%Paper: 
%From: Pivovarov <aapiv@theory.kek.jp>
%Date: Fri, 04 Mar 1994 10:30:56 +0900


\documentstyle[12pt]{article}
\textwidth 15cm
\textheight 22.5cm

\def\beq{\begin{equation}}
\def\eeq{\end{equation}}
\def\bea{\begin{eqnarray}}
\def\eea{\end{eqnarray}}
\def\bq{\begin{quote}}
\def\eq{\end{quote}}

\def\ga{\left(}
\def\dr{\right)}
\def\aga{\left\{}
\def\adr{\right\}}

\def\rar{\rightarrow}

\def\la{\langle}
\def\ra{\rangle}
\begin{document}
\topmargin -1.0cm
\oddsidemargin +0.2cm
\evensidemargin -1.0cm
\pagestyle{empty}
\begin{flushright}
{CERN-TH.7140/94}\\
PM 93/16 \\
{KEK Preprint 93-184}
\end{flushright}
\vspace*{5mm}
\begin{center}
{{\bf QSSR ESTIMATE OF THE $B_B$ PARAMETER \\
AT NEXT-TO-LEADING
 ORDER}}
 \\
\vspace*{1cm}
{\bf S. Narison} \\
\vspace{0.3cm}
Theoretical Physics Division, CERN\\
CH - 1211 Geneva 23, Switzerland\\
and\\
Laboratoire de Physique Math\'ematique\\
Universit\'e de Montpellier II\\
Place Eug\`ene Bataillon\\
34095  Montpellier Cedex 05, France\\
and\\
{\bf A.A. Pivovarov
\footnote{On leave from
Institute for Nuclear Research of the Russian Academy of
Sciences, Moscow, Russia}}\\
 National Laboratory for High Energy Physics (KEK),\\
1-1 Oho, Tsukuba,
Ibaraki 305,
Japan \\
\vspace*{1.0cm}
{\bf ABSTRACT} \\ \end{center}
\vspace*{2mm}
\noindent
We compute the leading $\alpha_s$ corrections
to the two-point correlator of
the $O_{\Delta B=2}$ operator which controls the $B^0 \bar B^0$ mixing.
Using this result within the QCD spectral sum rules
approach and some phenomenologically reasonable assumptions in the
parametrization of the spectral function,
we conclude
that the vacuum saturation values
$B_B\simeq B_{B^*}\simeq 1$ are satisfied within 15\%.

\noindent
%\rule[.1in]{15.0cm}{.002in}

 \vspace*{1.5cm}

\begin{flushleft}
CERN-TH.7140/94 \\
PM 93/16\\
{KEK Preprint 93-184}\\
January  1994
\end{flushleft}
\vfill\eject
\pagestyle{empty}

\setcounter{page}{1}
\pagestyle{plain}

\vskip 2cm

The violation of the CP symmetry is still one of
the most intriguing phenomena in particle physics.
The standard model (SM) offers a pattern for an explanation of
this violation through the complex phase of the unitary
Cabibbo-Kobayashi-Maskawa quark mixing matrix for three generations.
The rigorous experimental test of the pattern
requires knowing the
numerical values of some hadronic matrix elements
at low energies with some non-perturbative QCD methods.

In this paper we discuss an estimate of the $B_d^0$-$\bar B_d^0$
mixing parameter within the QCD spectral sum rules (QSSR)
approach [1,2] along the lines of Ref. [3],
but by including the new $\alpha_s$ corrections and by
taking care on the detailed contributions of different
$B$-like states to the spectral function.
In so doing, we estimate the two-point correlator of the
 $O_{\Delta B=2}=(\bar b_L \gamma_\mu d_L)^2$
operator, where $q_L$ are left-handed quark fields
$$
T(x)
=\langle 0|TO_{\Delta B=2}(x)O_{\Delta B=2}(0)| 0 \rangle .
\eqno (1)
$$
The leading term has a trivial expression in
the configuration space.
Indeed, to leading order in $\alpha_s$, it simply reads
$$
T_0(x)=2 N_c^2 \left(1+{1\over N_c}\right) 16
S'(x,m)S(-x,0)S'(x,m)S(-x,0)
$$
$$
=2 \left(1+{1\over N_c}\right)\mbox{tr}[S(x,m)S(-x,0)]
\mbox{tr}[S(x,m)S(-x,0)]
=2 \left(1+{1\over N_c}\right)\Pi_5(x)\Pi_5(x)
\eqno (2)
$$
where $S(x,m)$ is the free fermion propagator
and $N_c$ stands for the number of quark colours.
The prime means
taking only the part of the propagator
that is proportional to a $\gamma$ matrix.
The function
$\Pi_5(x)=\langle 0|Tj_5(x)j_5(0)| 0 \rangle$
is the two-point correlator
associated to the current $j_5 = \bar b i\gamma_5 d$.

One can also rewrite Eq.~(2) in the form
$$
T_0(x)
=2 \ga 1+{1\over N_c}\dr \Pi_{\mu\nu}(x)\Pi^{\mu\nu}(x),
\eqno (3)
$$
where
$\Pi^{\mu\nu}(x)=\langle 0|Tj_L^\mu(x)j_L^\nu(0)| 0 \rangle$
and
$j_L^\mu=\bar b_L \gamma^\mu d_L$,
which has the following
Lorentz decomposition in $x$-space
$$
\Pi^{\mu\nu}(x)
=(-\partial^\mu\partial^\nu+g^{\mu\nu}\partial^2)\Pi_T(x^2)
-\partial^\mu \partial^\nu\Pi_L(x^2).
$$
Formulae (2) and (3) demonstrate an explicit factorization
of the correlator (1) in the configuration
space to leading order in $\alpha_s$.

The dispersion representation in $x$-space for any
two-point correlator $\Pi_j(x)$ ($j=T,L,5$) has the form
$$
i\Pi_j(x^2)=\int_{s_j}^\infty r_j(s)D(x,s)ds,
\eqno (4)
$$
where $D(x,s)$ is a free boson
propagator with the ``mass" $\sqrt s$. The spectral functions $r_j$,
read to leading order in $\alpha_s$:
$$
r_L^{(0)}(s)=N_c{1\over 16 \pi^2}z(1-z)^2,
{}~~r_T^{(0)}(s)=N_c{1\over 16 \pi^2}{1\over 3}(1-z)^2(2+z),
$$
$$
r_5^{(0)}(s)=m_b^2 N_c {1\over 16\pi^2} 2 {(1-z)^2\over z},
\eqno (5)
$$
where $z=m_b^2/s$, $m_b$ is the $b$-quark pole mass.

One can define the spectral function $\rho(s)$ of the
full correlator $T(x)$ in the same way as in Eq.~(4) and express
it, to first order in $\alpha_s$,
in terms of the spectral functions $r_j(s)$ associated
to the two-line correlators. Therefore
$$
\rho(s)=\int r_1(s_1)r_2(s_2)\Phi(s;s_1,s_2)ds_1ds_2,
\eqno (6)
$$
where
$$
\Phi(s;s_1,s_2)={1\over 16\pi^2 s}
\sqrt{(s-s_1-s_2)^2-4 s_1 s_2}
\eqno (7)
$$
is the two-body phase-space factor, and the concrete form
of the spectral functions $r_j(s)$ entering Eq.~(6)
depends on the representation chosen for the correlator
$T(x)$ (as in Eqs.~(2,3) for $T_0(x)$).
The integration region in Eq.~(6) is determined by the properties
of the phase-space factor (7) for corresponding
representation of the whole correlator;
$\Phi(s;s_1,s_2)$ is supposed to be equal to zero within
kinematically forbidden regions.

To leading order in $1/N_c$, one can write the correlator $T(x)$
as a product of two two-line correlators
given in Eq.~(4). It is worthwhile to notice that
this decomposition is gauge-invariant
and finite, i.e. it does not require any renormalization
that is a reflection of the vanishing of
the operator $O_{\Delta B=2}$
anomalous dimension in leading order in $1/N_c$.

Including $\alpha_s$ corrections, the spectral function
in the factorization approximation reads:
$$
\rho_{fact}(s)=\rho_0(s)
(1+\Delta \rho_f(s)),
\eqno (8)
$$
where $\rho_0(s)$ generates the leading-order term
and $\Delta \rho_f(s)$ is a (properly normalized)
factorized correction in the $\alpha_s$ order.
The colour structure is the following
$$
\rho_0(s)=N_c^2\left(1+{1\over N_c}\right)\tilde\rho_0(s),
{}~~~\Delta \rho_f(s)=C_F{\alpha_s\over \pi}\Delta
\tilde \rho_f(s),
$$
where $C_F=(N_c^2-1)/2N_c$ for the $SU(N_c)$ colour
group and the quantities with the tilde contain
no explicit $N_c$ dependence.

The representation of the spectral density $\rho_{fact}(s)$
through those of two-line correlators for
the vector-like decomposition in Eq.~(3) is:
$$
\rho_{fact}(s)= \int ds_1ds_2
\Phi(s;s_1,s_2)
\{ \ga {s^2_{12}\over 4}+2s_1 s_2\dr r_T(s_1)r_T(s_2)
$$
$$
+\ga{s^2_{12}\over 4}-s_1 s_2\dr
\ga r_T(s_1)r_L(s_2)+r_L(s_1)r_T(s_2)\dr
+{s^2_{12}\over 4}r_L(s_1)r_L(s_2 \}
$$
where $s_{12}=s-s_1-s_2$.
The non-factorizable corrections are of the $1/N_c$ order
and the full spectral density can be written
in the form
$$
\rho(s)=
\rho_0(s)\left(1+\Delta \rho_f(s)+\Delta
\rho_{nf}(s)\right)
\eqno (9a)
$$
and
$$
\Delta
\rho_{nf}(s)=
{C_F\over N_c+1}{\alpha_s\over \pi}\Delta \tilde \rho_{nf}(s)
=
{1\over 2}\left(1-{1\over N_c}\right){\alpha_s\over \pi}
\Delta \tilde\rho_{nf}(s).
\eqno (9b)
$$
One of the diagrams contributing to the non-factorizable
part of the whole spectral density is given in Fig.~1.

