux
	4 2
	roll
	}
	if
	Mrot
	180 eq
	{
	4 2
        roll
	brotaux
	4 2
	roll
	brotaux
	}
	if
	Mrot
	270 eq
	{
	4 2
	roll
	brotaux
	}
	if
} bind def
/brotaux {
	neg
	exch
	neg
} bind def
/Mabswid {
	Mimatrix
	0 get
	Mgmatrix
	0 get
	div
	mul
	setlinewidth
} bind def
/Mabsdash {
	exch
	Mimatrix
	0 get
	Mgmatrix
	0 get
	div
	[
	3 1 roll
	exch
	{
	exch
	dup
	3 -1 roll
	mul
	exch
	}
	forall
	pop ]
	exch
	setdash
} bind def
/colorimage where
{ pop }
{
/colorimage {
3 1 roll
 pop pop
 5 -1 roll
 mul
 4 1 roll
{
currentfile
1 index
readhexstring
pop }
image
} bind def
} ifelse
/sampledsound where
{ pop}
{ /sampledsound {
exch
pop
exch
5 1 roll
mul
4 idiv
mul
2 idiv
exch pop
exch
/Mtempproc exch def
{ Mtempproc pop }
repeat
} bind def
} ifelse

/Mleft		95.000000 def
/Mbottom	306.047974 def
/Mwidth		371.769226 def
/Mheight	230.047974 def
/Mfontsize 12 def
/Plain /Courier findfont def
%!
%%Creator: Mathematica
%%AspectRatio: 0.61803
MathPictureStart
/Courier findfont 10  scalefont  setfont
% Scaling calculations
-0.716931 0.021164 0.531999 1.94974 [
[(40)] 0.12963 0 0 2 Msboxa
[(50)] 0.34127 0 0 2 Msboxa
[(60)] 0.55291 0 0 2 Msboxa
[(70)] 0.76455 0 0 2 Msboxa
[(80)] 0.97619 0 0 2 Msboxa
[(-0.25)] -0.0125 0.04456 1 0 Msboxa
[(-0.2)] -0.0125 0.14205 1 0 Msboxa
[(-0.15)] -0.0125 0.23954 1 0 Msboxa
[(-0.1)] -0.0125 0.33703 1 0 Msboxa
[(-0.05)] -0.0125 0.43451 1 0 Msboxa
[(0)] -0.0125 0.532 1 0 Msboxa
[ -0.001 -0.001 0 0 ]
[ 1.001 0.61903 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
%%Object: Graphics
[ ] 0 setdash
0 setgray
gsave
gsave
0.002 setlinewidth
0.12963 0 moveto
0.12963 0.00625 lineto
stroke
grestore
[(40)] 0.12963 0 0 2 Mshowa
gsave
0.002 setlinewidth
0.34127 0 moveto
0.34127 0.00625 lineto
stroke
grestore
[(50)] 0.34127 0 0 2 Mshowa
gsave
0.002 setlinewidth
0.55291 0 moveto
0.55291 0.00625 lineto
stroke
grestore
[(60)] 0.55291 0 0 2 Mshowa
gsave
0.002 setlinewidth
0.76455 0 moveto
0.76455 0.00625 lineto
stroke
grestore
[(70)] 0.76455 0 0 2 Mshowa
gsave
0.002 setlinewidth
0.97619 0 moveto
0.97619 0.00625 lineto
stroke
grestore
[(80)] 0.97619 0 0 2 Mshowa
gsave
0.001 setlinewidth
0.17196 0 moveto
0.17196 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.21429 0 moveto
0.21429 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.25661 0 moveto
0.25661 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.29894 0 moveto
0.29894 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.3836 0 moveto
0.3836 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.42593 0 moveto
0.42593 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.46825 0 moveto
0.46825 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.51058 0 moveto
0.51058 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.59524 0 moveto
0.59524 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.63757 0 moveto
0.63757 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.67989 0 moveto
0.67989 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.72222 0 moveto
0.72222 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.80688 0 moveto
0.80688 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.84921 0 moveto
0.84921 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.89153 0 moveto
0.89153 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.93386 0 moveto
0.93386 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.0873 0 moveto
0.0873 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.04497 0 moveto
0.04497 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.00265 0 moveto
0.00265 0.00375 lineto
stroke
grestore
gsave
0.002 setlinewidth
0 0 moveto
1 0 lineto
stroke
grestore
gsave
0.002 setlinewidth
0 0.04456 moveto
0.00625 0.04456 lineto
stroke
grestore
[(-0.25)] -0.0125 0.04456 1 0 Mshowa
gsave
0.002 setlinewidth
0 0.14205 moveto
0.00625 0.14205 lineto
stroke
grestore
[(-0.2)] -0.0125 0.14205 1 0 Mshowa
gsave
0.002 setlinewidth
0 0.23954 moveto
0.00625 0.23954 lineto
stroke
grestore
[(-0.15)] -0.0125 0.23954 1 0 Mshowa
gsave
0.002 setlinewidth
0 0.33703 moveto
0.00625 0.33703 lineto
stroke
grestore
[(-0.1)] -0.0125 0.33703 1 0 Mshowa
gsave
0.002 setlinewidth
0 0.43451 moveto
0.00625 0.43451 lineto
stroke
grestore
[(-0.05)] -0.0125 0.43451 1 0 Mshowa
gsave
0.002 setlinewidth
0 0.532 moveto
0.00625 0.532 lineto
stroke
grestore
[(0)] -0.0125 0.532 1 0 Mshowa
gsave
0.001 setlinewidth
0 0.06406 moveto
0.00375 0.06406 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.08356 moveto
0.00375 0.08356 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.10306 moveto
0.00375 0.10306 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.12255 moveto
0.00375 0.12255 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.16155 moveto
0.00375 0.16155 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.18105 moveto
0.00375 0.18105 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.20054 moveto
0.00375 0.20054 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.22004 moveto
0.00375 0.22004 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.25904 moveto
0.00375 0.25904 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.27853 moveto
0.00375 0.27853 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.29803 moveto
0.00375 0.29803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.31753 moveto
0.00375 0.31753 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.35652 moveto
0.00375 0.35652 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.37602 moveto
0.00375 0.37602 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.39552 moveto
0.00375 0.39552 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.41501 moveto
0.00375 0.41501 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.45401 moveto
0.00375 0.45401 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.47351 moveto
0.00375 0.47351 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.493 moveto
0.00375 0.493 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.5125 moveto
0.00375 0.5125 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.02507 moveto
0.00375 0.02507 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.00557 moveto
0.00375 0.00557 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.5515 moveto
0.00375 0.5515 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.57099 moveto
0.00375 0.57099 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.59049 moveto
0.00375 0.59049 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.60999 moveto
0.00375 0.60999 lineto
stroke
grestore
gsave
0.002 setlinewidth
0 0 moveto
0 0.61803 lineto
stroke
grestore
grestore
gsave
gsave
0.002 setlinewidth
0.12963 0.61178 moveto
0.12963 0.61803 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.34127 0.61178 moveto
0.34127 0.61803 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.55291 0.61178 moveto
0.55291 0.61803 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.76455 0.61178 moveto
0.76455 0.61803 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.97619 0.61178 moveto
0.97619 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.17196 0.61428 moveto
0.17196 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.21429 0.61428 moveto
0.21429 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.25661 0.61428 moveto
0.25661 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.29894 0.61428 moveto
0.29894 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.3836 0.61428 moveto
0.3836 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.42593 0.61428 moveto
0.42593 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.46825 0.61428 moveto
0.46825 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.51058 0.61428 moveto
0.51058 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.59524 0.61428 moveto
0.59524 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.63757 0.61428 moveto
0.63757 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.67989 0.61428 moveto
0.67989 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.72222 0.61428 moveto
0.72222 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.80688 0.61428 moveto
0.80688 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.84921 0.61428 moveto
0.84921 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.89153 0.61428 moveto
0.89153 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.93386 0.61428 moveto
0.93386 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.0873 0.61428 moveto
0.0873 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.04497 0.61428 moveto
0.04497 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.00265 0.61428 moveto
0.00265 0.61803 lineto
stroke
grestore
gsave
0.002 setlinewidth
0 0.61803 moveto
1 0.61803 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.99375 0.04456 moveto
1 0.04456 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.99375 0.14205 moveto
1 0.14205 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.99375 0.23954 moveto
1 0.23954 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.99375 0.33703 moveto
1 0.33703 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.99375 0.43451 moveto
1 0.43451 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.99375 0.532 moveto
1 0.532 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.06406 moveto
1 0.06406 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.08356 moveto
1 0.08356 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.10306 moveto
1 0.10306 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.12255 moveto
1 0.12255 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.16155 moveto
1 0.16155 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.18105 moveto
1 0.18105 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.20054 moveto
1 0.20054 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.22004 moveto
1 0.22004 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.25904 moveto
1 0.25904 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.27853 moveto
1 0.27853 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.29803 moveto
1 0.29803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.31753 moveto
1 0.31753 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.35652 moveto
1 0.35652 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.37602 moveto
1 0.37602 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.39552 moveto
1 0.39552 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.41501 moveto
1 0.41501 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.45401 moveto
1 0.45401 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.47351 moveto
1 0.47351 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.493 moveto
1 0.493 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.5125 moveto
1 0.5125 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.02507 moveto
1 0.02507 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.00557 moveto
1 0.00557 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.5515 moveto
1 0.5515 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.57099 moveto
1 0.57099 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.59049 moveto
1 0.59049 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.60999 moveto
1 0.60999 lineto
stroke
grestore
gsave
0.002 setlinewidth
1 0 moveto
1 0.61803 lineto
stroke
grestore
grestore
gsave
grestore
0 0 moveto
1 0 lineto
1 0.61803 lineto
0 0.61803 lineto
closepath
clip
newpath
gsave
gsave
gsave
gsave
0.004 setlinewidth
0.02381 0.59609 moveto
0.06349 0.58655 lineto
0.10317 0.57808 lineto
0.14286 0.57036 lineto
0.18254 0.56318 lineto
0.22222 0.55634 lineto
0.2619 0.54969 lineto
0.30159 0.54311 lineto
0.34127 0.53649 lineto
0.38095 0.52975 lineto
0.42063 0.52279 lineto
0.46032 0.51555 lineto
0.5 0.50796 lineto
0.53968 0.49995 lineto
0.57937 0.49146 lineto
0.61905 0.48243 lineto
0.65873 0.47281 lineto
0.69841 0.46253 lineto
0.7381 0.45155 lineto
0.77778 0.4398 lineto
0.81746 0.42724 lineto
0.85714 0.41381 lineto
0.89683 0.39944 lineto
0.93651 0.3841 lineto
0.97619 0.36771 lineto
stroke
grestore
grestore
grestore
gsave
gsave
gsave
0.004 setlinewidth
0.02381 0.58163 moveto
0.06349 0.56898 lineto
0.10317 0.55692 lineto
0.14286 0.54507 lineto
0.18254 0.53315 lineto
0.22222 0.52092 lineto
0.2619 0.50818 lineto
0.30159 0.49475 lineto
0.34127 0.48044 lineto
0.38095 0.46511 lineto
0.42063 0.4486 lineto
0.46032 0.43078 lineto
0.5 0.4115 lineto
0.53968 0.39061 lineto
0.57937 0.36799 lineto
0.61905 0.34348 lineto
0.65873 0.31696 lineto
0.69841 0.28828 lineto
0.7381 0.2573 lineto
0.77778 0.22387 lineto
0.81746 0.18784 lineto
0.85714 0.14906 lineto
0.89683 0.10739 lineto
0.93651 0.06266 lineto
0.97619 0.01472 lineto
stroke
grestore
grestore
grestore
gsave
gsave
gsave
0.004 setlinewidth
0.02381 0.60332 moveto
0.06349 0.59533 lineto
0.10317 0.58866 lineto
0.14286 0.58301 lineto
0.18254 0.57819 lineto
0.22222 0.57404 lineto
0.2619 0.57044 lineto
0.30159 0.56729 lineto
0.34127 0.56452 lineto
0.38095 0.56207 lineto
0.42063 0.55989 lineto
0.46032 0.55794 lineto
0.5 0.5562 lineto
0.53968 0.55462 lineto
0.57937 0.5532 lineto
0.61905 0.55191 lineto
0.65873 0.55073 lineto
0.69841 0.54966 lineto
0.7381 0.54868 lineto
0.77778 0.54777 lineto
0.81746 0.54694 lineto
0.85714 0.54618 lineto
0.89683 0.54547 lineto
0.93651 0.54481 lineto
0.97619 0.54421 lineto
stroke
grestore
grestore
grestore
grestore
% End of Graphics
MathPictureEnd%%PSTrailer
end

%%PageTrailer
%%DocumentFonts: Times-Roman
%%Trailer
%%DocumentFonts: Times-Roman
%%Pages: 1 1
%%BoundingBox:156 307 487 633


%%EndDocument
count __NXEPSOpCount sub {pop} repeat countdictstack __NXEPSDictCount sub {end}
repeat __NXEPSSave restore
grestore
grestore
0 0 0 setup
gsave
/Helvetica findfont 12 scalefont [1 0 0 -1 0 0] makefont
10
exch
defineuserobject
10 execuserobject setfont
0 nxsetgray
[1 0 0 -1 0 859] concat
10 execuserobject setfont
0 nxsetgray
404 434 moveto (Mh) show
grestore
grestore
0 0 0 setup
gsave
10 execuserobject setfont
0 nxsetgray
[1 0 0 -1 0 1287] concat
10 execuserobject setfont
0 nxsetgray
50 648 moveto (\(Tc-To\)/To) show
grestore
grestore
0 0 0 setup
gsave
10 execuserobject setfont
0 nxsetgray
[1 0 0 -1 0 1285] concat
10 execuserobject setfont
0 nxsetgray
389 647 moveto (1) show
grestore
grestore
0 0 0 setup
gsave
10 execuserobject setfont
0 nxsetgray
[1 0 0 -1 0 1195] concat
10 execuserobject setfont
0 nxsetgray
408 602 moveto (2) show
grestore
grestore
0 0 0 setup
grestore
0 setgray
0.333333 setgray
gsave
0 0 540 720 rectclip
[1 0 0 -1 0 720] concat
gsave
1 nxsetgray
400 202 12 15 rectfill
10 execuserobject setfont
0 nxsetgray
402 214 moveto (3) show
grestore
grestore
grestore
grestore
showpage
__NXsheetsavetoken restore
%%PageTrailer
%%DocumentFonts: Helvetica
%%Trailer
%%DocumentFonts: Helvetica
%%Pages: 1 1
%%BoundingBox:156 307 487 633



%%%%fig2.ps


%!PS-Adobe-2.0
%%Title: UNTITLED
%%Creator: Draw
%%CreationDate: Fri Jun 11 10:37:01 1993
%%For: mshaposh
%%DocumentFonts: (atend)
%%Pages: (atend) 1
%%BoundingBox: (atend)
%%DocumentPaperSizes: Letter
%%Orientation: Portrait
%%NXNextStepVersion: 3.0
%%EndComments

%%BeginProcSet: /usr/lib/NextStep/printPackage.ps 3.0
%!
% NeXT Printing Package
% Version: 3.0
% Copyright: 1988, NeXT, Inc.

