%Paper: 
%From: bgrin@sscux1.ssc.gov (Benjamin Grinstein)
%Date: Wed, 29 Apr 92 11:51:09 -0500


%Instructions for TeXing:
%Uses harvmac.tex macros
%One postscript figure is appended. Should be extracted as separate file
%and printed on postscript printer.


%%%% Last changed Monday, 4/27 at 7:30 pm by BG
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\input harvmac
\def\Oops{(2.2)}

% The following command eliminates black boxes which appear when
% equations run over RHS margins:

\overfullrule=0pt

% Aliases

\def\as{\alpha_s}
\def\bar#1{\overline{#1}}
\def\bas{{\alpha}_s}
%\def\bas{\overline{\alpha}_s}
\def\bLambdabar{{{\overline \Lambda} \over 2 m_b}}
\def\bv{b_v}
\def\ccdot{\hbox{\kern-.1em$\cdot$\kern-.1em}}
\def\CD{{\cal D}}
\def\coupling{ {\bas(m_c) \over \pi}}
\def\cLambdabar{{{\overline \Lambda} \over 2m_c}}
\def\cvp{\overline{c}_{v'}}
\def\Dl{\overleftarrow{\CD}}
\def\Dlslash{{\overleftarrow{\CD}} \hskip-0.75 em / \hskip+0.40 em}
\def\Dlalpha{\overleftarrow{\CD}\null^\alpha}
\def\Dlmu{\overleftarrow{\CD}\null^\mu}
\def\Dslash{\CD\hskip-0.65 em / \hskip+0.30 em}
\def\GeV{\>\, \rm GeV}
\def\gfive{\gamma^5}
\def\gu{\gamma^\mu}
\def\hv{h_v^{{\scriptscriptstyle{(Q)}}}}
\def\hvbar{{\overline{h}_v^{{\scriptscriptstyle{(Q)}}}}}
\def\ie{{\it i.e.}}
\def\imb{\displaystyle{i \over m_b}}
\def\imc{\displaystyle{i \over m_c}}
\def\imu{i \mu^\epsilon\,}
\def\IW{\eta(v \ccdot v')}
\def\Lambdabar{{{\overline \Lambda} \over m}}
\def\Lambdab{\Lambda_b(v,s)}
\def\Lambdac{\Lambda_c(v',s')}
\def\LB{\Lambda_b}
\def\LC{\Lambda_c}
\def\mb{m_b}
\def\mc{m_c}
\def\mQ{{m_{\scriptscriptstyle Q}}}
\def\muep{\mu^\epsilon}
\def\muhalf{\mu^{\epsilon /2}}
\def\nF{n_{\scriptscriptstyle F}}
\def\OMIT#1{\null}
\def\Q{{\scriptscriptstyle Q}}
\def\suv{\sigma^{\mu\nu}}
\def\sl#1{#1\hskip-0.5em /}  % Mike Luke's macro for slashes thru vectors.
\def\sp{\>\>}
\def\ubar{\, {\overline u}(v',s')}
\def\u{u(v,s)}
\def\v{v^\mu}
\def\vp{v'^\mu}
\def\vsl{v \hskip-5pt /}
\def\vv{v \ccdot v'}

% Fractions

\def\fourthirds{{4 \over 3}}
\def\half{{1 \over 2}}
\def\third{{1 \over 3}}
\def\twothirds{{2 \over 3}}

% Journal aliases

\def\np#1#2#3{Nucl. Phys. {\bf #1} (#2) #3}
\def\pl#1#2#3{Phys. Lett. {\bf #1} (#2) #3}
\def\prl#1#2#3{Phys. Rev. Lett. {\bf #1} (#2) #3}
\def\pr#1#2#3{Phys. Rev. {\bf #1} (#2) #3}
\def\sjnp#1#2#3{Sov. J. Nucl. Phys. {\bf #1} (#2) #3}
\def\blankref#1#2#3{   {\bf #1} (#2) #3}

% Kathy Benson's bold Greek letter macro:

% Style-sensitive Poor-Man's-Bold command, produces bold greek letters.
% Usage $ ... \pmb\gamma ... $
% Adapted from TeXbook p386 (\pmb) and p360 (\mathpallette)
\newdimen\pmboffset
\pmboffset 0.022em
\def\oldpmb#1{\setbox0=\hbox{#1}%
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 \kern\pmboffset\box0}
\def\pmb#1{\mathchoice{\oldpmb{$\displaystyle#1$}}{\oldpmb{$\textstyle#1$}}
      {\oldpmb{$\scriptstyle#1$}}{\oldpmb{$\scriptscriptstyle#1$}}}

% ----------------------------------------------------------------------
% References:
% ----------------------------------------------------------------------

\nref\IsgurWise{N. Isgur and M.B. Wise, \pl{B232}{1989}{113};
  \pl{B237}{1990}{527}.}
\nref\Eichten{E. Eichten and B. Hill, \pl{B234}{1990}{511}.}
\nref\Georgi{H. Georgi, \pl{B240}{1990}{447}.}
\nref\Grinstein{B. Grinstein, \np{B339}{1990}{253}.}
\nref\Volopol{M.B. Voloshin and M.A. Shifman, \sjnp{45}{1987}{292}\semi
  H.D. Politzer and M.B. Wise, \pl{B206}{1988}{681};
  \pl{B208}{1988}{504}.}
\nref\FGGW{A. Falk, H. Georgi, B. Grinstein and M.B. Wise,
  \np{B343}{1990}{1}.}
\nref\Falk{A. Falk and B. Grinstein, \pl{B247}{1990}{406}.}
\nref\EichtenHill{E. Eichten and B. Hill, \pl{B243}{1990}{427}\semi
  M. Golden and B. Hill, \pl{B254}{1991}{225}\semi
  A.F. Falk and B. Grinstein, \pl{B249}{1990}{314}.}
\nref\FGL{A. Falk, B. Grinstein and M. Luke, \np{B357}{1991}{185}.}
\nref\Luke{M.E. Luke, \pl{B252}{1990}{447}.}
\nref\GGW{H. Georgi, B. Grinstein and M. B. Wise, \pl{252B}{1990}{456}.}
\nref\Boyd{C.G. Boyd and D. Brahm, Phys. Lett {\bf B257} (1991) 393.}
% \nref\Politzer{H.D. Politzer, Nucl. Phys. {\bf B172} (1980) 349.}
\nref\Lebed{R.F. Lebed and M. Suzuki, Phys. Rev. {\bf D44} (1991) 829.}
\nref\Wise{M.B. Wise, CALT-68-1721, Lectures presented at the Lake
  Louise Winter Institute.}
\nref\Baryonrefs{N. Isgur and M.B. Wise, \np{B348}{1991}{276}\semi
  H. Georgi, \np{B348}{1991}{293}\semi
  T. Mannel, W. Roberts and Z.Ryzak, \np{B355}{1991}{38};
  \pl{B255}{1991}{593}.}

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% for figure caption.

\def\listfigs{\vfill\eject\immediate\closeout\ffile{\parindent40pt
\baselineskip14pt\centerline{{\bf Figure Caption}}\nobreak\medskip
\escapechar=` \input figs.tmp\vfill\eject}}
%
\nfig\Graphs{One-loop Feynman diagrams in the intermediate and final HQET's
whose difference determines the $O(\bas(m_c))$ matching contributions to the
${C^{(3)}_j}^{(\prime)}$ and ${C^{(4)}_k}^{(\prime)}$ coefficients in
eqn.~\fulltoeff.  Solid boxes denote $P_0^{(\prime)}$ and $Q_1^{(\prime)}$
current operators while solid dots represent $O_1$ and $O_2$ Lagrangian
operator insertions.}

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% Title page:
% ----------------------------------------------------------------------

% Modified title definition to allow long titles to be broken up into two
% lines.