Several comments are in order here. The decomposition (9)
is gauge-invariant. The same is true for
the anomalous dimension of the operator $O_{\Delta B=2}$.
We use four-dimensional algebra of Dirac's $\gamma$ matrices
throughout the computation.
This seems quite natural because it allows one
to make Fierz rearrangements freely, which
is crucial for establishing the validity of
factorization.  At the same time this approach simply implies
the special choice of the renormalization scheme.
So, this scheme is not the standard
$\overline{\rm{MS}}$ one and
it is not the real dimensional reduction as used in [4]
either.
To the considered order in $\alpha_s$,
however, the scheme dependence reduces to
a certain choice of the normalization parameter $\mu$.
In principle, one can fix the scheme by direct comparison
of our results
with the massless limit for corresponding correlator
[5] or, to put it another way, by
comparing the non-logarithmic parts of corrections in the massless
limit one can obtain the relation between our parameter $\mu$
and
the corresponding $\mu_{\overline{MS}}$ or $\mu_{DimRed}$.
Thus, the answer in any desired scheme can be easily recovered
by considering the massless limit.
In the present
paper
we
do not dwell on this point.

We have computed numerically the spectral density $\rho(s)$
in the first non-leading
order in $\alpha_s$. We analyse our results,
paying special attention to the presentation of the
entire spectral density
$\rho(s)$
as a sum of factorizable and
non-factorizable pieces, as in Eq.~(9).
This decomposition is useful from the theoretical point of
view. It is also interesting from the $1/N_c$ analysis,
and
it is quite convenient technically.  As for the factorizable
part of the spectral density (Eq.~8) the analytical expressions for
two-line spectral functions $r_{T,L}(s)$
are well known
to  first order in $\alpha_s$,
and we
use them as they have been
given in Refs. [6,7].
For the non-factorizable part of the spectral density, we have to
compute the gluon-exchange diagram both for unequal mass
lines and for equal mass lines of a two-line correlator.  We
have done it using the REDUCE system of analytical
computation [8]
and the table of two-loop integrals given in
[6,7].
After using a Fierz transformation, these non-factorizable
diagrams
can be represented in form analogous to that of the factorizable
diagrams, i.e. the corresponding
analytical expression is given by
a product of two traces in Dirac's
indices.
The transformed diagrams are given in Fig.~2.

For diagrams with a gluon connecting $b$ or $d$-quarks in the loop
(Fig.~2(a,b)), the resulting representation can be rendered
into a product of two scalar spectral densities of two-line correlators.
The relevant part of the spectral density reads:
$$
r_m(s)={1\over 16\pi^2}s\left\{(2(1-2 z)v
+C_F{\alpha_s\over \pi}
\left(-4 v (1-2 z)({1\over \epsilon}+2\ln{\mu^2\over m_b^2}) \right.\right.
$$
$$
+4(1-2 z)(1-v)\ln z+(1+v)(4zv+(3+v)(z-1))\ln{1-v\over 1+v}
$$
$$
\left.\left.+(1-2z)^2\phi(u)+v(18z-13)+16z-8\right)\right\},
$$
where $\epsilon=2-D/2$, $D$
is the dimensional regularization parameter,
$v=\sqrt{1-{4 m_b^2\over s}}\equiv\sqrt{1-4z}$,
$\phi(u)=8(Sp(u^2)-Sp(-u))+4(2\ln(1-u^2)-\ln(1+u))\ln u $,
$u=(1-v)/(1+v)$,
$$
Sp(u)=-\int_0^u{\ln(1-t)\over t}dt.
$$
For a zero mass correlator
($d$-quark), the spectral density has the form
$$
r_0^(s)={1\over 16\pi^2}s\left\{2+C_F{\alpha_s\over \pi}
\left(-4 ({1\over \epsilon}+2\ln {\mu^2\over s} )-21\right)\right\} .
$$

The corresponding representation
for diagrams, with different quark flavours tied with a gluon in the
loop,
is of the vector type. The
nonfactorizable first order corrections to the spectral densities
are:
$$
r_{L,T}(s)=r_{L,T}^{(0)}(s)+C_F{\alpha_s\over \pi}r_{L,T}^{(1)}(s),
$$
$$
r_L^{(1)}(s)=z(1-z)^2({1\over \epsilon}+2\ln{\mu^2\over m_b^2})
-2z(1-z)^2\ln(1-z)\ln({z\over 1-z})
$$
$$
+z(1-z)^2(4z^2-3z+{1\over 2})\ln({z\over 1-z})
+4z(1-z)^2 Sp(-{z\over 1-z})
+z(1-z)(2z-3)\ln(1-z)
$$
$$
z(4z^2-7z+{3\over 2})\ln z
+{65\over 12}z^3-{17\over 2}z^2+{21\over 4}z-{2\over 3},
$$
$$
3 r_T^{(1)}(s)=(z+2)(1-z)^2({1\over \epsilon}+2\ln{\mu^2\over m_b^2})
-2(z+2)(1-z)^2\ln(1-z)\ln({z\over 1-z})
$$
$$
+(1-z)^2(2z^3-2z^2+{5\over 2}z+2)\ln({z\over 1-z})
+4(z+2)(1-z)^2 Sp(-{z\over 1-z})
$$
$$
+z(1-z)(2z+1)\ln(1-z)
+(3z^3+2z^2-{9\over 2}z+2)\ln z
+{41\over 12}z^3+{3\over 2}z^2-{75\over 4}z+{46\over 3}.
$$

The whole computation can be subjected to a
powerful test consisting in the cancellation of
divergences by the one-loop renormalization constant of the
operator $O_{\Delta B=2}$, which is known
to be $Z_{O_{\Delta B=2}}=1-3(1-1/N_c){\alpha_s\over 4\pi\epsilon}$.
We checked this cancellation explicitly.

The QCD results for the spectral density are given in Table 1.

At larger $s$ (say, $s\ge 5 m_b^2$),
where the perturbative QCD result makes sense,
one can notice that the
non-factorizable correction dies out faster than the
factorizable one, so that the full correction comes mainly
from that of the two-line correlator.
Therefore, at sufficiently large $s$, the factorization
(in the sense of Eqs.~(2) and (3)) becomes exact
and the `formal' $1/N_c$ suppression
of non-factorizable corrections becomes numerically valid.

Using the QSSR approach
for estimating $B_B$, we can work with the moments:
$$
M_i(s_{th})=\int_{4m^2_b}^{s_{th}}\rho(s)s^{-i}ds,
\eqno (10)
$$
which can be decomposed as:
$$
M_i(s_{th})=M_i^0(s_{th})
\left(
1+\Delta M_i^f(s_{th})+
\Delta M_i^{nf}(s_{th})
\right),
$$
according to the corresponding decomposition of
the spectral density, Eq.~(9a).

We show in Table 2 the strength
of the non-factorizable correction for $s\ge 5 m_b^2$
for the following set of input parameters:
$\Lambda^{(5)}_{\overline{MS}}=175~$MeV,
$m_b=4.6~$GeV,
and with the one-loop expression for the strong coupling constant
$\alpha_s(\mu)=6\pi/23\ln(\mu/\Lambda^{(5)}_{\overline{MS}})$
at the point $\mu=m_b$.
For given regions of integration
in Eq.~(10), the moments
of the factorizable spectral density are
practically independent of the power $i$
of the weight function $s^{-i}$.
They change by less than 5\% for $i$=1-10.
The non-factorizable correction changes its sign within
the integration region for $s\ge 5.5 m_b^2$,
and its moments are more sensitive to the power $i$.
One can notice that the non-factorizable
correction does not exceed a 15\% level with respect to the full
factorized spectral density at sufficiently large $s$.
The full order-$\alpha_s$ corrections (factorizable+non-factorizable)
can be quite large for both the spectral density itself and its moments
depending on the energy $s$ as they
can reach a magnitude of 100\% with respect to the leading
term. Hopefully, the non-factorizable corrections,
measured in terms of the fully factorized
(lowest order + $\alpha_s$ terms) spectral density
are, nevertheless, still moderate. However,
all the factorizable corrections
to the correlator (1),
no matter how large they are, can be absorbed into the calculation
of the decay constant $f_B$ from the two-point correlator with two
quark lines, in such a way that the relevant corrections to the $B_B$
parameter are only due to the non-factorizable ones.

Contrary to the QCD part, the estimate of the phenomenological
contributions to the correlator is much more involved.
For the analysis to be performed one might make the following
phenomenological assumptions:

\noindent
-- the minimal choice of operator:
$O_{\Delta B=2}=g_{\Delta B=2}\partial_\mu B \partial^\mu B$,
can give a good description of the spectral function.

\noindent
-- the contributions of
the $BB$ and
$B^* B^*$ pairs to the spectral function are equal
due to their approximate degeneracy
and to the equal values of their decay constants [9]
(this feature is fully satisfied in the large $m_b$ limit);

\noindent
--we do not have  exotic contributions due to
a singlet mixture of colored states or due
to some four-quark-like states which may
restore the $N_c$-structure of the correlator
in order to match the proper $(1+1/N_c)$
construction entering the standard definition
of the $B_B$ parameter.

Within these phenomenological assumptions,
we can conclude that the effect of inclusion of the perturbative
corrections into the QCD part of the correlator on the $B_B$ parameter
is reasonably small and the change is not larger than $15\%$.
The absolute value
of $B_B$ however cannot be unambiguously established
using the perturbative part of the correlator only.
Assuming that non-perturbative non-factorizable corrections are small
and the factorizable corrections are properly taken into account
through $f_B$ we find after correcting for exotic contributions
in theoretical part of the correlator
$$
B_B \simeq B_{B^*}
\simeq (1.00\pm 0.15)
$$
where we have not explicitly written the small effect due to the
anomalous dimension of the operator $O_{\Delta B=2}$.