/__NXdef{1 index where{pop pop pop}{def}ifelse}bind def
/__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def
/UserObjects 10 array __NXdef
/defineuserobject{
	exch dup 1 add dup UserObjects length gt{
		array dup 0 UserObjects putinterval
		/UserObjects exch def
	}{pop}ifelse UserObjects exch 3 -1 roll put
}__NXbdef
/undefineuserobject{UserObjects exch null put}__NXbdef
/execuserobject{UserObjects exch get exec}__NXbdef
/__NXRectPath{4 2 roll moveto 1 index 0 rlineto
0 exch rlineto neg 0 rlineto closepath}__NXbdef
/__NXProcessRectArgs{
	1 index type /arraytype eq{
		exch 0 4 2 index length 1 sub{
			dup 3 add 1 exch{1 index exch get exch}for
			5 1 roll 5 index exec
		}for pop pop
	}{exec}ifelse
}__NXbdef
/rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs
grestore}__NXbdef
/rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef
/rectstroke{
	gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{
		{gsave __NXRectPath null concat stroke grestore}
		dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs
	}{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore
}__NXbdef
/_NXLevel2 systemdict /languagelevel known {languagelevel 2 ge}{false}ifelse
__NXdef
/xyshow{
	0 1 3 index length 1 sub{
		currentpoint 4 index 3 index 1 getinterval show
		3 index 3 index 2 mul 1 add get add exch
		3 index	3 index 2 mul get add exch moveto pop
	}for pop pop
}__NXbdef
/xshow{
	0 1 3 index length 1 sub{
		currentpoint 4 index 3 index 1 getinterval show
		exch 3 index 3 index get add exch moveto pop
	}for pop pop
}__NXbdef
/yshow{
	0 1 3 index length 1 sub{
		currentpoint 4 index 3 index 1 getinterval show
		3 index 3 index get add moveto pop
	}for pop pop
}__NXbdef
/arct{arcto pop pop pop pop}__NXbdef
/setbbox{pop pop pop pop}__NXbdef
/ucache{}__NXbdef
/ucachestatus{mark 0 0 0 0 0}__NXbdef
/setucacheparams{cleartomark}__NXbdef
/uappend{systemdict begin cvx exec end}__NXbdef
/ueofill{gsave newpath uappend eofill grestore}__NXbdef
/ufill{gsave newpath uappend fill grestore}__NXbdef
/ustroke{
	gsave newpath dup length 6 eq
	{exch uappend concat}{uappend}ifelse
	stroke grestore
}__NXbdef
/__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse
/ustrokepath{
	newpath dup length 6 eq{
		exch uappend __NXustrokepathMatrix currentmatrix exch concat
		strokepath setmatrix
	}{uappend strokepath}ifelse
} __NXbdef
/upath{
	[exch {/ucache cvx}if pathbbox /setbbox cvx
	 {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx
} __NXbdef
/setstrokeadjust{pop}__NXbdef
/currentstrokeadjust{false}__NXbdef
/selectfont{exch findfont exch
dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef
/_NXCombineArrays{
	counttomark dup 2 add index dup length 3 -1 roll {
		2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch
	}repeat pop pop pop
}__NXbdef
/flushgraphics{}def
/setwindowtype{pop pop}def
/currentwindowtype{pop 0}def
/setalpha{pop}def
/currentalpha{1.0}def
/hidecursor{}def
/obscurecursor{}def
/revealcursor{}def
/setcursor{4 {pop}repeat}bind def
/showcursor{}def
/NextStepEncoding where not{
/NextStepEncoding StandardEncoding 256 array copy def
0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave
/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis
/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute
/Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright
176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior
204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave
/aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute
/ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth
/ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute
/ucircumflex 246/udieresis/yacute 252/thorn/ydieresis]
{dup type /nametype eq
 {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse
}forall pop
/NextStepEncoding NextStepEncoding readonly def
/_NXfstr 128 string dup 0 (_NX) putinterval def
/_NXfindfont /findfont load def
/findfont{
 % Because we can never let NextStepEncoding get into
 % SharedFontDirectory, we cannot reencode a font to NextStepEncoding
 % if we are in shared mode.  So if currentshared is true,
 % we call the normal findfont and return that
 /currentshared where {pop currentshared} {false} ifelse
 {_NXfindfont}
 {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll
  getinterval cvn exch FontDirectory 2 index known
  {pop FontDirectory exch get}
  {_NXfindfont dup /Encoding get StandardEncoding eq
   {	dup length dict exch
	{1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall
	 dup /Encoding NextStepEncoding put definefont
	}{exch pop} ifelse
   }ifelse
 }ifelse
}bind def
}{pop}ifelse
/_NXImageString {/__NXImageString where{pop}{/__NXImageString 4000 string
__NXdef}ifelse __NXImageString}__NXbdef
/_NXDoImageOp{
	3 dict begin /parr 5 array def 1 index{dup}{1}ifelse /chans exch def
	chans 2 add 2 roll parr 0 chans getinterval astore pop
	5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1
add}ifelse
	4 index mul /totbytes exch def pop exch pop
	gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore
	{0 1 chans 1 sub{parr exch get exec length totbytes exch sub /totbytes exch
def}for totbytes 0 le{exit}if}loop end
}__NXbdef
/alphaimage{1 add _NXDoImageOp}def
_NXLevel2{
	/NXCalibratedRGBColorSpace where{pop}{
		/NXCalibratedRGBColorSpace
		{mark /NXCalibratedRGB /ColorSpace findresource exch pop}stopped
		{cleartomark /NXCalibratedRGB[/CIEBasedABC 2 dict dup begin
		/MatrixLMN[.4124 .2126 .0193 .3576 .7152 .1192 .1805 .0722 .9505]def
		/WhitePoint[.9505 1 1.089] def end] /ColorSpace defineresource}if def}ifelse
	/nxsetrgbcolor{NXCalibratedRGBColorSpace setcolorspace setcolor}__NXbdef
	/nxsetgray{dup dup nxsetrgbcolor}__NXbdef
	/_NXCalibratedImage{exch{array astore dup length true}{false}ifelse
		8 -1 roll{NXCalibratedRGBColorSpace setcolorspace}if
		8 dict dup 9 1 roll begin /ImageType 1 def /MultipleDataSources exch def
		currentcolorspace 0 get /Indexed eq{pop /Decode[0 2 6 index exp 1 sub]def}
		{2 mul dup array /Decode exch def 1 sub 0 1 3 -1 roll{Decode exch dup 2 mod
put}for}ifelse
		/DataSource exch def /ImageMatrix exch def
		/BitsPerComponent exch def /Height exch def /Width exch def end
image}__NXbdef
} {
	/setcmykcolor{
		1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll
		4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if
setrgbcolor}__NXbdef
	/currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef
	/colorimage{_NXDoImageOp}__NXbdef
	/nxsetrgbcolor{setrgbcolor}__NXbdef /nxsetgray{setgray}__NXbdef
	/setpattern{pop .5 setgray}__NXbdef
	/_NXCalibratedImage{dup 1 eq {pop pop image}{colorimage}ifelse pop}__NXbdef
} ifelse
/_NXSetCMYKOrRGB where{pop}{
	mark{systemdict /currentwindow get exec}stopped
	{{pop pop pop setcmykcolor}}{{nxsetrgbcolor pop pop pop pop}}ifelse
/_NXSetCMYKOrRGB exch def cleartomark
}ifelse
%%EndProcSet

gsave
-20 -28 translate
 /__NXbasematrix matrix currentmatrix def
grestore
%%EndProlog
%%BeginSetup
%%PaperSize: Letter
/oval {
    translate scale newpath 0.5 0.5 0.5 0 360 arc closepath
} def /line {
    moveto rlineto stroke
} def /setup {
    setlinewidth setlinecap setlinejoin gsave
} def /arrow {
    newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto
closepath gsave 0 setlinejoin stroke grestore fill neg rotate
} def
%%EndSetup

%%Page: 1 1
%%PageBoundingBox: 156 307 487 633
%%PageFonts: (atend)
%%BeginPageSetup
%%PaperSize: Letter
/__NXsheetsavetoken save def
36 36 translate
gsave
-20 -28 translate
 /__NXbasematrix matrix currentmatrix def
grestore
gsave
0 0 translate
%%EndPageSetup
gsave
0 0 540 720 rectclip
0 0 540 720 rectclip
0 0 0 setup
-38.000000 -176.000000 transform
gsave __NXbasematrix setmatrix itransform translate
0 0 612 792 rectclip

/__NXEPSSave save def /showpage {} def
_NXLevel2{/_NXsethsb where{pop}{/_NXsethsb /sethsbcolor load def}ifelse
/sethsbcolor{_NXsethsb currentrgbcolor nxsetrgbcolor}def
/setrgbcolor{nxsetrgbcolor}bind def /setgray{nxsetgray}bind def
/_NXcimage where{pop}{/_NXcimage /colorimage load def}ifelse /colorimage{dup 3
eq{true 2 index{1 index}{1}ifelse 7 add 1 roll
_NXCalibratedImage}{_NXcimage}ifelse}def}if
0 setgray 0 setlinecap 1 setlinewidth
0 setlinejoin 10 setmiterlimit [] 0 setdash newpath count /__NXEPSOpCount exch
def /__NXEPSDictCount countdictstack def
%%BeginDocument:
%!PS-Adobe-2.0
%%Title: sphal.ma  -  /Net/nxth06/Users/mshaposh
%%Creator: Mathematica
%%CreationDate: Fri Jun 11 10:22:05 1993
%%For: mshaposh
%%DocumentFonts: (atend)
%%Pages: (atend) 1
%%BoundingBox: (atend)
%%DocumentPaperSizes: Letter
%%Orientation: Portrait
%%NXNextStepVersion: 3.0
%%EndComments

%%BeginProcSet: /usr/lib/NextStep/printPackage.ps 3.0
%!
% NeXT Printing Package
% Version: 3.0
% Copyright: 1988, NeXT, Inc.