An improvement of our result needs an explicit quantitative check of
the previous phenomenological assumptions.
Most probably, the QSSR approach based on the three-point function
[10] may be more appropriate, as it does not need some of the assumptions
which we have used for the two-point function. Unfortunately,
one has to face, in this case, a highly involved computation of the
non-recursive three-loop non-factorizable diagrams
in order to obtain the $\alpha_s$ corrections.

{\bf Acknowledgement}

S.N. would like to thank A. Pich for discussions.
A.A.P. acknowledges the kind hospitality extended to him at
the Laboratoire de Physique Math\'ematique of Montpellier,
where the main part of the present
computation
has been done
and thanks the Centre International des Etudiants et Stagiaires (CIES)
of the European Community for financial support.
The work of A.A.P. is partly supported by Japan Society for the Promotion
of Science (JSPS).


\begin{thebibliography}{99}
\bibitem{1} M.A. Shifman, A.I. Vainshtein and V.I. Zakharov,
            Nucl.Phys. B147 (1979) 385, 448.
\bibitem{2} For a recent review, see e.g.:
            S. Narison, QCD spectral sum rules,\\
            World Scientific Lecture Notes
            in Physics, vol. 26 (1989).
\bibitem{3} A. Pich, Phys.Lett.  B206(1988)322.
\bibitem{4} G. Altarelli, G. Curci, G. Martinelli and S. Petrarca,
            Nucl.Phys. B187(1981)461.
\bibitem{5} A. Pich and E.~de Rafael, Phys.Lett.  B158(1985)477.
\bibitem{6} S.C. Generalis, PhD thesis, Open University preprint
            OUT-4102-13 (1984).
\bibitem{7} S.C. Generalis, J.Phys. G16(1990)785.
\bibitem{8} A.C. Hearn, REDUCE user's manual, RAND Publication CP78(Rev 7/91),
            1991.
\bibitem{9} S. Narison, Phys.Lett. B198(1987) 104; B216(1988)191,
B308 (1993) 365,
Z. Phys. C55 (1992) 55
and
Talk given at the Third Workshop on $\tau$ Charm Factory, 1-6th June
1993, Marbella, Spain, CERN preprint TH-7042/93 (1993).
\bibitem{10} A.A.Ovchinnikov and A.A.Pivovarov, Phys.Lett. B207(1988)333.

\end{thebibliography}

\newpage
\begin{table}
\begin{center}
\begin{tabular}{|c|c|c|c|} \hline

$s/m_b^2$   &$\Delta\rho_f$ &$\Delta\rho_{nf}$
&$\Delta\rho_{nf}/(1+\Delta\rho_f)$\\ \hline

5.5 &1.03   &0.02     &0.01 \\ \hline
6.0 &0.95   &0.21     &0.11  \\ \hline
6.5 &0.89   &0.29     &0.15  \\ \hline
7.0 &0.84   &0.32     &0.17  \\ \hline
\end{tabular}
\caption{Normalized spectral densities}
%\end{table}
\vspace{3cm}
%\begin{table}
\begin{tabular}{|c|c|c|c|c|} \hline

$i$&$s_{th}/m_b^2$&$\Delta M_f$ &$\Delta M_{nf}$ &$\Delta
M_{nf}/(1+\Delta M_f)$\\ \hline

0&5.5   &1.07 &-0.16 &-0.08  \\ \cline{2-5}
 &6.0   &0.99  &0.11  &0.06  \\ \cline{2-5}
 &6.5   &0.93  &0.23  &0.12  \\ \cline{2-5}
 &7.0   &0.88  &0.29  &0.15  \\ \hline

5&5.5   &1.08 &-0.21 &-0.10  \\ \cline{2-5}
 &6.0   &1.00  &0.08  &0.04  \\ \cline{2-5}
 &6.5   &0.94  &0.20  &0.11  \\ \cline{2-5}
 &7.0   &0.89  &0.27  &0.14  \\ \hline

10&5.5   &1.09 &-0.27 &-0.13  \\ \cline{2-5}
  &6.0   &1.01  &0.02  &0.01  \\ \cline{2-5}
  &6.5   &0.96  &0.16  &0.08  \\ \cline{2-5}
  &7.0   &0.91  &0.23  &0.12  \\ \hline
\end{tabular}
\end{center}
\caption{Normalized moments of spectral densities}
\end{table}

\end{document}
****************
===================================
PostScript source file for figures
===================================
%!PS-Adobe-3.0 EPSF-3.0
%%Creator: Adobe Illustrator(TM) 5.0
%%For: (Arlette) (CERN)
%%Title: (Narison25)
%%CreationDate: (3/2/94) (11:34)
%%BoundingBox: 142 153 493 587
%%DocumentProcessColors: Black
%%DocumentFonts: Helvetica
%%DocumentSuppliedResources: procset Adobe_packedarray 2.0 0
%%+ procset Adobe_cshow 1.1 0
%%+ procset Adobe_customcolor 1.0 0
%%+ procset Adobe_typography_AI3 1.0 1
%%+ procset Adobe_pattern_AI3 1.0 0
%%+ procset Adobe_Illustrator_AI3 1.0 1
%AI3_ColorUsage: Black&White
%AI3_IncludePlacedImages
%AI3_TemplateBox: 305.5 396.5 305.5 396.5
%AI3_TileBox: 29 -32 589 765
%AI3_DocumentPreview: Header
%%EndComments
%%BeginProlog
%%BeginResource: procset Adobe_packedarray 2.0 0
%%Title: (Packed Array Operators)
%%Version: 2.0
%%CreationDate: (8/2/90) ()
%%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved)
userdict /Adobe_packedarray 5 dict dup begin put
/initialize
{
/packedarray where
	{
	pop
	}
	{
	Adobe_packedarray begin
	Adobe_packedarray
		{
		dup xcheck
			{
			bind
			} if
		userdict 3 1 roll put
		} forall
 end
	} ifelse
} def
/terminate
{
} def
/packedarray
{
array astore readonly
} def
/setpacking
{
pop
} def
/currentpacking
{
false
} def
currentdict readonly pop end
%%EndResource
Adobe_packedarray /initialize get exec
%%BeginResource: procset Adobe_cshow 1.1 0
%%Title: (cshow Operator)
%%Version: 1.1
%%CreationDate: (1/23/89) ()
%%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved)
currentpacking true setpacking
userdict /Adobe_cshow 3 dict dup begin put
/initialize
{
/cshow where
	{
	pop
	}
	{
	userdict /Adobe_cshow_vars 1 dict dup begin put
	/_cshow
		{} def
	Adobe_cshow begin
	Adobe_cshow
		{
		dup xcheck
			{
			bind
			} if
		userdict 3 1 roll put
		} forall
 end
 end
	} ifelse
} def
/terminate
{
} def
/cshow
{
exch
Adobe_cshow_vars
	exch /_cshow
	exch put
	{
	0 0 Adobe_cshow_vars /_cshow get exec
	} forall
} def
currentdict readonly pop end
setpacking
%%EndResource
%%BeginResource: procset Adobe_customcolor 1.0 0
%%Title: (Custom Color Operators)
%%Version: 1.0
%%CreationDate: (5/9/88) ()
%%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved)
currentpacking true setpacking
userdict /Adobe_customcolor 5 dict dup begin put
/initialize
{
/setcustomcolor where
	{
	pop
	}
	{
	Adobe_customcolor begin
	Adobe_customcolor
		{
		dup xcheck
			{
			bind
			} if
		pop pop
		} forall
 end
	Adobe_customcolor begin
	} ifelse
} def
/terminate
{
currentdict Adobe_customcolor eq
	{
 end
	} if
} def
/findcmykcustomcolor
{
5 packedarray
}  def
/setcustomcolor
{
exch
aload pop pop
4
	{
	4 index mul 4 1 roll
	} repeat
5 -1 roll pop
setcmykcolor
} def
/setoverprint
{
pop
} def
currentdict readonly pop end
setpacking
%%EndResource
%%BeginResource: procset Adobe_typography_AI3 2.0 0
%%Title: (Typography Operators)
%%Version: 2.0
%%CreationDate:(5/31/90) ()
%%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved)
currentpacking true setpacking
userdict /Adobe_typography_AI3 48 dict dup begin put
/initialize
{
/TZ
 where
	{
	pop
	}
	{
	Adobe_typography_AI3 begin
	Adobe_typography_AI3
		{
		dup xcheck
			{
			bind
			} if
		pop pop
		} forall
 end
	Adobe_typography_AI3 begin
	} ifelse
} def
/terminate
{
currentdict Adobe_typography_AI3 eq
	{
 end
	} if
} def
/modifyEncoding
{
	/_tempEncode exch ddef

	/_pntr 0 ddef

	{
		counttomark -1 roll
		dup type dup /marktype eq
		{
			pop pop exit
		}
		{
			/nametype eq
			{
				_tempEncode /_pntr dup load dup 3 1 roll 1 add ddef 3 -1 roll
				put
			}
			{
				/_pntr exch ddef
			}
			ifelse
		}
		ifelse
	}
	loop