/__NXdef{1 index where{pop pop pop}{def}ifelse}bind def
/__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def
/UserObjects 10 array __NXdef
/defineuserobject{
	exch dup 1 add dup UserObjects length gt{
		array dup 0 UserObjects putinterval
		/UserObjects exch def
	}{pop}ifelse UserObjects exch 3 -1 roll put
}__NXbdef
/undefineuserobject{UserObjects exch null put}__NXbdef
/execuserobject{UserObjects exch get exec}__NXbdef
/__NXRectPath{4 2 roll moveto 1 index 0 rlineto
0 exch rlineto neg 0 rlineto closepath}__NXbdef
/__NXProcessRectArgs{
	1 index type /arraytype eq{
		exch 0 4 2 index length 1 sub{
			dup 3 add 1 exch{1 index exch get exch}for
			5 1 roll 5 index exec
		}for pop pop
	}{exec}ifelse
}__NXbdef
/rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs
grestore}__NXbdef
/rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef
/rectstroke{
	gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{
		{gsave __NXRectPath null concat stroke grestore}
		dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs
	}{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore
}__NXbdef
/_NXLevel2 systemdict /languagelevel known {languagelevel 2 ge}{false}ifelse
__NXdef
/xyshow{
	0 1 3 index length 1 sub{
		currentpoint 4 index 3 index 1 getinterval show
		3 index 3 index 2 mul 1 add get add exch
		3 index	3 index 2 mul get add exch moveto pop
	}for pop pop
}__NXbdef
/xshow{
	0 1 3 index length 1 sub{
		currentpoint 4 index 3 index 1 getinterval show
		exch 3 index 3 index get add exch moveto pop
	}for pop pop
}__NXbdef
/yshow{
	0 1 3 index length 1 sub{
		currentpoint 4 index 3 index 1 getinterval show
		3 index 3 index get add moveto pop
	}for pop pop
}__NXbdef
/arct{arcto pop pop pop pop}__NXbdef
/setbbox{pop pop pop pop}__NXbdef
/ucache{}__NXbdef
/ucachestatus{mark 0 0 0 0 0}__NXbdef
/setucacheparams{cleartomark}__NXbdef
/uappend{systemdict begin cvx exec end}__NXbdef
/ueofill{gsave newpath uappend eofill grestore}__NXbdef
/ufill{gsave newpath uappend fill grestore}__NXbdef
/ustroke{
	gsave newpath dup length 6 eq
	{exch uappend concat}{uappend}ifelse
	stroke grestore
}__NXbdef
/__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse
/ustrokepath{
	newpath dup length 6 eq{
		exch uappend __NXustrokepathMatrix currentmatrix exch concat
		strokepath setmatrix
	}{uappend strokepath}ifelse
} __NXbdef
/upath{
	[exch {/ucache cvx}if pathbbox /setbbox cvx
	 {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx
} __NXbdef
/setstrokeadjust{pop}__NXbdef
/currentstrokeadjust{false}__NXbdef
/selectfont{exch findfont exch
dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef
/_NXCombineArrays{
	counttomark dup 2 add index dup length 3 -1 roll {
		2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch
	}repeat pop pop pop
}__NXbdef
/flushgraphics{}def
/setwindowtype{pop pop}def
/currentwindowtype{pop 0}def
/setalpha{pop}def
/currentalpha{1.0}def
/hidecursor{}def
/obscurecursor{}def
/revealcursor{}def
/setcursor{4 {pop}repeat}bind def
/showcursor{}def
/NextStepEncoding where not{
/NextStepEncoding StandardEncoding 256 array copy def
0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave
/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis
/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute
/Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright
176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior
204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave
/aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute
/ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth
/ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute
/ucircumflex 246/udieresis/yacute 252/thorn/ydieresis]
{dup type /nametype eq
 {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse
}forall pop
/NextStepEncoding NextStepEncoding readonly def
/_NXfstr 128 string dup 0 (_NX) putinterval def
/_NXfindfont /findfont load def
/findfont{
 % Because we can never let NextStepEncoding get into
 % SharedFontDirectory, we cannot reencode a font to NextStepEncoding
 % if we are in shared mode.  So if currentshared is true,
 % we call the normal findfont and return that
 /currentshared where {pop currentshared} {false} ifelse
 {_NXfindfont}
 {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll
  getinterval cvn exch FontDirectory 2 index known
  {pop FontDirectory exch get}
  {_NXfindfont dup /Encoding get StandardEncoding eq
   {	dup length dict exch
	{1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall
	 dup /Encoding NextStepEncoding put definefont
	}{exch pop} ifelse
   }ifelse
 }ifelse
}bind def
}{pop}ifelse
/_NXImageString {/__NXImageString where{pop}{/__NXImageString 4000 string
__NXdef}ifelse __NXImageString}__NXbdef
/_NXDoImageOp{
	3 dict begin /parr 5 array def 1 index{dup}{1}ifelse /chans exch def
	chans 2 add 2 roll parr 0 chans getinterval astore pop
	5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1
add}ifelse
	4 index mul /totbytes exch def pop exch pop
	gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore
	{0 1 chans 1 sub{parr exch get exec length totbytes exch sub /totbytes exch
def}for totbytes 0 le{exit}if}loop end
}__NXbdef
/alphaimage{1 add _NXDoImageOp}def
_NXLevel2{
	/NXCalibratedRGBColorSpace where{pop}{
		/NXCalibratedRGBColorSpace
		{mark /NXCalibratedRGB /ColorSpace findresource exch pop}stopped
		{cleartomark /NXCalibratedRGB[/CIEBasedABC 2 dict dup begin
		/MatrixLMN[.4124 .2126 .0193 .3576 .7152 .1192 .1805 .0722 .9505]def
		/WhitePoint[.9505 1 1.089] def end] /ColorSpace defineresource}if def}ifelse
	/nxsetrgbcolor{NXCalibratedRGBColorSpace setcolorspace setcolor}__NXbdef
	/nxsetgray{dup dup nxsetrgbcolor}__NXbdef
	/_NXCalibratedImage{exch{array astore dup length true}{false}ifelse
		8 -1 roll{NXCalibratedRGBColorSpace setcolorspace}if
		8 dict dup 9 1 roll begin /ImageType 1 def /MultipleDataSources exch def
		currentcolorspace 0 get /Indexed eq{pop /Decode[0 2 6 index exp 1 sub]def}
		{2 mul dup array /Decode exch def 1 sub 0 1 3 -1 roll{Decode exch dup 2 mod
put}for}ifelse
		/DataSource exch def /ImageMatrix exch def
		/BitsPerComponent exch def /Height exch def /Width exch def end
image}__NXbdef
} {
	/setcmykcolor{
		1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll
		4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if
setrgbcolor}__NXbdef
	/currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef
	/colorimage{_NXDoImageOp}__NXbdef
	/nxsetrgbcolor{setrgbcolor}__NXbdef /nxsetgray{setgray}__NXbdef
	/setpattern{pop .5 setgray}__NXbdef
	/_NXCalibratedImage{dup 1 eq {pop pop image}{colorimage}ifelse pop}__NXbdef
} ifelse
/_NXSetCMYKOrRGB where{pop}{
	mark{systemdict /currentwindow get exec}stopped
	{{pop pop pop setcmykcolor}}{{nxsetrgbcolor pop pop pop pop}}ifelse
/_NXSetCMYKOrRGB exch def cleartomark
}ifelse
%%EndProcSet

_NXLevel2{/_NXsethsb where{pop}{/_NXsethsb /sethsbcolor load def}ifelse
/sethsbcolor{_NXsethsb currentrgbcolor nxsetrgbcolor}def
/setrgbcolor{nxsetrgbcolor}bind def /setgray{nxsetgray}bind def
}if
gsave
-20 9972 translate
 /__NXbasematrix matrix currentmatrix def
grestore
%%EndProlog
%%BeginSetup
%%PaperSize: Letter
%%EndSetup

%%Page: 1 1
%%PageBoundingBox: 156 307 487 633
%%PageFonts: (atend)
%%BeginPageSetup
%%PaperSize: Letter
/__NXsheetsavetoken save def
0 0 translate
gsave
-20 9972 translate
 /__NXbasematrix matrix currentmatrix def
grestore
gsave
[1 0 0 -1 -19 10744] concat
19 9952 translate
%%EndPageSetup
gsave
0 0 612 792 rectclip
gsave
54 72 467 648 rectclip
1 setlinewidth 0 setgray
gsave
95 76 371.769226 230 rectclip
/Mnodistort true def
100 dict begin
/Mfixwid true def
/Mrot 0 def
/Mpstart {
    MathPictureStart
} bind def
/Mpend {
    MathPictureEnd
} bind def
/Mscale {
    0 1 0 1
    5 -1 roll
    MathScale
} bind def
/Plain	/Courier findfont def
/Bold	/Courier-Bold findfont def
/Italic /Courier-Oblique findfont def
/MathPictureStart {
	/Mimatrix
	 matrix currentmatrix
	def
	gsave
	newpath
	Mleft
	Mbottom
	translate
	1 -1 scale
	/Mtmatrix
	matrix currentmatrix
	def
	Plain
	Mfontsize scalefont
	setfont
	0 setgray
	0 setlinewidth
} bind def
/MathPictureEnd {
	grestore
} bind def
/MathSubStart {
        Mgmatrix Mtmatrix
        Mleft Mbottom
        Mwidth Mheight
        8 -2 roll
        moveto
        Mtmatrix setmatrix
        currentpoint
        Mgmatrix setmatrix
        10 -2 roll
        moveto
        Mtmatrix setmatrix
        currentpoint
        2 copy translate
        /Mtmatrix matrix currentmatrix def
        /Mleft 0 def
        /Mbottom 0 def
        3 -1 roll
        exch sub
        /Mheight exch def
        sub
        /Mwidth exch def
} bind def
/MathSubEnd {
        /Mheight exch def
        /Mwidth exch def
        /Mbottom exch def
        /Mleft exch def
        /Mtmatrix exch def
        dup setmatrix
        /Mgmatrix exch def
} bind def
/Mdot {
	moveto
	0 0 rlineto
	stroke
} bind def
/Mtetra {
	moveto
	lineto
	lineto
	lineto
	fill
} bind def
/Metetra {
	moveto
	lineto
	lineto
	lineto
	closepath
	gsave
	fill
	grestore
	0 setgray
	stroke
} bind def
/Mistroke {
	flattenpath
	0 0 0
	{
	4 2 roll
	pop pop
	}
	{
	4 -1 roll
	2 index
	sub dup mul
	4 -1 roll
	2 index
	sub dup mul
	add sqrt
	4 -1 roll
	add
	3 1 roll
	}
	{
	stop
	}
	{
	stop
	}
	pathforall
	pop pop
	currentpoint
	stroke
	moveto
	currentdash
	3 -1 roll
	add
	setdash
} bind def
/Mfstroke {
	stroke
	currentdash
	pop 0
	setdash
} bind def
/Mrotsboxa {
	gsave
	dup
	/Mrot
	exch def
	Mrotcheck
	Mtmatrix
	dup
	setmatrix
	7 1 roll
	4 index
	4 index
	translate
	rotate
	3 index
	-1 mul
	3 index
	-1 mul
	translate
	/Mtmatrix
	matrix
	currentmatrix
	def
	grestore
	Msboxa
	3  -1 roll
	/Mtmatrix
	exch def
	/Mrot
	0 def
} bind def
/Msboxa {
	newpath
	5 -1 roll
	Mvboxa
	pop
	Mboxout
	6 -1 roll
	5 -1 roll
	4 -1 roll
	Msboxa1
	5 -3 roll
	Msboxa1
	Mboxrot
	[
	7 -2 roll
	2 copy
	[
	3 1 roll
	10 -1 roll
	9 -1 roll
	]
	6 1 roll
	5 -2 roll
	]
} bind def
/Msboxa1 {
	sub
	2 div
	dup
	2 index
	1 add
	mul
	3 -1 roll
	-1 add
	3 -1 roll
	mul
} bind def
/Mvboxa	{
	Mfixwid
	{
	Mvboxa1
	}
	{
	dup
	Mwidthcal
	0 exch
	{
	add
	}
	forall
	exch
	Mvboxa1
	4 index
	7 -1 roll
	add
	4 -1 roll
	pop
	3 1 roll
	}
	ifelse
} bind def
/Mvboxa1 {
	gsave
	newpath
	[ true
	3 -1 roll
	{
	Mbbox
	5 -1 roll
	{
	0
	5 1 roll
	}
	{
	7 -1 roll
	exch sub
	(m) stringwidth pop
	.3 mul
	sub
	7 1 roll
	6 -1 roll
	4 -1 roll
	Mmin
	3 -1 roll
	5 index
	add
	5 -1 roll
	4 -1 roll
	Mmax
	4 -1 roll
	}
	ifelse
	false
	}
	forall
	{ stop } if
	counttomark
	1 add
	4 roll
	]
	grestore
} bind def
/Mbbox {
	0 0 moveto
	false charpath
	flattenpath
	pathbbox
	newpath
} bind def
/Mmin {
	2 copy
	gt
	{ exch } if
	pop
} bind def
/Mmax {
	2 copy
	lt
	{ exch } if
	pop
} bind def
/Mrotshowa {
	dup
	/Mrot
	exch def
	Mrotcheck
	Mtmatrix
	dup
	setmatrix
	7 1 roll
	4 index
	4 index
	translate
	rotate
	3 index
	-1 mul
	3 index
	-1 mul
	translate
	/Mtmatrix
	matrix
	currentmatrix
	def
	Mgmatrix setmatrix
	Mshowa
	/Mtmatrix
	exch def
	/Mrot 0 def
} bind def
/Mshowa {
	4 -2 roll
	moveto
	2 index
	Mtmatrix setmatrix
	Mvboxa
	7 1 roll
	Mboxout
	6 -1 roll
	5 -1 roll
	4 -1 roll
	Mshowa1
	4 1 roll
	Mshowa1
	rmoveto
	currentpoint
	Mfixwid
	{
	Mshowax
	}
	{
	Mshoway
	}
	ifelse
	pop pop pop pop
	Mgmatrix setmatrix
} bind def
/Mshowax {
	0 1
        4 index length
        -1 add
        {
        2 index
        4 index
        2 index
        get
        3 index
        add
        moveto
        4 index
        exch get
        show
        } for
} bind def
/Mshoway {
        3 index
        Mwidthcal
        5 1 roll
	0 1
	4 index length
	-1 add
	{
	2 index
	4 index
	2 index
	get
	3 index
	add
	moveto
	4 index
	exch get
	[
	6 index
	aload
	length
	2 add
	-1 roll
	{
	pop
	Strform
	stringwidth
	pop
	neg
	exch
	add
	0 rmoveto
	}
	exch
	kshow
	cleartomark
	} for
	pop
} bind def
/Mwidthcal {
	[
	exch
	{
	Mwidthcal1
	}
	forall
	]
	[
	exch
	dup
	Maxlen
	-1 add
	0 1
	3 -1 roll
	{
	[
	exch
	2 index
	{
	1 index
	Mget
	exch
	}
	forall
	pop
	Maxget
	exch
	}
	for
	pop
	]
	Mreva
} bind def
/Mreva	{
	[
	exch
	aload
	length
	-1 1
	{1 roll}
	for
	]
} bind def
/Mget	{
	1 index
	length
	-1 add
	1 index
	ge
	{
	get
	}
	{
	pop pop
	0
	}
	ifelse
} bind def
/Maxlen	{
	[
	exch
	{
	length
	}
	forall
	Maxget
} bind def
/Maxget	{
	counttomark
	-1 add
	1 1
	3 -1 roll
	{
	pop
	Mmax
	}
	for
	exch
	pop
} bind def
/Mwidthcal1 {
	[
	exch
	{
	Strform
	stringwidth
	pop
	}
	forall
	]
} bind def
/Strform {
	/tem (x) def
	tem 0
	3 -1 roll
	put
	tem
} bind def
/Mshowa1 {
	2 copy
	add
	4 1 roll
	sub
	mul
	sub
	-2 div
} bind def
/MathScale {
	Mwidth
	Mheight
	Mlp
	translate
	scale
	/Msaveaa exch def
	/Msavebb exch def
	/Msavecc exch def
	/Msavedd exch def
	/Mgmatrix
	matrix currentmatrix
	def
} bind def
/Mlp {
	3 copy
	Mlpfirst
	{
	Mnodistort
	{
	Mmin
	dup
	} if
	4 index
	2 index
	2 index
	Mlprun
	11 index
	11 -1 roll
	10 -4 roll
	Mlp1
	8 index
	9 -5 roll
	Mlp1
	4 -1 roll
	and
	{ exit } if
	3 -1 roll
	pop pop
	} loop
	exch
	3 1 roll
	7 -3 roll
	pop pop pop
} bind def
/Mlpfirst {
	3 -1 roll
	dup length
	2 copy
	-2 add
	get
	aload
	pop pop pop
	4 -2 roll
	-1 add
	get
	aload
	pop pop pop
	6 -1 roll
	3 -1 roll
	5 -1 roll
	sub
	dup /MsaveAx exch def
	div
	4 1 roll
	exch sub
	dup /MsaveAy exch def
	div
} bind def
/Mlprun {
	2 copy
	4 index
	0 get
	dup
	4 1 roll
	Mlprun1
	3 copy
	8 -2 roll
	9 -1 roll
	{
	3 copy
	Mlprun1
	3 copy
	11 -3 roll
	/gt Mlpminmax
	8 3 roll
	11 -3 roll
	/lt Mlpminmax
	8 3 roll
	} forall
	pop pop pop pop
	3 1 roll
	pop pop
	aload pop
	5 -1 roll
	aload pop
	exch
	6 -1 roll
	Mlprun2
	8 2 roll
	4 -1 roll
	Mlprun2
	6 2 roll
	3 -1 roll
	Mlprun2
	4 2 roll
	exch
	Mlprun2
	6 2 roll
} bind def
/Mlprun1 {
	aload pop
	exch
	6 -1 roll
	5 -1 roll
	mul add
	4 -2 roll
	mul
	3 -1 roll
	add
} bind def
/Mlprun2 {
	2 copy
	add 2 div
	3 1 roll
	exch sub
} bind def
/Mlpminmax {
	cvx
	2 index
	6 index
	2 index
	exec
	{
	7 -3 roll
	4 -1 roll
	} if
	1 index
	5 index
	3 -1 roll
	exec
	{
	4 1 roll
	pop
	5 -1 roll
	aload
	pop pop
	4 -1 roll
	aload pop
	[
	8 -2 roll
	pop
	5 -2 roll
	pop
	6 -2 roll
	pop
	5 -1 roll
	]
	4 1 roll
	pop
	}
	{
	pop pop pop
	} ifelse
} bind def
/Mlp1 {
	5 index
	3 index	sub
	5 index
	2 index mul
	1 index
	le
	1 index
	0 le
	or
	dup
	not
	{
	1 index
	3 index	div
	.99999 mul
	8 -1 roll
	pop
	7 1 roll
	}
	if
	8 -1 roll
	2 div
	7 -2 roll
	pop sub
	5 index
	6 -3 roll
	pop pop
	mul sub
	exch
} bind def
/intop 0 def
/inrht 0 def
/inflag 0 def
/outflag 0 def
/xadrht 0 def
/xadlft 0 def
/yadtop 0 def
/yadbot 0 def
/Minner {
	outflag
	1
	eq
	{
	/outflag 0 def
	/intop 0 def
	/inrht 0 def
	} if
	5 index
	gsave
	Mtmatrix setmatrix
	Mvboxa pop
	grestore
	3 -1 roll
	pop
	dup
	intop
	gt
	{
	/intop
	exch def
	}
	{ pop }
	ifelse
	dup
	inrht
	gt
	{
	/inrht
	exch def
	}
	{ pop }
	ifelse
	pop
	/inflag
	1 def
} bind def
/Mouter {
	/xadrht 0 def
	/xadlft 0 def
	/yadtop 0 def
	/yadbot 0 def
	inflag
	1 eq
	{
	dup
	0 lt
	{
	dup
	intop
	mul
	neg
	/yadtop
	exch def
	} if
	dup
	0 gt
	{
	dup
	intop
	mul
	/yadbot
	exch def
	}
	if
	pop
	dup
	0 lt
	{
	dup
	inrht
	mul
	neg
	/xadrht
	exch def
	} if
	dup
	0 gt
	{
	dup
	inrht
	mul
	/xadlft
	exch def
	} if
	pop
	/outflag 1 def
	}
	{ pop pop}
	ifelse
	/inflag 0 def
	/inrht 0 def
	/intop 0 def
} bind def
/Mboxout {
	outflag
	1
	eq
	{
	4 -1
	roll
	xadlft
	leadjust
	add
	sub
	4 1 roll
	3 -1
	roll
	yadbot
	leadjust
	add
	sub
	3 1
	roll
	exch
	xadrht
	leadjust
	add
	add
	exch
	yadtop
	leadjust
	add
	add
	/outflag 0 def
	/xadlft 0 def
	/yadbot 0 def
	/xadrht 0 def
	/yadtop 0 def
	} if
} bind def
/leadjust {
	(m) stringwidth pop
	.5 mul
} bind def
/Mrotcheck {
	dup
	90
	eq
	{
	yadbot
	/yadbot
	xadrht
	def
	/xadrht
	yadtop
	def
	/yadtop
	xadlft
	def
	/xadlft
	exch
	def
	}
	if
	dup
	cos
	1 index
	sin
	Checkaux
	dup
	cos
	1 index
	sin neg
	exch
	Checkaux
	3 1 roll
	pop pop
} bind def
/Checkaux {
	4 index
	exch
	4 index
	mul
	3 1 roll
	mul add
	4 1 roll
} bind def
/Mboxrot {
	Mrot
	90 eq
	{
	brotaux
	4 2
	roll
	}
	if
	Mrot
	180 eq
	{
	4 2
        roll
	brotaux
	4 2
	roll
	brotaux
	}
	if
	Mrot
	270 eq
	{
	4 2
	roll
	brotaux
	}
	if
} bind def
/brotaux {
	neg
	exch
	neg
} bind def
/Mabswid {
	Mimatrix
	0 get
	Mgmatrix
	0 get
	div
	mul
	setlinewidth
} bind def
/Mabsdash {
	exch
	Mimatrix
	0 get
	Mgmatrix
	0 get
	div
	[
	3 1 roll
	exch
	{
	exch
	dup
	3 -1 roll
	mul
	exch
	}
	forall
	pop ]
	exch
	setdash
} bind def
/colorimage where
{ pop }
{
/colorimage {
3 1 roll
 pop pop
 5 -1 roll
 mul
 4 1 roll
{
currentfile
1 index
readhexstring
pop }
image
} bind def
} ifelse
/sampledsound where
{ pop}
{ /sampledsound {
exch
pop
exch
5 1 roll
mul
4 idiv
mul
2 idiv
exch pop
exch
/Mtempproc exch def
{ Mtempproc pop }
repeat
} bind def
} ifelse