	_tempEncode
}
def
/TE
{
	StandardEncoding 256 array copy modifyEncoding
	/_nativeEncoding exch def
} def
%
/TZ
{
	dup type /arraytype eq {/_wv exch def} {/_wv 0 def} ifelse
	/_useNativeEncoding exch def
	pop pop

	findfont _wv type /arraytype eq {_wv makeblendedfont} if dup length 2 add dict

 begin

		mark exch
		{
			1 index /FID ne { def } if cleartomark mark
		}
		forall
		pop

		/FontName exch def

		counttomark 0 eq
		{
			1 _useNativeEncoding eq
			{
				/Encoding _nativeEncoding def
			}
			if
			cleartomark
		}
		{
			/Encoding load 256 array copy
			modifyEncoding /Encoding exch def
		}
		ifelse
		FontName currentdict
 end

	definefont pop
}
def
/tr
{
_ax _ay 3 2 roll
} def
/trj
{
_cx _cy _sp _ax _ay 6 5 roll
} def
/a0
{
/Tx
	{
	dup
	currentpoint 3 2 roll
	tr _psf
	newpath moveto
	tr _ctm _pss
	} ddef
/Tj
	{
	dup
	currentpoint 3 2 roll
	trj _pjsf
	newpath moveto
	trj _ctm _pjss
	} ddef

} def
/a1
{
/Tx
	{
	dup currentpoint 4 2 roll gsave
	dup currentpoint 3 2 roll
	tr _psf
	newpath moveto
	tr _ctm _pss
	grestore 3 1 roll moveto tr sp
	} ddef
/Tj
	{
	dup currentpoint 4 2 roll gsave
	dup currentpoint 3 2 roll
	trj _pjsf
	newpath moveto
	trj _ctm _pjss
	grestore 3 1 roll moveto tr sp
	} ddef

} def
/e0
{
/Tx
	{
	tr _psf
	} ddef
/Tj
	{
	trj _pjsf
	} ddef
} def
/e1
{
/Tx
	{
	dup currentpoint 4 2 roll gsave
	tr _psf
	grestore 3 1 roll moveto tr sp
	} ddef
/Tj
	{
	dup currentpoint 4 2 roll gsave
	trj _pjsf
	grestore 3 1 roll moveto tr sp
	} ddef
} def
/i0
{
/Tx
	{
	tr sp
	} ddef
/Tj
	{
	trj jsp
	} ddef
} def
/i1
{
W N
} def
/o0
{
/Tx
	{
	tr sw rmoveto
	} ddef
/Tj
	{
	trj swj rmoveto
	} ddef
} def
/r0
{
/Tx
	{
	tr _ctm _pss
	} ddef
/Tj
	{
	trj _ctm _pjss
	} ddef
} def
/r1
{
/Tx
	{
	dup currentpoint 4 2 roll currentpoint gsave newpath moveto
	tr _ctm _pss
	grestore 3 1 roll moveto tr sp
	} ddef
/Tj
	{
	dup currentpoint 4 2 roll currentpoint gsave newpath moveto
	trj _ctm _pjss
	grestore 3 1 roll moveto tr sp
	} ddef
} def
/To
{
	pop _ctm currentmatrix pop
} def
/TO
{
	iTe _ctm setmatrix newpath
} def
/Tp
{
	pop _tm astore pop _ctm setmatrix
	_tDict begin /W {} def /h {} def
} def
/TP
{
 end
	iTm 0 0 moveto
} def
/Tr
{
	_render 3 le {currentpoint newpath moveto} if
	dup 8 eq {pop 0} {dup 9 eq {pop 1} if} ifelse
	dup /_render exch ddef
	_renderStart exch get load exec
} def
/iTm
{
_ctm setmatrix _tm concat 0 _rise translate _hs 1 scale
} def
/Tm
{
_tm astore pop iTm 0 0 moveto
} def
/Td
{
_mtx translate _tm _tm concatmatrix pop iTm 0 0 moveto
} def
/iTe
{
	_render -1 eq {} {_renderEnd _render get dup null ne {load exec} {pop} ifelse}
	/_render -1 ddef
} def
/Ta
{
pop
} def
/Tf
{
dup 1000 div /_fScl exch ddef
exch findfont exch scalefont setfont
} def
/Tl
{
pop
0 exch _leading astore pop
} def
/Tt
{
pop
} def
/TW
{
3 npop
} def
/Tw
{
/_cx exch ddef
} def
/TC
{
3 npop
} def
/Tc
{
/_ax exch ddef
} def
/Ts
{
/_rise exch ddef
currentpoint
iTm
moveto
} def
/Ti
{
3 npop
} def
/Tz
{
100 div /_hs exch ddef
iTm
} def
/TA
{
pop
} def
/Tq
{
pop
} def
/Th
{
pop pop pop pop pop
} def
/TX {pop} def
%/Tx
%/Tj
/Tk
{
exch pop _fScl mul neg 0 rmoveto
} def
/TK
{
2 npop
} def
/T*
{
_leading aload pop neg Td
} def
/T*-
{
_leading aload pop Td
} def
/T-
{
_hyphen Tx
} def
/T+
{} def
/TR
{
_ctm currentmatrix pop
_tm astore pop
iTm 0 0 moveto
} def
/TS
{
0 eq {Tx} {Tj} ifelse
} def
currentdict readonly pop end
setpacking
%%EndResource
%%BeginResource: procset Adobe_pattern_AI3 1.0 0
%%Title: (Adobe Illustrator (R) Version 3.0 Pattern Operators)
%%Version: 1.0
%%CreationDate: (7/21/89) ()
%%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved)
currentpacking true setpacking
userdict /Adobe_pattern_AI3 16 dict dup begin put
/initialize
{
/definepattern where
	{
	pop
	}
	{
	Adobe_pattern_AI3 begin
	Adobe_pattern_AI3
		{
		dup xcheck
			{
			bind
			} if
		pop pop
		} forall
	mark
	cachestatus 7 1 roll pop pop pop pop exch pop exch
		{
		{
		10000 add
		dup 2 index gt
			{
			break
			} if
		dup setcachelimit
		} loop
		} stopped
	cleartomark
	} ifelse
} def
/terminate
{
currentdict Adobe_pattern_AI3 eq
	{
 end
	} if
} def
errordict
/nocurrentpoint
{
pop
stop
} put
errordict
/invalidaccess
{
pop
stop
} put
/patternencoding
256 array def
0 1 255
{
patternencoding exch ( ) 2 copy exch 0 exch put cvn put
} for
/definepattern
{
17 dict begin
/uniform exch def
/cache exch def
/key exch def
/procarray exch def
/mtx exch matrix invertmatrix def
/height exch def
/width exch def
/ctm matrix currentmatrix def
/ptm matrix def
/str 32 string def
/slice 9 dict def
slice /s 1 put
slice /q 256 procarray length div sqrt floor cvi put
slice /b 0 put
/FontBBox [0 0 0 0] def
/FontMatrix mtx matrix copy def
/Encoding patternencoding def
/FontType 3 def
/BuildChar
	{
	exch
 begin
	slice begin
	dup q dup mul mod s idiv /i exch def
	dup q dup mul mod s mod /j exch def
	q dup mul idiv procarray exch get
	/xl j width s div mul def
	/xg j 1 add width s div mul def
	/yl i height s div mul def
	/yg i 1 add height s div mul def
	uniform
		{
		1 1
		}
		{
		width 0 dtransform
		dup mul exch dup mul add sqrt dup 1 add exch div
		0 height dtransform
		dup mul exch dup mul add sqrt dup 1 add exch div
		} ifelse
	width 0 cache
		{
		xl 4 index mul yl 4 index mul xg 6 index mul yg 6 index mul
		setcachedevice
		}
		{
		setcharwidth
		} ifelse
	gsave
	scale
	newpath
	xl yl moveto
	xg yl lineto
	xg yg lineto
	xl yg lineto
	closepath
	clip
	newpath
 end
 end
	exec
	grestore
	} def
key currentdict definefont
end
} def
/patterncachesize
{
gsave
newpath
0 0 moveto
width 0 lineto
width height lineto
0 height lineto
closepath
patternmatrix setmatrix
pathbbox
exch ceiling 4 -1 roll floor sub 3 1 roll
ceiling exch floor sub
mul 1 add
grestore
} def
/patterncachelimit
{
cachestatus 7 1 roll 6 npop 8 mul
} def
/patternpath
{
exch dup begin setfont
ctm setmatrix
concat
slice exch /b exch slice /q get dup mul mul put
FontMatrix concat
uniform
	{
	width 0 dtransform round width div exch round width div exch
	0 height dtransform round height div exch height div exch
	0 0 transform round exch round exch
	ptm astore setmatrix
	}
	{
	ptm currentmatrix pop
	} ifelse
{currentpoint} stopped not
	{
	2 npop
	pathbbox
	true
	4 index 3 index eq
	4 index 3 index eq
	and
		{
		pop false
			{
			{2 npop}
			{3 npop true}
			{7 npop true}
			{pop true}
			pathforall
			} stopped
			{
			5 npop true
			} if
		} if
		{
		height div ceiling height mul 4 1 roll
		width div ceiling width mul 4 1 roll
		height div floor height mul 4 1 roll
		width div floor width mul 4 1 roll
		2 index sub height div ceiling cvi exch
		3 index sub width div ceiling cvi exch
		4 2 roll moveto
		FontMatrix mtx invertmatrix
		dup dup 4 get exch 5 get rmoveto
		ptm ptm concatmatrix pop
		slice /s
		patterncachesize patterncachelimit div ceiling sqrt ceiling cvi
		dup slice /q get gt
			{
			pop slice /q get
			} if
		put
		0 1 slice /s get dup mul 1 sub
			{
			slice /b get add
			gsave
			0 1 str length 1 sub
				{
				str exch 2 index put
				} for
			pop
			dup
				{
				gsave
				ptm setmatrix
				1 index str length idiv {str show} repeat
				1 index str length mod str exch 0 exch getinterval show
				grestore
				0 height rmoveto
				} repeat
			grestore
			} for
		2 npop
		}
		{
		4 npop
		} ifelse
	} if
end
} def
/patternclip
{
clip
} def
/patternstrokepath
{
strokepath
} def
/patternmatrix
matrix def
/patternfill
{
dup type /dicttype eq
	{
	Adobe_pattern_AI3 /patternmatrix get
	} if
gsave
patternclip
Adobe_pattern_AI3 /patternpath get exec
grestore
newpath
} def
/patternstroke
{
dup type /dicttype eq
	{
	Adobe_pattern_AI3 /patternmatrix get
	} if
gsave
patternstrokepath
true
	{
		{
			{
			newpath
			moveto
			}
			{
			lineto
			}
			{
			curveto
			}
			{
			closepath
			3 copy
			Adobe_pattern_AI3 /patternfill get exec
			} pathforall
		3 npop
		} stopped
			{
			5 npop
			patternclip
			Adobe_pattern_AI3 /patternfill get exec
			} if
	}
	{
	patternclip
	Adobe_pattern_AI3 /patternfill get exec
	} ifelse
grestore
newpath
} def
/patternashow
{
3 index type /dicttype eq
	{
	Adobe_pattern_AI3 /patternmatrix get 4 1 roll
	} if
	{
	2 npop (0) exch
	2 copy 0 exch put pop
	gsave
	false charpath currentpoint
	6 index 6 index 6 index
	Adobe_pattern_AI3 /patternfill get exec
	grestore
	newpath moveto
	2 copy rmoveto
	} exch cshow
5 npop
} def
/patternawidthshow
{
6 index type /dicttype eq
	{
	Adobe_pattern_AI3 /patternmatrix get 7 1 roll
	} if
	{
	2 npop (0) exch
	2 copy 0 exch put
	gsave
	_sp eq {5 index 5 index rmoveto} if
	false charpath currentpoint
	9 index 9 index 9 index
	Adobe_pattern_AI3 /patternfill get exec
	grestore
	newpath moveto
	2 copy rmoveto
	} exch cshow
8 npop
} def
/patternashowstroke
{
4 index type /dicttype eq
	{
	patternmatrix /patternmatrix get 5 1 roll
	} if
4 1 roll
	{
	2 npop (0) exch
	2 copy 0 exch put pop
	gsave
	false charpath
	currentpoint
	4 index setmatrix
	7 index 7 index 7 index
	Adobe_pattern_AI3 /patternstroke get exec
	grestore
	newpath moveto
	2 copy rmoveto
	} exch cshow
6 npop
} def
/patternawidthshowstroke
{
7 index type /dicttype eq
	{
	patternmatrix /patternmatrix get 8 1 roll
	} if
7 1 roll
	{
	2 npop (0) exch
	2 copy 0 exch put
	gsave
	_sp eq {5 index 5 index rmoveto} if
	false charpath currentpoint
	7 index setmatrix