/Mleft		95.000000 def
/Mbottom	306.047974 def
/Mwidth		371.769226 def
/Mheight	230.047974 def
/Mfontsize 12 def
/Plain /Courier findfont def
%!
%%Creator: Mathematica
%%AspectRatio: 0.61803
MathPictureStart
/Courier findfont 10  scalefont  setfont
% Scaling calculations
0.02381 0.015873 0.334052 1.366114e-08 [
[(0)] 0.02381 0 0 2 Msboxa
[(10)] 0.18254 0 0 2 Msboxa
[(20)] 0.34127 0 0 2 Msboxa
[(30)] 0.5 0 0 2 Msboxa
[(40)] 0.65873 0 0 2 Msboxa
[(50)] 0.81746 0 0 2 Msboxa
[(60)] 0.97619 0 0 2 Msboxa
[(      7)(-2. 10)] -0.0125 0.06083 1 0 Msboxa
[(      7)(-1. 10)] -0.0125 0.19744 1 0 Msboxa
[(0)] -0.0125 0.33405 1 0 Msboxa
[(     7)(1. 10)] -0.0125 0.47066 1 0 Msboxa
[(     7)(2. 10)] -0.0125 0.60727 1 0 Msboxa
[ -0.001 -0.001 0 0 ]
[ 1.001 0.61903 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
%%Object: Graphics
[ ] 0 setdash
0 setgray
gsave
gsave
0.002 setlinewidth
0.02381 0 moveto
0.02381 0.00625 lineto
stroke
grestore
[(0)] 0.02381 0 0 2 Mshowa
gsave
0.002 setlinewidth
0.18254 0 moveto
0.18254 0.00625 lineto
stroke
grestore
[(10)] 0.18254 0 0 2 Mshowa
gsave
0.002 setlinewidth
0.34127 0 moveto
0.34127 0.00625 lineto
stroke
grestore
[(20)] 0.34127 0 0 2 Mshowa
gsave
0.002 setlinewidth
0.5 0 moveto
0.5 0.00625 lineto
stroke
grestore
[(30)] 0.5 0 0 2 Mshowa
gsave
0.002 setlinewidth
0.65873 0 moveto
0.65873 0.00625 lineto
stroke
grestore
[(40)] 0.65873 0 0 2 Mshowa
gsave
0.002 setlinewidth
0.81746 0 moveto
0.81746 0.00625 lineto
stroke
grestore
[(50)] 0.81746 0 0 2 Mshowa
gsave
0.002 setlinewidth
0.97619 0 moveto
0.97619 0.00625 lineto
stroke
grestore
[(60)] 0.97619 0 0 2 Mshowa
gsave
0.001 setlinewidth
0.05556 0 moveto
0.05556 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.0873 0 moveto
0.0873 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.11905 0 moveto
0.11905 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.15079 0 moveto
0.15079 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.21429 0 moveto
0.21429 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.24603 0 moveto
0.24603 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.27778 0 moveto
0.27778 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.30952 0 moveto
0.30952 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.37302 0 moveto
0.37302 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.40476 0 moveto
0.40476 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.43651 0 moveto
0.43651 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.46825 0 moveto
0.46825 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.53175 0 moveto
0.53175 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.56349 0 moveto
0.56349 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.59524 0 moveto
0.59524 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.62698 0 moveto
0.62698 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.69048 0 moveto
0.69048 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.72222 0 moveto
0.72222 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.75397 0 moveto
0.75397 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.78571 0 moveto
0.78571 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.84921 0 moveto
0.84921 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.88095 0 moveto
0.88095 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.9127 0 moveto
0.9127 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.94444 0 moveto
0.94444 0.00375 lineto
stroke
grestore
gsave
0.002 setlinewidth
0 0 moveto
1 0 lineto
stroke
grestore
gsave
0.002 setlinewidth
0 0.06083 moveto
0.00625 0.06083 lineto
stroke
grestore
[(      7)(-2. 10)] -0.0125 0.06083 1 0 Mshowa
gsave
0.002 setlinewidth
0 0.19744 moveto
0.00625 0.19744 lineto
stroke
grestore
[(      7)(-1. 10)] -0.0125 0.19744 1 0 Mshowa
gsave
0.002 setlinewidth
0 0.33405 moveto
0.00625 0.33405 lineto
stroke
grestore
[(0)] -0.0125 0.33405 1 0 Mshowa
gsave
0.002 setlinewidth
0 0.47066 moveto
0.00625 0.47066 lineto
stroke
grestore
[(     7)(1. 10)] -0.0125 0.47066 1 0 Mshowa
gsave
0.002 setlinewidth
0 0.60727 moveto
0.00625 0.60727 lineto
stroke
grestore
[(     7)(2. 10)] -0.0125 0.60727 1 0 Mshowa
gsave
0.001 setlinewidth
0 0.08815 moveto
0.00375 0.08815 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.11547 moveto
0.00375 0.11547 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.1428 moveto
0.00375 0.1428 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.17012 moveto
0.00375 0.17012 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.22476 moveto
0.00375 0.22476 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.25208 moveto
0.00375 0.25208 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.27941 moveto
0.00375 0.27941 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.30673 moveto
0.00375 0.30673 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.36137 moveto
0.00375 0.36137 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.3887 moveto
0.00375 0.3887 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.41602 moveto
0.00375 0.41602 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.44334 moveto
0.00375 0.44334 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.49799 moveto
0.00375 0.49799 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.52531 moveto
0.00375 0.52531 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.55263 moveto
0.00375 0.55263 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.57995 moveto
0.00375 0.57995 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.03351 moveto
0.00375 0.03351 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.00618 moveto
0.00375 0.00618 lineto
stroke
grestore
gsave
0.002 setlinewidth
0 0 moveto
0 0.61803 lineto
stroke
grestore
grestore
gsave
gsave
0.002 setlinewidth
0.02381 0.61178 moveto
0.02381 0.61803 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.18254 0.61178 moveto
0.18254 0.61803 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.34127 0.61178 moveto
0.34127 0.61803 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.5 0.61178 moveto
0.5 0.61803 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.65873 0.61178 moveto
0.65873 0.61803 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.81746 0.61178 moveto
0.81746 0.61803 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.97619 0.61178 moveto
0.97619 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.05556 0.61428 moveto
0.05556 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.0873 0.61428 moveto
0.0873 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.11905 0.61428 moveto
0.11905 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.15079 0.61428 moveto
0.15079 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.21429 0.61428 moveto
0.21429 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.24603 0.61428 moveto
0.24603 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.27778 0.61428 moveto
0.27778 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.30952 0.61428 moveto
0.30952 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.37302 0.61428 moveto
0.37302 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.40476 0.61428 moveto
0.40476 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.43651 0.61428 moveto
0.43651 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.46825 0.61428 moveto
0.46825 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.53175 0.61428 moveto
0.53175 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.56349 0.61428 moveto
0.56349 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.59524 0.61428 moveto
0.59524 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.62698 0.61428 moveto
0.62698 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.69048 0.61428 moveto
0.69048 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.72222 0.61428 moveto
0.72222 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.75397 0.61428 moveto
0.75397 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.78571 0.61428 moveto
0.78571 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.84921 0.61428 moveto
0.84921 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.88095 0.61428 moveto
0.88095 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.9127 0.61428 moveto
0.9127 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.94444 0.61428 moveto
0.94444 0.61803 lineto
stroke
grestore
gsave
0.002 setlinewidth
0 0.61803 moveto
1 0.61803 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.99375 0.06083 moveto
1 0.06083 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.99375 0.19744 moveto
1 0.19744 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.99375 0.33405 moveto
1 0.33405 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.99375 0.47066 moveto
1 0.47066 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.99375 0.60727 moveto
1 0.60727 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.08815 moveto
1 0.08815 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.11547 moveto
1 0.11547 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.1428 moveto
1 0.1428 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.17012 moveto
1 0.17012 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.22476 moveto
1 0.22476 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.25208 moveto
1 0.25208 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.27941 moveto
1 0.27941 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.30673 moveto
1 0.30673 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.36137 moveto
1 0.36137 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.3887 moveto
1 0.3887 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.41602 moveto
1 0.41602 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.44334 moveto
1 0.44334 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.49799 moveto
1 0.49799 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.52531 moveto
1 0.52531 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.55263 moveto
1 0.55263 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.57995 moveto
1 0.57995 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.03351 moveto
1 0.03351 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.00618 moveto
1 0.00618 lineto
stroke
grestore
gsave
0.002 setlinewidth
1 0 moveto
1 0.61803 lineto
stroke
grestore
grestore
gsave
grestore
0 0 moveto
1 0 lineto
1 0.61803 lineto
0 0.61803 lineto
closepath
clip
newpath
gsave
gsave
gsave
gsave
0.004 setlinewidth
0.02381 0.33405 moveto
0.02505 0.33407 lineto
0.02629 0.33413 lineto
0.02753 0.33423 lineto
0.02877 0.33437 lineto
0.03125 0.33476 lineto
0.03373 0.3353 lineto
0.03869 0.33683 lineto
0.04365 0.33892 lineto
0.05357 0.34453 lineto
0.06349 0.35159 lineto
0.10318 0.38316 lineto
0.12302 0.39548 lineto
0.13294 0.40025 lineto
0.14286 0.40416 lineto
0.15278 0.40731 lineto
0.1627 0.40985 lineto
0.18254 0.41367 lineto
0.20238 0.41669 lineto
0.22222 0.41985 lineto
0.24206 0.42391 lineto
0.26191 0.42949 lineto
0.28175 0.43718 lineto
0.30159 0.44754 lineto
0.32143 0.46115 lineto
0.34127 0.4786 lineto
0.36111 0.50055 lineto
0.38095 0.52769 lineto
0.42064 0.6005 lineto
stroke
0.42739 0.61803 moveto
0.42064 0.6005 lineto
stroke
stroke
stroke
stroke
stroke
stroke
stroke
stroke
stroke
stroke
stroke
stroke
stroke
stroke
stroke
grestore
grestore
grestore
gsave
gsave
gsave
0.004 setlinewidth
0.02381 0.33405 moveto
0.02505 0.33406 lineto
0.02629 0.3341 lineto
0.02753 0.33416 lineto
0.02877 0.33424 lineto
0.03125 0.33447 lineto
0.03373 0.33479 lineto
0.03869 0.33569 lineto
0.04365 0.33692 lineto
0.05357 0.34019 lineto
0.06349 0.34424 lineto
0.08333 0.3531 lineto
0.09326 0.35719 lineto
0.10318 0.3607 lineto
0.1131 0.36348 lineto
0.11806 0.36456 lineto
0.12302 0.36544 lineto
0.12798 0.36612 lineto
0.13046 0.36638 lineto
0.13294 0.36659 lineto
0.13542 0.36676 lineto
0.13666 0.36682 lineto
0.1379 0.36687 lineto
0.13914 0.36691 lineto
0.14038 0.36694 lineto
0.14162 0.36696 lineto
0.14286 0.36697 lineto
0.1441 0.36697 lineto
0.14534 0.36695 lineto
0.14658 0.36693 lineto
0.14782 0.36689 lineto
0.1503 0.36679 lineto
0.15278 0.36665 lineto
0.15774 0.36626 lineto
0.1627 0.36572 lineto
0.17262 0.36429 lineto
0.18254 0.36244 lineto
0.22222 0.35257 lineto
0.26191 0.34189 lineto
0.28175 0.33731 lineto
0.29167 0.33537 lineto
0.30159 0.33373 lineto
0.30655 0.33304 lineto
0.31151 0.33244 lineto
0.31647 0.33194 lineto
0.32143 0.33155 lineto
0.32391 0.3314 lineto
0.32639 0.33127 lineto
0.32763 0.33122 lineto
0.32887 0.33117 lineto
Mistroke
0.33011 0.33114 lineto
0.33135 0.33111 lineto
0.33259 0.33109 lineto
0.33383 0.33107 lineto
0.33507 0.33107 lineto
0.33631 0.33107 lineto
0.33755 0.33108 lineto
0.33879 0.3311 lineto
0.34003 0.33113 lineto
0.34127 0.33117 lineto
0.34375 0.33127 lineto
0.34623 0.3314 lineto
0.34871 0.33158 lineto
0.35119 0.33179 lineto
0.35615 0.33232 lineto
0.36111 0.33302 lineto
0.37103 0.33492 lineto
0.38095 0.33756 lineto
0.39087 0.34099 lineto
0.40079 0.34529 lineto
0.42064 0.35672 lineto
0.44048 0.37242 lineto
0.46032 0.39298 lineto
0.48016 0.419 lineto
0.5 0.45114 lineto
0.53968 0.53654 lineto
Mfstroke
0.56698 0.61803 moveto
0.53968 0.53654 lineto
stroke
stroke
stroke
stroke
stroke
stroke
stroke
stroke
stroke
stroke
stroke
stroke
grestore
grestore
grestore
gsave
gsave
gsave
0.004 setlinewidth
0.02381 0.33405 moveto
0.02505 0.33406 lineto
0.02629 0.33409 lineto
0.02753 0.33413 lineto
0.02877 0.3342 lineto
0.03125 0.33438 lineto
0.03373 0.33462 lineto
0.03869 0.33532 lineto
0.04365 0.33626 lineto
0.05357 0.33876 lineto
0.06349 0.34183 lineto
0.08333 0.34833 lineto
0.09326 0.35117 lineto
0.09822 0.35238 lineto
0.10318 0.35344 lineto
0.10814 0.35432 lineto
0.1131 0.35501 lineto
0.11558 0.35528 lineto
0.11806 0.35551 lineto
0.12054 0.35569 lineto
0.12178 0.35576 lineto
0.12302 0.35582 lineto
0.12426 0.35587 lineto
0.1255 0.35591 lineto
0.12674 0.35593 lineto
0.12798 0.35594 lineto
0.12922 0.35594 lineto
0.13046 0.35593 lineto
0.1317 0.35591 lineto
0.13294 0.35587 lineto
0.13542 0.35577 lineto
0.13666 0.3557 lineto
0.1379 0.35562 lineto
0.14286 0.35519 lineto
0.14782 0.3546 lineto
0.15278 0.35385 lineto
0.1627 0.35192 lineto
0.18254 0.3466 lineto
0.22222 0.33218 lineto
0.26191 0.31572 lineto
0.30159 0.29997 lineto
0.32143 0.29315 lineto
0.34127 0.28748 lineto
0.35119 0.28519 lineto
0.36111 0.28332 lineto
0.36607 0.28256 lineto
0.37103 0.28193 lineto
0.37599 0.28142 lineto
0.37847 0.28122 lineto
0.38095 0.28106 lineto
Mistroke
0.38343 0.28093 lineto
0.38467 0.28088 lineto
0.38591 0.28083 lineto
0.38715 0.2808 lineto
0.38839 0.28078 lineto
0.38963 0.28076 lineto
0.39087 0.28076 lineto
0.39211 0.28077 lineto
0.39335 0.28078 lineto
0.39459 0.28081 lineto
0.39583 0.28085 lineto
0.39707 0.28089 lineto
0.39831 0.28095 lineto
0.40079 0.28109 lineto
0.40327 0.28128 lineto
0.40575 0.28151 lineto
0.41072 0.28211 lineto
0.41568 0.28289 lineto
0.42064 0.28387 lineto
0.43056 0.28642 lineto
0.44048 0.28984 lineto
0.4504 0.29418 lineto
0.46032 0.2995 lineto
0.48016 0.31336 lineto
0.5 0.33196 lineto
0.51984 0.35586 lineto
0.53968 0.38567 lineto
0.57937 0.4655 lineto
0.61905 0.57671 lineto
Mfstroke
0.63011 0.61803 moveto
0.61905 0.57671 lineto
stroke
stroke
stroke
stroke
stroke
stroke
stroke
stroke
stroke
stroke
grestore
grestore
grestore
gsave
gsave
gsave
0.004 setlinewidth
0.02381 0.33405 moveto
0.02505 0.33405 lineto
0.02629 0.33406 lineto
0.02753 0.33407 lineto
0.02877 0.33408 lineto
0.03125 0.33411 lineto
0.03373 0.33416 lineto
0.03869 0.33429 lineto
0.04365 0.33445 lineto
0.05357 0.33485 lineto
0.05853 0.33505 lineto
0.06349 0.33524 lineto
0.06597 0.33532 lineto
0.06845 0.33539 lineto
0.07093 0.33545 lineto
0.07217 0.33547 lineto
0.07341 0.33549 lineto
0.07465 0.3355 lineto
0.07589 0.33551 lineto
0.07713 0.33552 lineto
0.07837 0.33552 lineto
0.07961 0.33552 lineto
0.08085 0.33551 lineto
0.08209 0.33549 lineto
0.08333 0.33547 lineto
0.08457 0.33545 lineto
0.08581 0.33541 lineto
0.0883 0.33533 lineto
0.09078 0.33522 lineto
0.09326 0.33509 lineto
0.09822 0.33473 lineto
0.10318 0.33425 lineto
0.1131 0.33291 lineto
0.12302 0.33105 lineto
0.14286 0.32577 lineto
0.1627 0.31853 lineto
0.18254 0.30959 lineto
0.22222 0.28749 lineto
0.26191 0.26093 lineto
0.30159 0.23098 lineto
0.34127 0.19863 lineto
0.38095 0.16497 lineto
0.42064 0.13123 lineto
0.46032 0.0988 lineto
0.5 0.06925 lineto
0.53968 0.04428 lineto
0.55952 0.03411 lineto
0.57937 0.0258 lineto
0.58929 0.02242 lineto
0.59921 0.01961 lineto
Mistroke
0.60913 0.01741 lineto
0.61409 0.01654 lineto
0.61905 0.01583 lineto
0.62153 0.01554 lineto
0.62401 0.0153 lineto
0.62649 0.01509 lineto
0.62897 0.01493 lineto
0.63145 0.01481 lineto
0.63269 0.01477 lineto
0.63393 0.01474 lineto
0.63517 0.01472 lineto
0.63641 0.01472 lineto
0.63765 0.01472 lineto
0.63889 0.01473 lineto
0.64013 0.01476 lineto
0.64137 0.0148 lineto
0.64261 0.01485 lineto
0.64385 0.01491 lineto
0.64633 0.01507 lineto
0.64881 0.01528 lineto
0.65377 0.01585 lineto
0.65873 0.01661 lineto
0.66865 0.01876 lineto
0.67857 0.02176 lineto
0.68849 0.02567 lineto
0.69841 0.03051 lineto
0.71825 0.04316 lineto
0.7381 0.06006 lineto
0.77778 0.10799 lineto
0.79762 0.13973 lineto
0.81746 0.17715 lineto
0.85714 0.27059 lineto
0.89683 0.39151 lineto
0.93651 0.54327 lineto
Mfstroke
0.95245 0.61803 moveto
0.93651 0.54327 lineto
stroke
stroke
grestore
grestore
grestore
grestore
% End of Graphics
MathPictureEnd%%PSTrailer
end

%%PageTrailer
%%DocumentFonts: Times-Roman
%%Trailer
%%DocumentFonts: Times-Roman
%%Pages: 1 1
%%BoundingBox:156 307 487 633


%%EndDocument
count __NXEPSOpCount sub {pop} repeat countdictstack __NXEPSDictCount sub {end}
repeat __NXEPSSave restore
grestore
grestore
0 0 0 setup
gsave
/Helvetica findfont 12 scalefont [1 0 0 -1 0 0] makefont
10
exch
defineuserobject
10 execuserobject setfont
0 nxsetgray
[1 0 0 -1 0 1033] concat
10 execuserobject setfont
0 nxsetgray
215 521 moveto (1) show
grestore
grestore
0 0 0 setup
gsave
10 execuserobject setfont
0 nxsetgray
[1 0 0 -1 0 1023] concat
10 execuserobject setfont
0 nxsetgray
262 516 moveto (2) show
grestore
grestore
0 0 0 setup
gsave
10 execuserobject setfont
0 nxsetgray
[1 0 0 -1 0 1035] concat
10 execuserobject setfont
0 nxsetgray
317 522 moveto (3) show
grestore
grestore
0 0 0 setup
gsave
10 execuserobject setfont
0 nxsetgray
[1 0 0 -1 0 1019] concat
10 execuserobject setfont
0 nxsetgray
394 514 moveto (4) show
grestore
grestore
0 0 0 setup
gsave
10 execuserobject setfont
0 nxsetgray
[1 0 0 -1 0 629] concat
10 execuserobject setfont
0 nxsetgray
399 319 moveto (z) show
grestore
grestore
0 0 0 setup
grestore
0 setgray
0.333333 setgray
gsave
0 0 540 720 rectclip
[1 0 0 -1 0 720] concat
gsave
1 nxsetgray
58 211 28 15 rectfill
10 execuserobject setfont
0 nxsetgray
60 223 moveto (V\(z\)) show
grestore
grestore
grestore
grestore
showpage
__NXsheetsavetoken restore
%%PageTrailer
%%DocumentFonts: Helvetica
%%Trailer
%%DocumentFonts: Helvetica
%%Pages: 1 1
%%BoundingBox:156 307 487 633


%%%%fig3.ps


%!PS-Adobe-2.0
%%Title: UNTITLED
%%Creator: Draw
%%CreationDate: Fri Jun 11 10:38:30 1993
%%For: mshaposh
%%DocumentFonts: (atend)
%%Pages: (atend) 1
%%BoundingBox: (atend)
%%DocumentPaperSizes: Letter
%%Orientation: Portrait
%%NXNextStepVersion: 3.0
%%EndComments

%%BeginProcSet: /usr/lib/NextStep/printPackage.ps 3.0
%!
% NeXT Printing Package
% Version: 3.0
% Copyright: 1988, NeXT, Inc.