	10 index 10 index 10 index
	Adobe_pattern_AI3 /patternstroke get exec
	grestore
	newpath moveto
	2 copy rmoveto
	} exch cshow
9 npop
} def
currentdict readonly pop end
setpacking
%%EndResource
%%BeginResource: procset Adobe_Illustrator_AI3 1.0 3
%%Title: (Adobe Illustrator (R) Version 3.0 Full Prolog)
%%Version: 1.0
%%CreationDate: (7/22/89) ()
%%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved)
currentpacking true setpacking
userdict /Adobe_Illustrator_AI3 71 dict dup begin put
/initialize
{
userdict /Adobe_Illustrator_AI3_vars 67 dict dup begin put
/_lp /none def
/_pf {} def
/_ps {} def
/_psf {} def
/_pss {} def
/_pjsf {} def
/_pjss {} def
/_pola 0 def
/_doClip 0 def
/cf	currentflat def
/_tm matrix def
/_renderStart [/e0 /r0 /a0 /o0 /e1 /r1 /a1 /i0] def
/_renderEnd [null null null null /i1 /i1 /i1 /i1] def
/_render -1 def
/_rise 0 def
/_ax 0 def
/_ay 0 def
/_cx 0 def
/_cy 0 def
/_leading [0 0] def
/_ctm matrix def
/_mtx matrix def
/_sp 16#020 def
/_hyphen (-) def
/_fScl 0 def
/_cnt 0 def
/_hs 1 def
/_nativeEncoding 0 def
/_useNativeEncoding 0 def
/_tempEncode 0 def
/_pntr 0 def
/_tDict 2 dict def
/_wv 0 def
/Tx {} def
/Tj {} def
/CRender {} def
/_AI3_savepage {} def
/_gf null def
/_cf 4 array def
/_if null def
/_of false def
/_fc {} def
/_gs null def
/_cs 4 array def
/_is null def
/_os false def
/_sc {} def
/_pd 1 dict def
/_ed 15 dict def
/_pm matrix def
/_fm null def
/_fd null def
/_fdd null def
/_sm null def
/_sd null def
/_sdd null def
/_i null def
Adobe_Illustrator_AI3 begin
Adobe_Illustrator_AI3 dup /nc get begin
	{
	dup xcheck
		{
		bind
		} if
	pop pop
	} forall
end
end
end
Adobe_Illustrator_AI3 begin
Adobe_Illustrator_AI3_vars begin
newpath
} def
/terminate
{
end
end
} def
/_
null def
/ddef
{
Adobe_Illustrator_AI3_vars 3 1 roll put
} def
/xput
{
dup load dup length exch maxlength eq
	{
	dup dup load dup
	length 2 mul dict copy def
	} if
load begin def end
} def
/npop
{
	{
	pop
	} repeat
} def
/sw
{
dup length exch stringwidth
exch 5 -1 roll 3 index mul add
4 1 roll 3 1 roll mul add
} def
/swj
{
dup 4 1 roll
dup length exch stringwidth
exch 5 -1 roll 3 index mul add
4 1 roll 3 1 roll mul add
6 2 roll /_cnt 0 ddef
{1 index eq {/_cnt _cnt 1 add ddef} if} forall pop
exch _cnt mul exch _cnt mul 2 index add 4 1 roll 2 index add 4 1 roll pop pop
} def
/ss
{
4 1 roll
	{
	2 npop
	(0) exch 2 copy 0 exch put pop
	gsave
	false charpath currentpoint
	4 index setmatrix
	stroke
	grestore
	moveto
	2 copy rmoveto
	} exch cshow
3 npop
} def
/jss
{
4 1 roll
	{
	2 npop
	(0) exch 2 copy 0 exch put
	gsave
	_sp eq
		{
		exch 6 index 6 index 6 index 5 -1 roll widthshow
		currentpoint
		}
		{
		false charpath currentpoint
		4 index setmatrix stroke
		}ifelse
	grestore
	moveto
	2 copy rmoveto
	} exch cshow
6 npop
} def
/sp
{
	{
	2 npop (0) exch
	2 copy 0 exch put pop
	false charpath
	2 copy rmoveto
	} exch cshow
2 npop
} def
/jsp
{
	{
	2 npop
	(0) exch 2 copy 0 exch put
	_sp eq
		{
		exch 5 index 5 index 5 index 5 -1 roll widthshow
		}
		{
		false charpath
		}ifelse
	2 copy rmoveto
	} exch cshow
5 npop
} def
/pl
{
transform
0.25 sub round 0.25 add exch
0.25 sub round 0.25 add exch
itransform
} def
/setstrokeadjust where
	{
	pop true setstrokeadjust
	/c
	{
	curveto
	} def
	/C
	/c load def
	/v
	{
	currentpoint 6 2 roll curveto
	} def
	/V
	/v load def
	/y
	{
	2 copy curveto
	} def
	/Y
	/y load def
	/l
	{
	lineto
	} def
	/L
	/l load def
	/m
	{
	moveto
	} def
	}
	{
	/c
	{
	pl curveto
	} def
	/C
	/c load def
	/v
	{
	currentpoint 6 2 roll pl curveto
	} def
	/V
	/v load def
	/y
	{
	pl 2 copy curveto
	} def
	/Y
	/y load def
	/l
	{
	pl lineto
	} def
	/L
	/l load def
	/m
	{
	pl moveto
	} def
	} ifelse
/d
{
setdash
} def
/cf	{} def
/i
{
dup 0 eq
	{
	pop cf
	} if
setflat
} def
/j
{
setlinejoin
} def
/J
{
setlinecap
} def
/M
{
setmiterlimit
} def
/w
{
setlinewidth
} def
/H
{} def
/h
{
closepath
} def
/N
{
_pola 0 eq
	{
	_doClip 1 eq {clip /_doClip 0 ddef} if
	newpath
	}
	{
	/CRender {N} ddef
	}ifelse
} def
/n
{N} def
/F
{
_pola 0 eq
	{
	_doClip 1 eq
		{
		gsave _pf grestore clip newpath /_lp /none ddef _fc
		/_doClip 0 ddef
		}
		{
		_pf
		}ifelse
	}
	{
	/CRender {F} ddef
	}ifelse
} def
/f
{
closepath
F
} def
/S
{
_pola 0 eq
	{
	_doClip 1 eq
		{
		gsave _ps grestore clip newpath /_lp /none ddef _sc
		/_doClip 0 ddef
		}
		{
		_ps
		}ifelse
	}
	{
	/CRender {S} ddef
	}ifelse
} def
/s
{
closepath
S
} def
/B
{
_pola 0 eq
	{
	_doClip 1 eq
	gsave F grestore
		{
		gsave S grestore clip newpath /_lp /none ddef _sc
		/_doClip 0 ddef
		}
		{
		S
		}ifelse
	}
	{
	/CRender {B} ddef
	}ifelse
} def
/b
{
closepath
B
} def
/W
{
/_doClip 1 ddef
} def
/*
{
count 0 ne
	{
	dup type (stringtype) eq {pop} if
	} if
_pola 0 eq {newpath} if
} def
/u
{} def
/U
{} def
/q
{
_pola 0 eq {gsave} if
} def
/Q
{
_pola 0 eq {grestore} if
} def
/*u
{
_pola 1 add /_pola exch ddef
} def
/*U
{
_pola 1 sub /_pola exch ddef
_pola 0 eq {CRender} if
} def
/D
{pop} def
/*w
{} def
/*W
{} def
/`
{
/_i save ddef
6 1 roll 4 npop
concat pop
userdict begin
/showpage {} def
0 setgray
0 setlinecap
1 setlinewidth
0 setlinejoin
10 setmiterlimit
[] 0 setdash
newpath
0 setgray
false setoverprint
} def
/~
{
end
_i restore
} def
/@
{} def
/&
{} def
/O
{
0 ne
/_of exch ddef
/_lp /none ddef
} def
/R
{
0 ne
/_os exch ddef
/_lp /none ddef
} def
/g
{
/_gf exch ddef
/_fc
{
_lp /fill ne
	{
	_of setoverprint
	_gf setgray
	/_lp /fill ddef
	} if
} ddef
/_pf
{
_fc
fill
} ddef
/_psf
{
_fc
ashow
} ddef
/_pjsf
{
_fc
awidthshow
} ddef
/_lp /none ddef
} def
/G
{
/_gs exch ddef
/_sc
{
_lp /stroke ne
	{
	_os setoverprint
	_gs setgray
	/_lp /stroke ddef
	} if
} ddef
/_ps
{
_sc
stroke
} ddef
/_pss
{
_sc
ss
} ddef
/_pjss
{
_sc
jss
} ddef
/_lp /none ddef
} def
/k
{
_cf astore pop
/_fc
{
_lp /fill ne
	{
	_of setoverprint
	_cf aload pop setcmykcolor
	/_lp /fill ddef
	} if
} ddef
/_pf
{
_fc
fill
} ddef
/_psf
{
_fc
ashow
} ddef
/_pjsf
{
_fc
awidthshow
} ddef
/_lp /none ddef
} def
/K
{
_cs astore pop
/_sc
{
_lp /stroke ne
	{
	_os setoverprint
	_cs aload pop setcmykcolor
	/_lp /stroke ddef
	} if
} ddef
/_ps
{
_sc
stroke
} ddef
/_pss
{
_sc
ss
} ddef
/_pjss
{
_sc
jss
} ddef
/_lp /none ddef
} def
/x
{
/_gf exch ddef
findcmykcustomcolor
/_if exch ddef
/_fc
{
_lp /fill ne
	{
	_of setoverprint
	_if _gf 1 exch sub setcustomcolor
	/_lp /fill ddef
	} if
} ddef
/_pf
{
_fc
fill
} ddef
/_psf
{
_fc
ashow
} ddef
/_pjsf
{
_fc
awidthshow
} ddef
/_lp /none ddef
} def
/X
{
/_gs exch ddef
findcmykcustomcolor
/_is exch ddef
/_sc
{
_lp /stroke ne
	{
	_os setoverprint
	_is _gs 1 exch sub setcustomcolor
	/_lp /stroke ddef
	} if
} ddef
/_ps
{
_sc
stroke
} ddef
/_pss
{
_sc
ss
} ddef
/_pjss
{
_sc
jss
} ddef
/_lp /none ddef
} def
/dp
{
dup null eq
{
pop
_dp 0 ne
	{
	0 1 _dp 1 sub _dl mod
		{
		_da exch get 3 get
		} for
	_dp 1 sub _dl mod 1 add packedarray
	_da 0 get aload pop 8 -1 roll 5 -1 roll pop 4 1 roll
	definepattern pop
	} if
}
{
_dp 0 ne _dp _dl mod 0 eq and
	{
	null dp
	} if
7 packedarray _da exch _dp _dl mod exch put
_dp _dl mod _da 0 get 4 get 2 packedarray
/_dp _dp 1 add def
} ifelse
} def
/E
{
_ed begin
dup 0 get type /arraytype ne
	{
	0
		{
		dup 1 add index type /arraytype eq
			{
			1 add
			}
			{
			exit
			} ifelse
		} loop
	array astore
	} if
/_dd exch def
/_ury exch def
/_urx exch def
/_lly exch def
/_llx exch def
/_n exch def
/_y 0 def
/_dl 4 def
/_dp 0 def
/_da _dl array def
0 1 _dd length 1 sub
	{
	/_d exch _dd exch get def
	0 2 _d length 2 sub
		{
		/_x exch def
		/_c _d _x get _ ne def
		/_r _d _x 1 add get cvlit def
		_r _ ne
			{
			_urx _llx sub _ury _lly sub [1 0 0 1 0 0]
				[
				/save cvx
				_llx neg _lly neg /translate cvx
				_c
					{
					nc /begin cvx
					} if
				_r dup type /stringtype eq
					{
					cvx
					}
					{
					{exec} /forall cvx
					} ifelse
				_c
					{
					/end cvx
					} if
				/restore cvx
				] cvx
			/_fn 12 _n length add string def
			_y _fn cvs pop
			/_y _y 1 add def
			_fn 12 _n putinterval
			_fn _c false dp
			_d exch _x 1 add exch put
			} if
		} for
	} for
null dp
_n _dd /_pd
end xput
} def
/fc
{
_fm dup concatmatrix pop
} def
/p
{
/_fm exch ddef
9 -2 roll _pm translate fc
7 -2 roll _pm scale fc
5 -1 roll _pm rotate fc
4 -2 roll exch 0 ne
	{
	dup _pm rotate fc
	1 -1 _pm scale fc
	neg _pm rotate fc
	}
	{
	pop
	} ifelse
dup _pm rotate fc
exch dup sin exch cos div 1 0 0 1 0 6 2 roll
_pm astore fc
neg _pm rotate fc
_pd exch get /_fdd exch ddef
/_pf
{
save
/_doClip 0 ddef
0 1 _fdd length 1 sub
	{
	/_fd exch _fdd exch get ddef
	_fd
	0 2 _fd length 2 sub
		{
		gsave
		2 copy get dup _ ne
			{
			cvx exec _fc
			}
			{
			pop
			} ifelse
		2 copy 1 add get dup _ ne
			{
			aload pop findfont _fm
			patternfill
			}
			{
			pop
			fill
			} ifelse
		grestore
		pop
		} for
	pop
	} for
restore
newpath
} ddef
/_psf
{
save
/_doClip 0 ddef
0 1 _fdd length 1 sub
	{
	/_fd exch _fdd exch get ddef
	_fd
	0 2 _fd length 2 sub
		{
		gsave
		2 copy get dup _ ne
			{
			cvx exec _fc
			}
			{
			pop
			} ifelse
		2 copy 1 add get dup _ ne
			{
			aload pop findfont _fm
			9 copy 6 npop patternashow
			}
			{
			pop
			6 copy 3 npop ashow
			} ifelse
		grestore
		pop
		} for
	pop
	} for
restore
%3 npop newpath
sw rmoveto
} ddef
/_pjsf
{
save
/_doClip 0 ddef
0 1 _fdd length 1 sub
	{
	/_fd exch _fdd exch get ddef
	_fd
	0 2 _fd length 2 sub
		{
		gsave
		2 copy get dup _ ne
			{
			cvx exec _fc
			}
			{
			pop
			} ifelse
		2 copy 1 add get dup _ ne
			{
			aload pop findfont _fm
			12 copy 6 npop patternawidthshow
			}
			{
			pop 9 copy 3 npop awidthshow
			} ifelse
		grestore
		pop
		} for
	pop
	} for
restore
swj rmoveto
} ddef
/_lp /none ddef
} def
/sc
{
_sm dup concatmatrix pop
} def
/P
{
/_sm exch ddef
9 -2 roll _pm translate sc
7 -2 roll _pm scale sc
5 -1 roll _pm rotate sc
4 -2 roll exch 0 ne
	{
	dup _pm rotate sc
	1 -1 _pm scale sc
	neg _pm rotate sc
	}
	{
	pop
	} ifelse
dup _pm rotate sc
exch dup sin exch cos div 1 0 0 1 0 6 2 roll
_pm astore sc
neg _pm rotate sc
_pd exch get /_sdd exch ddef
/_ps
{
save
/_doClip 0 ddef
0 1 _sdd length 1 sub
	{
	/_sd exch _sdd exch get ddef
	_sd
	0 2 _sd length 2 sub
		{
		gsave
		2 copy get dup _ ne
			{
			cvx exec _sc
			}
			{
			pop
			} ifelse
		2 copy 1 add get dup _ ne
			{
			aload pop findfont _sm
			patternstroke
			}
			{
			pop stroke
			} ifelse
		grestore
		pop
		} for
	pop
	} for
restore
newpath
} ddef
/_pss
{
save
/_doClip 0 ddef
0 1 _sdd length 1 sub
	{
	/_sd exch _sdd exch get ddef
	_sd
	0 2 _sd length 2 sub
		{
		gsave
		2 copy get dup _ ne
			{
			cvx exec _sc
			}
			{
			pop
			} ifelse
		2 copy 1 add get dup _ ne
			{
			aload pop findfont _sm
			10 copy 6 npop patternashowstroke
			}
			{
			pop 7 copy 3 npop ss
			} ifelse
		grestore
		pop
		} for
	pop
	} for
restore
pop sw rmoveto
} ddef
/_pjss
{
save
/_doClip 0 ddef
0 1 _sdd length 1 sub
	{
	/_sd exch _sdd exch get ddef
	_sd
	0 2 _sd length 2 sub
		{
		gsave
		2 copy get dup _ ne
			{
			cvx exec _sc
			}
			{
			pop
			} ifelse
		2 copy 1 add get dup _ ne
			{
			aload pop findfont _sm
			13 copy 6 npop patternawidthshowstroke
			}
			{
			pop 10 copy 3 npop jss
			} ifelse
		grestore
		pop
		} for
	pop
	} for
restore
pop swj rmoveto
} ddef
/_lp /none ddef
} def
/A
{
pop
} def
/nc 3 dict def
nc begin
/setgray
{
pop
} bind def
/setcmykcolor
{
4 npop
} bind def
/setcustomcolor
{
2 npop
} bind def
currentdict readonly pop end
currentdict readonly pop end
setpacking
/annotatepage
{
} def
%%EndResource
%%EndProlog
%%BeginSetup
%%IncludeFont: Helvetica
Adobe_cshow /initialize get exec
Adobe_customcolor /initialize get exec
Adobe_typography_AI3 /initialize get exec
Adobe_pattern_AI3 /initialize get exec
Adobe_Illustrator_AI3 /initialize get exec
[
39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis
/Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute
/egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde
/oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex
/udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls
/registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash
/.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef
/.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash
/questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef
/guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe
/endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide
/.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright
/fi/fl/daggerdbl/periodcentered/quotesinglbase/quotedblbase/perthousand
/Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex
/Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex
/Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla
/hungarumlaut/ogonek/caron
TE
%AI3_BeginEncoding: _Helvetica Helvetica
[/_Helvetica/Helvetica 0 0 1 TZ
%AI3_EndEncoding TrueType
%AI3_BeginPattern: (Yellow Stripe)
(Yellow Stripe) 8.4499 4.6 80.4499 76.6 [
%AI3_Tile
(0 O 0 R 0 0.4 1 0 k 0 0.4 1 0 K) @
(
0 i
0 J 0 j 3.6 w 4 M []0 d
%AI3_Note:
0 D
8.1999 8.1999 m
80.6999 8.1999 L
S
8.1999 22.6 m
80.6999 22.6 L
S
8.1999 37.0001 m
80.6999 37.0001 L
S
8.1999 51.3999 m
80.6999 51.3999 L
S
8.1999 65.8 m
80.6999 65.8 L
S
8.1999 15.3999 m
80.6999 15.3999 L
S
8.1999 29.8 m
80.6999 29.8 L
S
8.1999 44.1999 m
80.6999 44.1999 L
S
8.1999 58.6 m
80.6999 58.6 L
S
8.1999 73.0001 m
80.6999 73.0001 L
S
) &
] E
%AI3_EndPattern
%%EndSetup
0 A
0 O
0 g
0 i
0 J 0 j 1 w 10 M []0 d
%AI3_Note:
0 D
343.8808 519.3724 m
336.2008 521.8689 l
343.8808 524.3649 l
341.7688 521.8689 l
343.8808 519.3724 l
f
342.3808 563.3724 m
334.7008 565.8689 l
342.3808 568.3649 l
340.2688 565.8689 l
342.3808 563.3724 l
f
0 R
0 G
4 M
279.5141 565.4327 m
280.3067 565.8023 281.4207 565.0921 282.0018 563.8459 c
282.547 562.6768 282.2442 561.4698 281.5729 561.0177 c
S
283.333 556.4871 m
282.5423 556.3385 281.6923 557.0135 281.189 558.0929 c
280.6081 559.3386 280.7799 560.6479 281.5729 561.0177 c
S
283.333 556.4871 m
284.1062 556.7362 285.3862 556.2628 286.0887 555.0816 c
286.7352 553.9933 286.1071 552.4536 285.4844 552.2273 c
S
287.7471 547.8009 m
288.5314 548.1776 289.6776 547.3853 290.2137 546.2357 c
290.7354 545.1168 290.4663 543.8389 289.7853 543.4772 c
S
291.8586 538.9602 m
291.0656 538.5904 289.952 539.3009 289.3711 540.5466 c
288.7902 541.7923 288.9923 543.1074 289.7853 543.4772 c
S
291.7951 538.9307 m
292.6476 539.3503 293.7666 538.6164 294.3384 537.3902 c
294.9193 536.1445 294.6768 534.8189 293.8843 534.4493 c
S
296.1938 530.0513 m
296.1487 530.0204 296.1008 529.993 296.0509 529.9698 c
295.2579 529.6 294.1443 530.3104 293.5635 531.5561 c
292.9982 532.7683 293.1457 534.0409 293.8843 534.4493 c
S
296.0703 529.9981 m
296.8612 530.3394 297.9564 529.6314 298.5308 528.3997 c
299.1007 527.1776 298.9459 525.8934 298.1911 525.4962 c
S
300.1298 521.9341 m
299.347 521.6772 298.3097 521.378 297.7558 522.5657 c
297.1861 523.7873 297.3296 525.0934 298.1471 525.4746 c
S
287.5882 547.7157 m
286.7952 547.3459 285.6816 548.0563 285.1005 549.3025 c
284.5196 550.5482 284.6914 551.8575 285.4844 552.2273 c
S
0 O
0 g
10 M
342.4568 540.5904 m
350.1368 538.0939 l
342.4568 535.5979 l
344.5688 538.0939 l
342.4568 540.5904 l
f
342.4568 551.0904 m
350.1368 548.5939 l
342.4568 546.0979 l
344.5688 548.5939 l
342.4568 551.0904 l
f
0 R
0 G
4 M
363.7146 548.6267 m
363.7146 558.0197 354.1158 565.6347 344.7228 565.6347 C
278.7064 565.6347 L
269.3134 565.6347 259.7146 558.0197 259.7146 548.6267 C
363.7146 548.6267 L
s
259.7146 538.6747 m
259.7146 529.2817 269.3134 521.6667 278.7064 521.6667 C
344.7228 521.6667 L
354.1158 521.6667 363.7146 529.2817 363.7146 538.6747 C
259.7146 538.6747 L
s
0 To
1 0 0 1 309.484 570.016 0 Tp
TP
0 Tr
0 O
0 g
/_Helvetica 12 Tf
0 Ts
100 Tz
0 Tt
0 TA
0 0 5 TC
100 100 200 TW
0 0 0 Ti
0 Ta
0 Tq
0 0 Tl
0 Tc
0 Tw
(b) Tx
(\r) TX
TO
0 To
1 0 0 1 309.484 551 0 Tp
TP
0 Tr
(d) Tx
(\r) TX
TO
0 To
1 0 0 1 309.484 528 0 Tp
TP
0 Tr
(d) Tx
(\r) TX
TO
0 R
0 G
309.484 581.016 m
314.484 581.016 l
S
0 To
1 0 0 1 309.484 507.5 0 Tp
TP
0 Tr
0 O
0 g
(b) Tx
(\r) TX
TO
0 R
0 G
309.484 518.5 m
314.484 518.5 l
S
0 To
1 0 0 1 250 541.5 0 Tp
TP
0 Tr
0 O
0 g
(x) Tx
(\r) TX
TO
0 To
1 0 0 1 367.5 541.5 0 Tp
TP
0 Tr
(0) Tx
(\r) TX