/__NXdef{1 index where{pop pop pop}{def}ifelse}bind def
/__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def
/UserObjects 10 array __NXdef
/defineuserobject{
	exch dup 1 add dup UserObjects length gt{
		array dup 0 UserObjects putinterval
		/UserObjects exch def
	}{pop}ifelse UserObjects exch 3 -1 roll put
}__NXbdef
/undefineuserobject{UserObjects exch null put}__NXbdef
/execuserobject{UserObjects exch get exec}__NXbdef
/__NXRectPath{4 2 roll moveto 1 index 0 rlineto
0 exch rlineto neg 0 rlineto closepath}__NXbdef
/__NXProcessRectArgs{
	1 index type /arraytype eq{
		exch 0 4 2 index length 1 sub{
			dup 3 add 1 exch{1 index exch get exch}for
			5 1 roll 5 index exec
		}for pop pop
	}{exec}ifelse
}__NXbdef
/rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs
grestore}__NXbdef
/rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef
/rectstroke{
	gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{
		{gsave __NXRectPath null concat stroke grestore}
		dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs
	}{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore
}__NXbdef
/_NXLevel2 systemdict /languagelevel known {languagelevel 2 ge}{false}ifelse
__NXdef
/xyshow{
	0 1 3 index length 1 sub{
		currentpoint 4 index 3 index 1 getinterval show
		3 index 3 index 2 mul 1 add get add exch
		3 index	3 index 2 mul get add exch moveto pop
	}for pop pop
}__NXbdef
/xshow{
	0 1 3 index length 1 sub{
		currentpoint 4 index 3 index 1 getinterval show
		exch 3 index 3 index get add exch moveto pop
	}for pop pop
}__NXbdef
/yshow{
	0 1 3 index length 1 sub{
		currentpoint 4 index 3 index 1 getinterval show
		3 index 3 index get add moveto pop
	}for pop pop
}__NXbdef
/arct{arcto pop pop pop pop}__NXbdef
/setbbox{pop pop pop pop}__NXbdef
/ucache{}__NXbdef
/ucachestatus{mark 0 0 0 0 0}__NXbdef
/setucacheparams{cleartomark}__NXbdef
/uappend{systemdict begin cvx exec end}__NXbdef
/ueofill{gsave newpath uappend eofill grestore}__NXbdef
/ufill{gsave newpath uappend fill grestore}__NXbdef
/ustroke{
	gsave newpath dup length 6 eq
	{exch uappend concat}{uappend}ifelse
	stroke grestore
}__NXbdef
/__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse
/ustrokepath{
	newpath dup length 6 eq{
		exch uappend __NXustrokepathMatrix currentmatrix exch concat
		strokepath setmatrix
	}{uappend strokepath}ifelse
} __NXbdef
/upath{
	[exch {/ucache cvx}if pathbbox /setbbox cvx
	 {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx
} __NXbdef
/setstrokeadjust{pop}__NXbdef
/currentstrokeadjust{false}__NXbdef
/selectfont{exch findfont exch
dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef
/_NXCombineArrays{
	counttomark dup 2 add index dup length 3 -1 roll {
		2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch
	}repeat pop pop pop
}__NXbdef
/flushgraphics{}def
/setwindowtype{pop pop}def
/currentwindowtype{pop 0}def
/setalpha{pop}def
/currentalpha{1.0}def
/hidecursor{}def
/obscurecursor{}def
/revealcursor{}def
/setcursor{4 {pop}repeat}bind def
/showcursor{}def
/NextStepEncoding where not{
/NextStepEncoding StandardEncoding 256 array copy def
0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave
/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis
/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute
/Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright
176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior
204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave
/aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute
/ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth
/ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute
/ucircumflex 246/udieresis/yacute 252/thorn/ydieresis]
{dup type /nametype eq
 {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse
}forall pop
/NextStepEncoding NextStepEncoding readonly def
/_NXfstr 128 string dup 0 (_NX) putinterval def
/_NXfindfont /findfont load def
/findfont{
 % Because we can never let NextStepEncoding get into
 % SharedFontDirectory, we cannot reencode a font to NextStepEncoding
 % if we are in shared mode.  So if currentshared is true,
 % we call the normal findfont and return that
 /currentshared where {pop currentshared} {false} ifelse
 {_NXfindfont}
 {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll
  getinterval cvn exch FontDirectory 2 index known
  {pop FontDirectory exch get}
  {_NXfindfont dup /Encoding get StandardEncoding eq
   {	dup length dict exch
	{1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall
	 dup /Encoding NextStepEncoding put definefont
	}{exch pop} ifelse
   }ifelse
 }ifelse
}bind def
}{pop}ifelse
/_NXImageString {/__NXImageString where{pop}{/__NXImageString 4000 string
__NXdef}ifelse __NXImageString}__NXbdef
/_NXDoImageOp{
	3 dict begin /parr 5 array def 1 index{dup}{1}ifelse /chans exch def
	chans 2 add 2 roll parr 0 chans getinterval astore pop
	5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1
add}ifelse
	4 index mul /totbytes exch def pop exch pop
	gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore
	{0 1 chans 1 sub{parr exch get exec length totbytes exch sub /totbytes exch
def}for totbytes 0 le{exit}if}loop end
}__NXbdef
/alphaimage{1 add _NXDoImageOp}def
_NXLevel2{
	/NXCalibratedRGBColorSpace where{pop}{
		/NXCalibratedRGBColorSpace
		{mark /NXCalibratedRGB /ColorSpace findresource exch pop}stopped
		{cleartomark /NXCalibratedRGB[/CIEBasedABC 2 dict dup begin
		/MatrixLMN[.4124 .2126 .0193 .3576 .7152 .1192 .1805 .0722 .9505]def
		/WhitePoint[.9505 1 1.089] def end] /ColorSpace defineresource}if def}ifelse
	/nxsetrgbcolor{NXCalibratedRGBColorSpace setcolorspace setcolor}__NXbdef
	/nxsetgray{dup dup nxsetrgbcolor}__NXbdef
	/_NXCalibratedImage{exch{array astore dup length true}{false}ifelse
		8 -1 roll{NXCalibratedRGBColorSpace setcolorspace}if
		8 dict dup 9 1 roll begin /ImageType 1 def /MultipleDataSources exch def
		currentcolorspace 0 get /Indexed eq{pop /Decode[0 2 6 index exp 1 sub]def}
		{2 mul dup array /Decode exch def 1 sub 0 1 3 -1 roll{Decode exch dup 2 mod
put}for}ifelse
		/DataSource exch def /ImageMatrix exch def
		/BitsPerComponent exch def /Height exch def /Width exch def end
image}__NXbdef
} {
	/setcmykcolor{
		1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll
		4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if
setrgbcolor}__NXbdef
	/currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef
	/colorimage{_NXDoImageOp}__NXbdef
	/nxsetrgbcolor{setrgbcolor}__NXbdef /nxsetgray{setgray}__NXbdef
	/setpattern{pop .5 setgray}__NXbdef
	/_NXCalibratedImage{dup 1 eq {pop pop image}{colorimage}ifelse pop}__NXbdef
} ifelse
/_NXSetCMYKOrRGB where{pop}{
	mark{systemdict /currentwindow get exec}stopped
	{{pop pop pop setcmykcolor}}{{nxsetrgbcolor pop pop pop pop}}ifelse
/_NXSetCMYKOrRGB exch def cleartomark
}ifelse
%%EndProcSet

gsave
-20 -28 translate
 /__NXbasematrix matrix currentmatrix def
grestore
%%EndProlog
%%BeginSetup
%%PaperSize: Letter
/oval {
    translate scale newpath 0.5 0.5 0.5 0 360 arc closepath
} def /line {
    moveto rlineto stroke
} def /setup {
    setlinewidth setlinecap setlinejoin gsave
} def /arrow {
    newpath moveto dup rotate -13 6 rlineto 4 -6 rlineto -4 -6 rlineto
closepath gsave 0 setlinejoin stroke grestore fill neg rotate
} def
%%EndSetup

%%Page: 1 1
%%PageBoundingBox: 156 307 487 633
%%PageFonts: (atend)
%%BeginPageSetup
%%PaperSize: Letter
/__NXsheetsavetoken save def
36 36 translate
gsave
-20 -28 translate
 /__NXbasematrix matrix currentmatrix def
grestore
gsave
0 0 translate
%%EndPageSetup
gsave
0 0 540 720 rectclip
0 0 540 720 rectclip
0 0 0 setup
-9.000000 -94.000000 transform
gsave __NXbasematrix setmatrix itransform translate
0 0 612 792 rectclip

/__NXEPSSave save def /showpage {} def
_NXLevel2{/_NXsethsb where{pop}{/_NXsethsb /sethsbcolor load def}ifelse
/sethsbcolor{_NXsethsb currentrgbcolor nxsetrgbcolor}def
/setrgbcolor{nxsetrgbcolor}bind def /setgray{nxsetgray}bind def
/_NXcimage where{pop}{/_NXcimage /colorimage load def}ifelse /colorimage{dup 3
eq{true 2 index{1 index}{1}ifelse 7 add 1 roll
_NXCalibratedImage}{_NXcimage}ifelse}def}if
0 setgray 0 setlinecap 1 setlinewidth
0 setlinejoin 10 setmiterlimit [] 0 setdash newpath count /__NXEPSOpCount exch
def /__NXEPSDictCount countdictstack def
%%BeginDocument:
%!PS-Adobe-2.0
%%Title: sphal.ma  -  /Net/nxth06/Users/mshaposh
%%Creator: Mathematica
%%CreationDate: Fri Jun 11 10:22:36 1993
%%For: mshaposh
%%DocumentFonts: (atend)
%%Pages: (atend) 1
%%BoundingBox: (atend)
%%DocumentPaperSizes: Letter
%%Orientation: Portrait
%%NXNextStepVersion: 3.0
%%EndComments

%%BeginProcSet: /usr/lib/NextStep/printPackage.ps 3.0
%!
% NeXT Printing Package
% Version: 3.0
% Copyright: 1988, NeXT, Inc.

/__NXdef{1 index where{pop pop pop}{def}ifelse}bind def
/__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def
/UserObjects 10 array __NXdef
/defineuserobject{
	exch dup 1 add dup UserObjects length gt{
		array dup 0 UserObjects putinterval
		/UserObjects exch def
	}{pop}ifelse UserObjects exch 3 -1 roll put
}__NXbdef
/undefineuserobject{UserObjects exch null put}__NXbdef
/execuserobject{UserObjects exch get exec}__NXbdef
/__NXRectPath{4 2 roll moveto 1 index 0 rlineto
0 exch rlineto neg 0 rlineto closepath}__NXbdef
/__NXProcessRectArgs{
	1 index type /arraytype eq{
		exch 0 4 2 index length 1 sub{
			dup 3 add 1 exch{1 index exch get exch}for
			5 1 roll 5 index exec
		}for pop pop
	}{exec}ifelse
}__NXbdef
/rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs
grestore}__NXbdef
/rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef
/rectstroke{
	gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{
		{gsave __NXRectPath null concat stroke grestore}
		dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs
	}{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore
}__NXbdef
/_NXLevel2 systemdict /languagelevel known {languagelevel 2 ge}{false}ifelse
__NXdef
/xyshow{
	0 1 3 index length 1 sub{
		currentpoint 4 index 3 index 1 getinterval show
		3 index 3 index 2 mul 1 add get add exch
		3 index	3 index 2 mul get add exch moveto pop
	}for pop pop
}__NXbdef
/xshow{
	0 1 3 index length 1 sub{
		currentpoint 4 index 3 index 1 getinterval show
		exch 3 index 3 index get add exch moveto pop
	}for pop pop
}__NXbdef
/yshow{
	0 1 3 index length 1 sub{
		currentpoint 4 index 3 index 1 getinterval show
		3 index 3 index get add moveto pop
	}for pop pop
}__NXbdef
/arct{arcto pop pop pop pop}__NXbdef
/setbbox{pop pop pop pop}__NXbdef
/ucache{}__NXbdef
/ucachestatus{mark 0 0 0 0 0}__NXbdef
/setucacheparams{cleartomark}__NXbdef
/uappend{systemdict begin cvx exec end}__NXbdef
/ueofill{gsave newpath uappend eofill grestore}__NXbdef
/ufill{gsave newpath uappend fill grestore}__NXbdef
/ustroke{
	gsave newpath dup length 6 eq
	{exch uappend concat}{uappend}ifelse
	stroke grestore
}__NXbdef
/__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse
/ustrokepath{
	newpath dup length 6 eq{
		exch uappend __NXustrokepathMatrix currentmatrix exch concat
		strokepath setmatrix
	}{uappend strokepath}ifelse
} __NXbdef
/upath{
	[exch {/ucache cvx}if pathbbox /setbbox cvx
	 {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx
} __NXbdef
/setstrokeadjust{pop}__NXbdef
/currentstrokeadjust{false}__NXbdef
/selectfont{exch findfont exch
dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef
/_NXCombineArrays{
	counttomark dup 2 add index dup length 3 -1 roll {
		2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch
	}repeat pop pop pop
}__NXbdef
/flushgraphics{}def
/setwindowtype{pop pop}def
/currentwindowtype{pop 0}def
/setalpha{pop}def
/currentalpha{1.0}def
/hidecursor{}def
/obscurecursor{}def
/revealcursor{}def
/setcursor{4 {pop}repeat}bind def
/showcursor{}def
/NextStepEncoding where not{
/NextStepEncoding StandardEncoding 256 array copy def
0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave
/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis
/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute
/Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright
176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior
204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave
/aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute
/ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth
/ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute
/ucircumflex 246/udieresis/yacute 252/thorn/ydieresis]
{dup type /nametype eq
 {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse
}forall pop
/NextStepEncoding NextStepEncoding readonly def
/_NXfstr 128 string dup 0 (_NX) putinterval def
/_NXfindfont /findfont load def
/findfont{
 % Because we can never let NextStepEncoding get into
 % SharedFontDirectory, we cannot reencode a font to NextStepEncoding
 % if we are in shared mode.  So if currentshared is true,
 % we call the normal findfont and return that
 /currentshared where {pop currentshared} {false} ifelse
 {_NXfindfont}
 {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll
  getinterval cvn exch FontDirectory 2 index known
  {pop FontDirectory exch get}
  {_NXfindfont dup /Encoding get StandardEncoding eq
   {	dup length dict exch
	{1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall
	 dup /Encoding NextStepEncoding put definefont
	}{exch pop} ifelse
   }ifelse
 }ifelse
}bind def
}{pop}ifelse
/_NXImageString {/__NXImageString where{pop}{/__NXImageString 4000 string
__NXdef}ifelse __NXImageString}__NXbdef
/_NXDoImageOp{
	3 dict begin /parr 5 array def 1 index{dup}{1}ifelse /chans exch def
	chans 2 add 2 roll parr 0 chans getinterval astore pop
	5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1
add}ifelse
	4 index mul /totbytes exch def pop exch pop
	gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore
	{0 1 chans 1 sub{parr exch get exec length totbytes exch sub /totbytes exch
def}for totbytes 0 le{exit}if}loop end
}__NXbdef
/alphaimage{1 add _NXDoImageOp}def
_NXLevel2{
	/NXCalibratedRGBColorSpace where{pop}{
		/NXCalibratedRGBColorSpace
		{mark /NXCalibratedRGB /ColorSpace findresource exch pop}stopped
		{cleartomark /NXCalibratedRGB[/CIEBasedABC 2 dict dup begin
		/MatrixLMN[.4124 .2126 .0193 .3576 .7152 .1192 .1805 .0722 .9505]def
		/WhitePoint[.9505 1 1.089] def end] /ColorSpace defineresource}if def}ifelse
	/nxsetrgbcolor{NXCalibratedRGBColorSpace setcolorspace setcolor}__NXbdef
	/nxsetgray{dup dup nxsetrgbcolor}__NXbdef
	/_NXCalibratedImage{exch{array astore dup length true}{false}ifelse
		8 -1 roll{NXCalibratedRGBColorSpace setcolorspace}if
		8 dict dup 9 1 roll begin /ImageType 1 def /MultipleDataSources exch def
		currentcolorspace 0 get /Indexed eq{pop /Decode[0 2 6 index exp 1 sub]def}
		{2 mul dup array /Decode exch def 1 sub 0 1 3 -1 roll{Decode exch dup 2 mod
put}for}ifelse
		/DataSource exch def /ImageMatrix exch def
		/BitsPerComponent exch def /Height exch def /Width exch def end
image}__NXbdef
} {
	/setcmykcolor{
		1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll
		4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if
setrgbcolor}__NXbdef
	/currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef
	/colorimage{_NXDoImageOp}__NXbdef
	/nxsetrgbcolor{setrgbcolor}__NXbdef /nxsetgray{setgray}__NXbdef
	/setpattern{pop .5 setgray}__NXbdef
	/_NXCalibratedImage{dup 1 eq {pop pop image}{colorimage}ifelse pop}__NXbdef
} ifelse
/_NXSetCMYKOrRGB where{pop}{
	mark{systemdict /currentwindow get exec}stopped
	{{pop pop pop setcmykcolor}}{{nxsetrgbcolor pop pop pop pop}}ifelse
/_NXSetCMYKOrRGB exch def cleartomark
}ifelse
%%EndProcSet