TO
10 M
248.8808 367.8724 m
241.2008 370.3689 l
248.8808 372.8649 l
246.7688 370.3689 l
248.8808 367.8724 l
f
247.3808 411.8724 m
239.7008 414.3689 l
247.3808 416.8649 l
245.2688 414.3689 l
247.3808 411.8724 l
f
255.3808 394.8724 m
247.7008 397.3689 l
255.3808 399.8649 l
253.2688 397.3689 l
255.3808 394.8724 l
f
0 R
0 G
4 M
184.5141 413.9327 m
185.3067 414.3023 186.4207 413.5921 187.0018 412.3459 c
187.547 411.1768 187.2442 409.9698 186.5729 409.5177 c
S
188.333 404.9871 m
187.5423 404.8385 186.6923 405.5135 186.189 406.5929 c
185.6081 407.8386 185.7799 409.1479 186.5729 409.5177 c
S
188.333 404.9871 m
189.1062 405.2362 190.3862 404.7628 191.0887 403.5816 c
191.7352 402.4933 191.1071 400.9536 190.4844 400.7273 c
S
193.9215 396.8824 m
193.1285 396.5126 190.6816 396.5563 190.1005 397.8025 c
189.5196 399.0482 189.6914 400.3575 190.4844 400.7273 c
S
0 O
0 g
10 M
247.4568 389.0904 m
255.1368 386.5939 l
247.4568 384.0979 l
249.5688 386.5939 l
247.4568 389.0904 l
f
0 R
0 G
4 M
164.7146 387.1747 m
164.7146 377.7817 174.3134 370.1667 183.7064 370.1667 C
249.7228 370.1667 L
259.1158 370.1667 268.7146 377.7817 268.7146 387.1747 C
164.7146 387.1747 L
s
0 To
1 0 0 1 214.484 418.516 0 Tp
TP
0 Tr
0 O
0 g
(b) Tx
(\r) TX
TO
0 To
1 0 0 1 214.484 376.5 0 Tp
TP
0 Tr
(d) Tx
(\r) TX
TO
0 To
1 0 0 1 214.484 358.5 0 Tp
TP
0 Tr
(d) Tx
(\r) TX
TO
0 R
0 G
214.484 429.516 m
219.484 429.516 l
S
0 To
1 0 0 1 214.484 399.016 0 Tp
TP
0 Tr
0 O
0 g
(b) Tx
(\r) TX
TO
0 R
0 G
214.484 410.016 m
219.484 410.016 l
S
0 To
1 0 0 1 155 390 0 Tp
TP
0 Tr
0 O
0 g
(x) Tx
(\r) TX
TO
0 To
1 0 0 1 272.5 390 0 Tp
TP
0 Tr
(0) Tx
(\r) TX
TO
10 M
438.8808 411.8724 m
431.2008 414.3689 l
438.8808 416.8649 l
436.7688 414.3689 l
438.8808 411.8724 l
f
445.8808 394.8724 m
438.2008 397.3689 l
445.8808 399.8649 l
443.7688 397.3689 l
445.8808 394.8724 l
f
0 R
0 G
4 M
388.2951 387.4307 m
389.1476 387.8503 390.2666 387.1164 390.8384 385.8902 c
391.4193 384.6445 391.1768 383.3189 390.3843 382.9493 c
S
392.6938 378.5513 m
392.6487 378.5204 392.6008 378.493 392.5509 378.4698 c
391.7579 378.1 390.6443 378.8104 390.0635 380.0561 c
389.4982 381.2683 389.6457 382.5409 390.3843 382.9493 c
S
392.5703 378.4981 m
393.3612 378.8394 394.4564 378.1314 395.0308 376.8997 c
395.6007 375.6776 395.4459 374.3934 394.6911 373.9962 c
S
394.6911 373.9962 m
394.6763 373.9887 394.6616 373.9813 394.6471 373.9746 c
S
396.6298 370.4341 m
395.847 370.1772 394.8097 369.878 394.2558 371.0657 c
393.6861 372.2873 393.8296 373.5934 394.6471 373.9746 c
S
0 O
0 g
10 M
438.9568 389.0904 m
446.6368 386.5939 l
438.9568 384.0979 l
441.0688 386.5939 l
438.9568 389.0904 l
f
429.9568 372.5904 m
437.6368 370.0939 l
429.9568 367.5979 l
432.0688 370.0939 l
429.9568 372.5904 l
f
0 R
0 G
4 M
460.2146 397.1267 m
460.2146 406.5197 450.6158 414.1347 441.2228 414.1347 C
375.2064 414.1347 L
365.8134 414.1347 356.2146 406.5197 356.2146 397.1267 C
460.2146 397.1267 L
s
1 A
268.2146 397.1267 m
268.2146 406.5197 258.6158 414.1347 249.2228 414.1347 C
183.2064 414.1347 L
173.8134 414.1347 164.2146 406.5197 164.2146 397.1267 C
268.2146 397.1267 L
s
0 A
356.2146 387.1747 m
356.2146 377.7817 365.8134 370.1667 375.2064 370.1667 C
441.2228 370.1667 L
450.6158 370.1667 460.2146 377.7817 460.2146 387.1747 C
356.2146 387.1747 L
s
0 To
1 0 0 1 405.984 418.516 0 Tp
TP
0 Tr
0 O
0 g
(b) Tx
(\r) TX
TO
0 To
1 0 0 1 405.984 376.5 0 Tp
TP
0 Tr
(d) Tx
(\r) TX
TO
0 To
1 0 0 1 405.984 359 0 Tp
TP
0 Tr
(d) Tx
(\r) TX
TO
0 R
0 G
405.984 429.516 m
410.984 429.516 l
S
0 To
1 0 0 1 405.984 399.516 0 Tp
TP
0 Tr
0 O
0 g
(b) Tx
(\r) TX
TO
0 R
0 G
405.984 410.516 m
410.984 410.516 l
S
0 To
1 0 0 1 346.5 390 0 Tp
TP
0 Tr
0 O
0 g
(x) Tx
(\r) TX
TO
0 To
1 0 0 1 464 390 0 Tp
TP
0 Tr
(0) Tx
(\r) TX
TO
10 M
248.8808 213.3724 m
241.2008 215.8689 l
248.8808 218.3649 l
246.7688 215.8689 l
248.8808 213.3724 l
f
247.3808 257.3724 m
239.7008 259.8689 l
247.3808 262.3649 l
245.2688 259.8689 l
247.3808 257.3724 l
f
0 R
0 G
4 M
188.4821 259.4327 m
189.2747 259.8023 190.3887 259.0921 190.9698 257.8459 c
191.515 256.6768 191.2123 255.4698 190.5409 255.0177 c
S
192.3011 250.4871 m
191.5103 250.3385 190.6604 251.0135 190.157 252.0929 c
189.5762 253.3386 189.748 254.6479 190.5409 255.0177 c
S
192.3011 250.4871 m
193.0742 250.7362 194.3542 250.2628 195.0568 249.0816 c
195.7032 247.9933 195.0751 246.4536 194.4524 246.2273 c
S
207.1152 219.4746 m
S
196.5562 243.2157 m
195.7632 242.8459 194.6497 242.0563 194.0686 243.3025 c
193.4877 244.5482 193.6594 245.8575 194.4524 246.2273 c
S
0 O
0 g
10 M
247.4568 234.5904 m
255.1368 232.0939 l
247.4568 229.5979 l
249.5688 232.0939 l
247.4568 234.5904 l
f
247.4568 245.0904 m
255.1368 242.5939 l
247.4568 240.0979 l
249.5688 242.5939 l
247.4568 245.0904 l
f
0 R
0 G
4 M
268.7146 242.6267 m
268.7146 252.0197 259.1158 259.6347 249.7228 259.6347 C
183.7064 259.6347 L
174.3134 259.6347 164.7146 252.0197 164.7146 242.6267 C
268.7146 242.6267 L
s
164.7146 232.6747 m
164.7146 223.2817 174.3134 215.6667 183.7064 215.6667 C
249.7228 215.6667 L
259.1158 215.6667 268.7146 223.2817 268.7146 232.6747 C
164.7146 232.6747 L
s
0 To
1 0 0 1 214.484 264.016 0 Tp
TP
0 Tr
0 O
0 g
(b) Tx
(\r) TX
TO
0 To
1 0 0 1 214.484 245 0 Tp
TP
0 Tr
(d) Tx
(\r) TX
TO
0 To
1 0 0 1 214.484 222 0 Tp
TP
0 Tr
(d) Tx
(\r) TX
TO
0 R
0 G
214.484 275.016 m
219.484 275.016 l
S
0 To
1 0 0 1 214.484 201.5 0 Tp
TP
0 Tr
0 O
0 g
(b) Tx
(\r) TX
TO
0 R
0 G
214.484 212.5 m
219.484 212.5 l
S
0 To
1 0 0 1 155 235.5 0 Tp
TP
0 Tr
0 O
0 g
(x) Tx
(\r) TX
TO
0 To
1 0 0 1 272.5 235.5 0 Tp
TP
0 Tr
(0) Tx
(\r) TX
TO
10 M
440.3808 213.3724 m
432.7008 215.8689 l
440.3808 218.3649 l
438.2688 215.8689 l
440.3808 213.3724 l
f
438.8808 257.3724 m
431.2008 259.8689 l
438.8808 262.3649 l
436.7688 259.8689 l
438.8808 257.3724 l
f
0 R
0 G
4 M
388.2951 232.9307 m
389.1476 233.3503 390.2666 232.6164 390.8384 231.3902 c
391.4193 230.1445 391.1768 228.8189 390.3843 228.4493 c
S
392.6938 224.0513 m
392.6487 224.0204 392.6008 223.993 392.5509 223.9698 c
391.7579 223.6 390.6443 224.3104 390.0635 225.5561 c
389.4982 226.7683 389.6457 228.0409 390.3843 228.4493 c
S
392.5703 223.9981 m
393.3612 224.3394 394.4564 223.6314 395.0308 222.3997 c
395.6007 221.1776 395.4459 219.8934 394.6911 219.4962 c
S
394.6911 219.4962 m
394.6763 219.4887 394.6616 219.4813 394.6471 219.4746 c
S
396.6298 215.9341 m
395.847 215.6772 394.8097 215.378 394.2558 216.5657 c
393.6861 217.7873 393.8296 219.0934 394.6471 219.4746 c
S
0 O
0 g
10 M
438.9568 234.5904 m
446.6368 232.0939 l
438.9568 229.5979 l
441.0688 232.0939 l
438.9568 234.5904 l
f
438.9568 245.0904 m
446.6368 242.5939 l
438.9568 240.0979 l
441.0688 242.5939 l
438.9568 245.0904 l
f
0 R
0 G
4 M
460.2146 242.6267 m
460.2146 252.0197 450.6158 259.6347 441.2228 259.6347 C
375.2064 259.6347 L
365.8134 259.6347 356.2146 252.0197 356.2146 242.6267 C
460.2146 242.6267 L
s
356.2146 232.6747 m
356.2146 223.2817 365.8134 215.6667 375.2064 215.6667 C
441.2228 215.6667 L
450.6158 215.6667 460.2146 223.2817 460.2146 232.6747 C
356.2146 232.6747 L
s
0 To
1 0 0 1 405.984 264.016 0 Tp
TP
0 Tr
0 O
0 g
(b) Tx
(\r) TX
TO
0 To
1 0 0 1 405.984 245 0 Tp
TP
0 Tr
(d) Tx
(\r) TX
TO
0 To
1 0 0 1 405.984 222 0 Tp
TP
0 Tr
(d) Tx
(\r) TX
TO
0 R
0 G
405.984 275.016 m
410.984 275.016 l
S
0 To
1 0 0 1 405.984 201.5 0 Tp
TP
0 Tr
0 O
0 g
(b) Tx
(\r) TX
TO
0 R
0 G
405.984 212.5 m
410.984 212.5 l
S
0 To
1 0 0 1 346.5 235.5 0 Tp
TP
0 Tr
0 O
0 g
(x) Tx
(\r) TX
TO
0 To
1 0 0 1 464 235.5 0 Tp
TP
0 Tr
(0) Tx
(\r) TX
TO
0 To
1 0 0 1 280 332.5 0 Tp
TP
0 Tr
(\r) TX
TO
0 To
1 0 0 1 204.1667 477.8333 0 Tp
TP
0 Tr
(Fig. 1   Example of non-factorizable diagram) Tx
(\r) TX
TO
0 To
1 0 0 1 160.2945 161.8333 0 Tp
TP
0 Tr
(Fig. 2   Non-factorizable diagrams after Fierz rearrangement) Tx
(\r) TX
TO
%%PageTrailer
gsave annotatepage grestore showpage
%%Trailer
Adobe_Illustrator_AI3 /terminate get exec
Adobe_pattern_AI3 /terminate get exec
Adobe_typography_AI3 /terminate get exec
Adobe_customcolor /terminate get exec
Adobe_cshow /terminate get exec
Adobe_packedarray /terminate get exec
%%EOF