_NXLevel2{/_NXsethsb where{pop}{/_NXsethsb /sethsbcolor load def}ifelse
/sethsbcolor{_NXsethsb currentrgbcolor nxsetrgbcolor}def
/setrgbcolor{nxsetrgbcolor}bind def /setgray{nxsetgray}bind def
}if
gsave
-20 9972 translate
 /__NXbasematrix matrix currentmatrix def
grestore
%%EndProlog
%%BeginSetup
%%PaperSize: Letter
%%EndSetup

%%Page: 1 1
%%PageBoundingBox:156 307 487 633
%%PageFonts: (atend)
%%BeginPageSetup
%%PaperSize: Letter
/__NXsheetsavetoken save def
0 0 translate
gsave
-20 9972 translate
 /__NXbasematrix matrix currentmatrix def
grestore
gsave
[1 0 0 -1 -19 10744] concat
19 9952 translate
%%EndPageSetup
gsave
0 0 612 792 rectclip
gsave
54 72 467 648 rectclip
1 setlinewidth 0 setgray
gsave
95 76 371.769226 230 rectclip
/Mnodistort true def
100 dict begin
/Mfixwid true def
/Mrot 0 def
/Mpstart {
    MathPictureStart
} bind def
/Mpend {
    MathPictureEnd
} bind def
/Mscale {
    0 1 0 1
    5 -1 roll
    MathScale
} bind def
/Plain	/Courier findfont def
/Bold	/Courier-Bold findfont def
/Italic /Courier-Oblique findfont def
/MathPictureStart {
	/Mimatrix
	 matrix currentmatrix
	def
	gsave
	newpath
	Mleft
	Mbottom
	translate
	1 -1 scale
	/Mtmatrix
	matrix currentmatrix
	def
	Plain
	Mfontsize scalefont
	setfont
	0 setgray
	0 setlinewidth
} bind def
/MathPictureEnd {
	grestore
} bind def
/MathSubStart {
        Mgmatrix Mtmatrix
        Mleft Mbottom
        Mwidth Mheight
        8 -2 roll
        moveto
        Mtmatrix setmatrix
        currentpoint
        Mgmatrix setmatrix
        10 -2 roll
        moveto
        Mtmatrix setmatrix
        currentpoint
        2 copy translate
        /Mtmatrix matrix currentmatrix def
        /Mleft 0 def
        /Mbottom 0 def
        3 -1 roll
        exch sub
        /Mheight exch def
        sub
        /Mwidth exch def
} bind def
/MathSubEnd {
        /Mheight exch def
        /Mwidth exch def
        /Mbottom exch def
        /Mleft exch def
        /Mtmatrix exch def
        dup setmatrix
        /Mgmatrix exch def
} bind def
/Mdot {
	moveto
	0 0 rlineto
	stroke
} bind def
/Mtetra {
	moveto
	lineto
	lineto
	lineto
	fill
} bind def
/Metetra {
	moveto
	lineto
	lineto
	lineto
	closepath
	gsave
	fill
	grestore
	0 setgray
	stroke
} bind def
/Mistroke {
	flattenpath
	0 0 0
	{
	4 2 roll
	pop pop
	}
	{
	4 -1 roll
	2 index
	sub dup mul
	4 -1 roll
	2 index
	sub dup mul
	add sqrt
	4 -1 roll
	add
	3 1 roll
	}
	{
	stop
	}
	{
	stop
	}
	pathforall
	pop pop
	currentpoint
	stroke
	moveto
	currentdash
	3 -1 roll
	add
	setdash
} bind def
/Mfstroke {
	stroke
	currentdash
	pop 0
	setdash
} bind def
/Mrotsboxa {
	gsave
	dup
	/Mrot
	exch def
	Mrotcheck
	Mtmatrix
	dup
	setmatrix
	7 1 roll
	4 index
	4 index
	translate
	rotate
	3 index
	-1 mul
	3 index
	-1 mul
	translate
	/Mtmatrix
	matrix
	currentmatrix
	def
	grestore
	Msboxa
	3  -1 roll
	/Mtmatrix
	exch def
	/Mrot
	0 def
} bind def
/Msboxa {
	newpath
	5 -1 roll
	Mvboxa
	pop
	Mboxout
	6 -1 roll
	5 -1 roll
	4 -1 roll
	Msboxa1
	5 -3 roll
	Msboxa1
	Mboxrot
	[
	7 -2 roll
	2 copy
	[
	3 1 roll
	10 -1 roll
	9 -1 roll
	]
	6 1 roll
	5 -2 roll
	]
} bind def
/Msboxa1 {
	sub
	2 div
	dup
	2 index
	1 add
	mul
	3 -1 roll
	-1 add
	3 -1 roll
	mul
} bind def
/Mvboxa	{
	Mfixwid
	{
	Mvboxa1
	}
	{
	dup
	Mwidthcal
	0 exch
	{
	add
	}
	forall
	exch
	Mvboxa1
	4 index
	7 -1 roll
	add
	4 -1 roll
	pop
	3 1 roll
	}
	ifelse
} bind def
/Mvboxa1 {
	gsave
	newpath
	[ true
	3 -1 roll
	{
	Mbbox
	5 -1 roll
	{
	0
	5 1 roll
	}
	{
	7 -1 roll
	exch sub
	(m) stringwidth pop
	.3 mul
	sub
	7 1 roll
	6 -1 roll
	4 -1 roll
	Mmin
	3 -1 roll
	5 index
	add
	5 -1 roll
	4 -1 roll
	Mmax
	4 -1 roll
	}
	ifelse
	false
	}
	forall
	{ stop } if
	counttomark
	1 add
	4 roll
	]
	grestore
} bind def
/Mbbox {
	0 0 moveto
	false charpath
	flattenpath
	pathbbox
	newpath
} bind def
/Mmin {
	2 copy
	gt
	{ exch } if
	pop
} bind def
/Mmax {
	2 copy
	lt
	{ exch } if
	pop
} bind def
/Mrotshowa {
	dup
	/Mrot
	exch def
	Mrotcheck
	Mtmatrix
	dup
	setmatrix
	7 1 roll
	4 index
	4 index
	translate
	rotate
	3 index
	-1 mul
	3 index
	-1 mul
	translate
	/Mtmatrix
	matrix
	currentmatrix
	def
	Mgmatrix setmatrix
	Mshowa
	/Mtmatrix
	exch def
	/Mrot 0 def
} bind def
/Mshowa {
	4 -2 roll
	moveto
	2 index
	Mtmatrix setmatrix
	Mvboxa
	7 1 roll
	Mboxout
	6 -1 roll
	5 -1 roll
	4 -1 roll
	Mshowa1
	4 1 roll
	Mshowa1
	rmoveto
	currentpoint
	Mfixwid
	{
	Mshowax
	}
	{
	Mshoway
	}
	ifelse
	pop pop pop pop
	Mgmatrix setmatrix
} bind def
/Mshowax {
	0 1
        4 index length
        -1 add
        {
        2 index
        4 index
        2 index
        get
        3 index
        add
        moveto
        4 index
        exch get
        show
        } for
} bind def
/Mshoway {
        3 index
        Mwidthcal
        5 1 roll
	0 1
	4 index length
	-1 add
	{
	2 index
	4 index
	2 index
	get
	3 index
	add
	moveto
	4 index
	exch get
	[
	6 index
	aload
	length
	2 add
	-1 roll
	{
	pop
	Strform
	stringwidth
	pop
	neg
	exch
	add
	0 rmoveto
	}
	exch
	kshow
	cleartomark
	} for
	pop
} bind def
/Mwidthcal {
	[
	exch
	{
	Mwidthcal1
	}
	forall
	]
	[
	exch
	dup
	Maxlen
	-1 add
	0 1
	3 -1 roll
	{
	[
	exch
	2 index
	{
	1 index
	Mget
	exch
	}
	forall
	pop
	Maxget
	exch
	}
	for
	pop
	]
	Mreva
} bind def
/Mreva	{
	[
	exch
	aload
	length
	-1 1
	{1 roll}
	for
	]
} bind def
/Mget	{
	1 index
	length
	-1 add
	1 index
	ge
	{
	get
	}
	{
	pop pop
	0
	}
	ifelse
} bind def
/Maxlen	{
	[
	exch
	{
	length
	}
	forall
	Maxget
} bind def
/Maxget	{
	counttomark
	-1 add
	1 1
	3 -1 roll
	{
	pop
	Mmax
	}
	for
	exch
	pop
} bind def
/Mwidthcal1 {
	[
	exch
	{
	Strform
	stringwidth
	pop
	}
	forall
	]
} bind def
/Strform {
	/tem (x) def
	tem 0
	3 -1 roll
	put
	tem
} bind def
/Mshowa1 {
	2 copy
	add
	4 1 roll
	sub
	mul
	sub
	-2 div
} bind def
/MathScale {
	Mwidth
	Mheight
	Mlp
	translate
	scale
	/Msaveaa exch def
	/Msavebb exch def
	/Msavecc exch def
	/Msavedd exch def
	/Mgmatrix
	matrix currentmatrix
	def
} bind def
/Mlp {
	3 copy
	Mlpfirst
	{
	Mnodistort
	{
	Mmin
	dup
	} if
	4 index
	2 index
	2 index
	Mlprun
	11 index
	11 -1 roll
	10 -4 roll
	Mlp1
	8 index
	9 -5 roll
	Mlp1
	4 -1 roll
	and
	{ exit } if
	3 -1 roll
	pop pop
	} loop
	exch
	3 1 roll
	7 -3 roll
	pop pop pop
} bind def
/Mlpfirst {
	3 -1 roll
	dup length
	2 copy
	-2 add
	get
	aload
	pop pop pop
	4 -2 roll
	-1 add
	get
	aload
	pop pop pop
	6 -1 roll
	3 -1 roll
	5 -1 roll
	sub
	dup /MsaveAx exch def
	div
	4 1 roll
	exch sub
	dup /MsaveAy exch def
	div
} bind def
/Mlprun {
	2 copy
	4 index
	0 get
	dup
	4 1 roll
	Mlprun1
	3 copy
	8 -2 roll
	9 -1 roll
	{
	3 copy
	Mlprun1
	3 copy
	11 -3 roll
	/gt Mlpminmax
	8 3 roll
	11 -3 roll
	/lt Mlpminmax
	8 3 roll
	} forall
	pop pop pop pop
	3 1 roll
	pop pop
	aload pop
	5 -1 roll
	aload pop
	exch
	6 -1 roll
	Mlprun2
	8 2 roll
	4 -1 roll
	Mlprun2
	6 2 roll
	3 -1 roll
	Mlprun2
	4 2 roll
	exch
	Mlprun2
	6 2 roll
} bind def
/Mlprun1 {
	aload pop
	exch
	6 -1 roll
	5 -1 roll
	mul add
	4 -2 roll
	mul
	3 -1 roll
	add
} bind def
/Mlprun2 {
	2 copy
	add 2 div
	3 1 roll
	exch sub
} bind def
/Mlpminmax {
	cvx
	2 index
	6 index
	2 index
	exec
	{
	7 -3 roll
	4 -1 roll
	} if
	1 index
	5 index
	3 -1 roll
	exec
	{
	4 1 roll
	pop
	5 -1 roll
	aload
	pop pop
	4 -1 roll
	aload pop
	[
	8 -2 roll
	pop
	5 -2 roll
	pop
	6 -2 roll
	pop
	5 -1 roll
	]
	4 1 roll
	pop
	}
	{
	pop pop pop
	} ifelse
} bind def
/Mlp1 {
	5 index
	3 index	sub
	5 index
	2 index mul
	1 index
	le
	1 index
	0 le
	or
	dup
	not
	{
	1 index
	3 index	div
	.99999 mul
	8 -1 roll
	pop
	7 1 roll
	}
	if
	8 -1 roll
	2 div
	7 -2 roll
	pop sub
	5 index
	6 -3 roll
	pop pop
	mul sub
	exch
} bind def
/intop 0 def
/inrht 0 def
/inflag 0 def
/outflag 0 def
/xadrht 0 def
/xadlft 0 def
/yadtop 0 def
/yadbot 0 def
/Minner {
	outflag
	1
	eq
	{
	/outflag 0 def
	/intop 0 def
	/inrht 0 def
	} if
	5 index
	gsave
	Mtmatrix setmatrix
	Mvboxa pop
	grestore
	3 -1 roll
	pop
	dup
	intop
	gt
	{
	/intop
	exch def
	}
	{ pop }
	ifelse
	dup
	inrht
	gt
	{
	/inrht
	exch def
	}
	{ pop }
	ifelse
	pop
	/inflag
	1 def
} bind def
/Mouter {
	/xadrht 0 def
	/xadlft 0 def
	/yadtop 0 def
	/yadbot 0 def
	inflag
	1 eq
	{
	dup
	0 lt
	{
	dup
	intop
	mul
	neg
	/yadtop
	exch def
	} if
	dup
	0 gt
	{
	dup
	intop
	mul
	/yadbot
	exch def
	}
	if
	pop
	dup
	0 lt
	{
	dup
	inrht
	mul
	neg
	/xadrht
	exch def
	} if
	dup
	0 gt
	{
	dup
	inrht
	mul
	/xadlft
	exch def
	} if
	pop
	/outflag 1 def
	}
	{ pop pop}
	ifelse
	/inflag 0 def
	/inrht 0 def
	/intop 0 def
} bind def
/Mboxout {
	outflag
	1
	eq
	{
	4 -1
	roll
	xadlft
	leadjust
	add
	sub
	4 1 roll
	3 -1
	roll
	yadbot
	leadjust
	add
	sub
	3 1
	roll
	exch
	xadrht
	leadjust
	add
	add
	exch
	yadtop
	leadjust
	add
	add
	/outflag 0 def
	/xadlft 0 def
	/yadbot 0 def
	/xadrht 0 def
	/yadtop 0 def
	} if
} bind def
/leadjust {
	(m) stringwidth pop
	.5 mul
} bind def
/Mrotcheck {
	dup
	90
	eq
	{
	yadbot
	/yadbot
	xadrht
	def
	/xadrht
	yadtop
	def
	/yadtop
	xadlft
	def
	/xadlft
	exch
	def
	}
	if
	dup
	cos
	1 index
	sin
	Checkaux
	dup
	cos
	1 index
	sin neg
	exch
	Checkaux
	3 1 roll
	pop pop
} bind def
/Checkaux {
	4 index
	exch
	4 index
	mul
	3 1 roll
	mul add
	4 1 roll
} bind def
/Mboxrot {
	Mrot
	90 eq
	{
	brotaux
	4 2
	roll
	}
	if
	Mrot
	180 eq
	{
	4 2
        roll
	brotaux
	4 2
	roll
	brotaux
	}
	if
	Mrot
	270 eq
	{
	4 2
	roll
	brotaux
	}
	if
} bind def
/brotaux {
	neg
	exch
	neg
} bind def
/Mabswid {
	Mimatrix
	0 get
	Mgmatrix
	0 get
	div
	mul
	setlinewidth
} bind def
/Mabsdash {
	exch
	Mimatrix
	0 get
	Mgmatrix
	0 get
	div
	[
	3 1 roll
	exch
	{
	exch
	dup
	3 -1 roll
	mul
	exch
	}
	forall
	pop ]
	exch
	setdash
} bind def
/colorimage where
{ pop }
{
/colorimage {
3 1 roll
 pop pop
 5 -1 roll
 mul
 4 1 roll
{
currentfile
1 index
readhexstring
pop }
image
} bind def
} ifelse
/sampledsound where
{ pop}
{ /sampledsound {
exch
pop
exch
5 1 roll
mul
4 idiv
mul
2 idiv
exch pop
exch
/Mtempproc exch def
{ Mtempproc pop }
repeat
} bind def
} ifelse

/Mleft		95.000000 def
/Mbottom	306.047974 def
/Mwidth		371.769226 def
/Mheight	230.047974 def
/Mfontsize 12 def
/Plain /Courier findfont def
%!
%%Creator: Mathematica
%%AspectRatio: 0.61803
MathPictureStart
/Courier findfont 10  scalefont  setfont
% Scaling calculations
0.02381 0.119048 3.285946 2.721257e-06 [
[(0)] 0.02381 0 0 2 Msboxa
[(2)] 0.2619 0 0 2 Msboxa
[(4)] 0.5 0 0 2 Msboxa
[(6)] 0.7381 0 0 2 Msboxa
[(8)] 0.97619 0 0 2 Msboxa
[(       6)(-1.2 10)] -0.0125 0.02044 1 0 Msboxa
[(        6)(-1.15 10)] -0.0125 0.1565 1 0 Msboxa
[(       6)(-1.1 10)] -0.0125 0.29256 1 0 Msboxa
[(        6)(-1.05 10)] -0.0125 0.42863 1 0 Msboxa
[(      6)(-1. 10)] -0.0125 0.56469 1 0 Msboxa
[ -0.001 -0.001 0 0 ]
[ 1.001 0.61903 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
%%Object: Graphics
[ ] 0 setdash
0 setgray
gsave
gsave
0.002 setlinewidth
0.02381 0 moveto
0.02381 0.00625 lineto
stroke
grestore
[(0)] 0.02381 0 0 2 Mshowa
gsave
0.002 setlinewidth
0.2619 0 moveto
0.2619 0.00625 lineto
stroke
grestore
[(2)] 0.2619 0 0 2 Mshowa
gsave
0.002 setlinewidth
0.5 0 moveto
0.5 0.00625 lineto
stroke
grestore
[(4)] 0.5 0 0 2 Mshowa
gsave
0.002 setlinewidth
0.7381 0 moveto
0.7381 0.00625 lineto
stroke
grestore
[(6)] 0.7381 0 0 2 Mshowa
gsave
0.002 setlinewidth
0.97619 0 moveto
0.97619 0.00625 lineto
stroke
grestore
[(8)] 0.97619 0 0 2 Mshowa
gsave
0.001 setlinewidth
0.07143 0 moveto
0.07143 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.11905 0 moveto
0.11905 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.16667 0 moveto
0.16667 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.21429 0 moveto
0.21429 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.30952 0 moveto
0.30952 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.35714 0 moveto
0.35714 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.40476 0 moveto
0.40476 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.45238 0 moveto
0.45238 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.54762 0 moveto
0.54762 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.59524 0 moveto
0.59524 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.64286 0 moveto
0.64286 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.69048 0 moveto
0.69048 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.78571 0 moveto
0.78571 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.83333 0 moveto
0.83333 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.88095 0 moveto
0.88095 0.00375 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.92857 0 moveto
0.92857 0.00375 lineto
stroke
grestore
gsave
0.002 setlinewidth
0 0 moveto
1 0 lineto
stroke
grestore
gsave
0.002 setlinewidth
0 0.02044 moveto
0.00625 0.02044 lineto
stroke
grestore
[(       6)(-1.2 10)] -0.0125 0.02044 1 0 Mshowa
gsave
0.002 setlinewidth
0 0.1565 moveto
0.00625 0.1565 lineto
stroke
grestore
[(        6)(-1.15 10)] -0.0125 0.1565 1 0 Mshowa
gsave
0.002 setlinewidth
0 0.29256 moveto
0.00625 0.29256 lineto
stroke
grestore
[(       6)(-1.1 10)] -0.0125 0.29256 1 0 Mshowa
gsave
0.002 setlinewidth
0 0.42863 moveto
0.00625 0.42863 lineto
stroke
grestore
[(        6)(-1.05 10)] -0.0125 0.42863 1 0 Mshowa
gsave
0.002 setlinewidth
0 0.56469 moveto
0.00625 0.56469 lineto
stroke
grestore
[(      6)(-1. 10)] -0.0125 0.56469 1 0 Mshowa
gsave
0.001 setlinewidth
0 0.04765 moveto
0.00375 0.04765 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.07486 moveto
0.00375 0.07486 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.10208 moveto
0.00375 0.10208 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.12929 moveto
0.00375 0.12929 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.18371 moveto
0.00375 0.18371 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.21093 moveto
0.00375 0.21093 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.23814 moveto
0.00375 0.23814 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.26535 moveto
0.00375 0.26535 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.31978 moveto
0.00375 0.31978 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.34699 moveto
0.00375 0.34699 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.3742 moveto
0.00375 0.3742 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.40141 moveto
0.00375 0.40141 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.45584 moveto
0.00375 0.45584 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.48305 moveto
0.00375 0.48305 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.51026 moveto
0.00375 0.51026 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.53748 moveto
0.00375 0.53748 lineto
stroke
grestore
gsave
0.001 setlinewidth
0 0.5919 moveto
0.00375 0.5919 lineto
stroke
grestore
gsave
0.002 setlinewidth
0 0 moveto
0 0.61803 lineto
stroke
grestore
grestore
gsave
gsave
0.002 setlinewidth
0.02381 0.61178 moveto
0.02381 0.61803 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.2619 0.61178 moveto
0.2619 0.61803 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.5 0.61178 moveto
0.5 0.61803 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.7381 0.61178 moveto
0.7381 0.61803 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.97619 0.61178 moveto
0.97619 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.07143 0.61428 moveto
0.07143 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.11905 0.61428 moveto
0.11905 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.16667 0.61428 moveto
0.16667 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.21429 0.61428 moveto
0.21429 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.30952 0.61428 moveto
0.30952 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.35714 0.61428 moveto
0.35714 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.40476 0.61428 moveto
0.40476 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.45238 0.61428 moveto
0.45238 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.54762 0.61428 moveto
0.54762 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.59524 0.61428 moveto
0.59524 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.64286 0.61428 moveto
0.64286 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.69048 0.61428 moveto
0.69048 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.78571 0.61428 moveto
0.78571 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.83333 0.61428 moveto
0.83333 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.88095 0.61428 moveto
0.88095 0.61803 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.92857 0.61428 moveto
0.92857 0.61803 lineto
stroke
grestore
gsave
0.002 setlinewidth
0 0.61803 moveto
1 0.61803 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.99375 0.02044 moveto
1 0.02044 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.99375 0.1565 moveto
1 0.1565 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.99375 0.29256 moveto
1 0.29256 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.99375 0.42863 moveto
1 0.42863 lineto
stroke
grestore
gsave
0.002 setlinewidth
0.99375 0.56469 moveto
1 0.56469 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.04765 moveto
1 0.04765 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.07486 moveto
1 0.07486 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.10208 moveto
1 0.10208 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.12929 moveto
1 0.12929 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.18371 moveto
1 0.18371 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.21093 moveto
1 0.21093 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.23814 moveto
1 0.23814 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.26535 moveto
1 0.26535 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.31978 moveto
1 0.31978 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.34699 moveto
1 0.34699 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.3742 moveto
1 0.3742 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.40141 moveto
1 0.40141 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.45584 moveto
1 0.45584 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.48305 moveto
1 0.48305 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.51026 moveto
1 0.51026 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.53748 moveto
1 0.53748 lineto
stroke
grestore
gsave
0.001 setlinewidth
0.99625 0.5919 moveto
1 0.5919 lineto
stroke
grestore
gsave
0.002 setlinewidth
1 0 moveto
1 0.61803 lineto
stroke
grestore
grestore
gsave
grestore
0 0 moveto
1 0 lineto
1 0.61803 lineto
0 0.61803 lineto
closepath
clip
newpath
gsave
gsave
0.004 setlinewidth
0.02382 0.53263 moveto
0.02506 0.53264 lineto
0.0263 0.53265 lineto
0.02754 0.53266 lineto
0.02878 0.53268 lineto
0.03126 0.53273 lineto
0.03374 0.53281 lineto
0.03622 0.53291 lineto
0.0387 0.53303 lineto
0.04366 0.53333 lineto
0.05358 0.5342 lineto
0.0635 0.53541 lineto
0.08334 0.53877 lineto
0.10319 0.54333 lineto
0.14287 0.55531 lineto
0.18255 0.56965 lineto
0.22223 0.58414 lineto
0.24207 0.59063 lineto
0.26191 0.59615 lineto
0.28175 0.60034 lineto
0.28671 0.60113 lineto
0.29168 0.60181 lineto
0.29664 0.60237 lineto
0.29912 0.60261 lineto
0.3016 0.60281 lineto
0.30408 0.60298 lineto
0.30656 0.60312 lineto
0.3078 0.60317 lineto
0.30904 0.60322 lineto
0.31028 0.60326 lineto
0.31152 0.60329 lineto
0.31276 0.60331 lineto
0.314 0.60332 lineto
0.31524 0.60332 lineto
0.31648 0.60331 lineto
0.31772 0.6033 lineto
0.31896 0.60327 lineto
0.3202 0.60324 lineto
0.32144 0.60319 lineto
0.32392 0.60307 lineto
0.3264 0.60291 lineto
0.33136 0.60248 lineto
0.33632 0.60188 lineto
0.34128 0.6011 lineto
0.3512 0.59901 lineto
0.36112 0.59617 lineto
0.37104 0.59252 lineto
0.38096 0.58802 lineto
0.4008 0.57631 lineto
0.42064 0.56069 lineto
Mistroke
0.44048 0.54082 lineto
0.46032 0.51641 lineto
0.50001 0.4528 lineto
0.53969 0.36779 lineto
0.57937 0.25967 lineto
0.61905 0.12709 lineto
Mfstroke
0.65096 0 moveto
0.61905 0.12709 lineto
stroke
stroke
stroke
stroke
stroke
stroke
stroke
stroke
stroke
stroke
grestore
grestore
% End of Graphics
MathPictureEnd%%PSTrailer
end

%%PageTrailer
%%DocumentFonts: Times-Roman
%%Trailer
%%DocumentFonts: Times-Roman
%%Pages: 1 1
%%BoundingBox:156 307 487 633


%%EndDocument
count __NXEPSOpCount sub {pop} repeat countdictstack __NXEPSDictCount sub {end}
repeat __NXEPSSave restore
grestore
grestore
0 0 0 setup
gsave
/Helvetica findfont 12 scalefont [1 0 0 -1 0 0] makefont
10
exch
defineuserobject
10 execuserobject setfont
0 nxsetgray
[1 0 0 -1 0 783] concat
10 execuserobject setfont
0 nxsetgray
418 396 moveto (z) show
grestore
grestore
0 0 0 setup
grestore
0 setgray
0.333333 setgray
gsave
0 0 540 720 rectclip
[1 0 0 -1 0 720] concat
gsave
1 nxsetgray
92 145 28 15 rectfill
10 execuserobject setfont
0 nxsetgray
94 157 moveto (V\(z\)) show
grestore
grestore
grestore
grestore
showpage
__NXsheetsavetoken restore
%%PageTrailer
%%DocumentFonts: Helvetica
%%Trailer
%%DocumentFonts: Helvetica
%%Pages: 1 1
%%BoundingBox:156 307 487 633