\def\LongTitle#1#2#3{\nopagenumbers\abstractfont\hsize=\hstitle\rightline{#1}%
\vskip 0.5in\centerline{\titlefont #2}\centerline{\titlefont #3}
\abstractfont\vskip 0.4in\pageno=0}
%
\LongTitle
  {\vbox{\hbox{SSCL--Preprint--111}\hbox{HUTP-92/A012}}}
  {Heavy Hadron Form Factor Relations} {for $m_c\ne\infty$ and $\bas(m_c)\ne0$}
%
\centerline{Peter Cho
  \footnote{$^\dagger$}{E-mail: Cho@huhepl.harvard.edu}}
\centerline{Lyman Laboratory of Physics}
\centerline{Harvard University}
\centerline{Cambridge, MA 02138}
\medskip\centerline{and}\medskip
\centerline{Benjam\'\i n Grinstein
  \footnote{$^\ddagger$}{E-mail: Grinstein@sscvx1.bitnet, @sscvx1.ssc.gov}
  \footnote{}{On leave of absence from Harvard University.}}
\centerline{Superconducting Super Collider Laboratory}
\centerline{2550 Beckleymeade Ave.}
\centerline{Dallas, TX 75237}

\vskip 0.6in

%Abstract:

        First order power corrections to current matrix elements between
heavy meson or $\Lambda_\Q$ baryon states are shown to vanish at the zero
recoil point to all orders in QCD.  Five relations among the six form
factors that parametrize the semileptonic decay $\Lambda_b \to \Lambda_c e
\overline{\nu}$ are also demonstrated to exist to all orders in the strong
coupling at order $1/\mQ$ .  The $O(\bas(m_c)/m_c)$ form factor
relations are displayed.

\vskip 0.5 in
\centerline{Submitted to \it{Physics Letters B}}

%\draft
\Date{April 1992} %replace this line by \draft  for preliminary versions
             %or specify \draftmode at some point
% -------------------------------------------------------------------------
\newsec{Introduction}
% -------------------------------------------------------------------------

        In the limit where the masses of the charm and bottom quarks are taken
to be infinitely greater than the QCD scale, matrix elements between hadron
states containing a single heavy quark are severely constrained \IsgurWise.
For example, all six form factors for the flavor changing currents which
mediate $B\to D$ and $B \to D^*$ transitions are given in terms of one
universal function. This so called ``Isgur-Wise'' function is also the form
factor of the $b$-number current between $B$ meson states.  It is
consequently normalized to unity at the maximum momentum transfers
$q^2_{\rm max}=0$ for $B\to B$ transitions and
$q^2_{\rm max}=(m_B-m_D)^2$ for $B\to D$ decays.

        A Heavy Quark Effective Theory (HQET) with manifest flavor and spin
symmetries that lead to these normalization constraints has recently been
developed \refs{\Eichten,\Georgi}.  Since the HQET is derived from
QCD \Grinstein,
its predictions are model independent.  Moreover, corrections to results
found in the infinite quark mass limit can be systematically investigated
in this effective theory.  Such corrections arise from QCD scaling
violations which depend logarithmically upon the charm and bottom
masses~\refs{\Volopol,\FGGW}.
In addition, terms suppressed by inverse powers of the
heavy quark masses enter at subleading order~\refs{\Falk,\EichtenHill,\FGL}.
We shall refer to these deviations from the infinite mass limit as ``scaling''
and ``power'' corrections respectively.

        First order power corrections to the predicted normalization of
flavor changing current matrix elements between $B$ and $D$ or
$D^*$ states have been shown to vanish at the zero recoil point \Luke.
This remarkable result is often called ``Luke's theorem'' and
holds as well for $\LB\to\LC$ transitions \GGW\
and for an entire class of heavy hadron processes \Boyd.
Luke's theorem was originally proved to zeroth order in the strong
interactions.  It consequently ruled out normalization corrections at
$O(1/m_c)$ but not $O(\as/m_c)$.  In this letter, we demonstrate that these
latter violations are also prohibited.  In fact, we show that
{\it there are no order 1/$m_c$ corrections to the zero recoil normalization
of the current matrix elements to all orders in $\as$.}

        We then focus our attention upon the semileptonic decay
$\LB\to\LC e \overline{\nu}$.  This process is of considerable interest
since an accurate value for the KM matrix element $|V_{cb}|$ may
be determined in the future from high precision measurements of its
endpoint spectrum.   The transition lends itself particularly well to HQET
analysis because it is tightly constrained by the heavy quark spin symmetry.
Like their mesonic counterparts, the six form factors that parametrize this
baryonic process are predicted at leading order in terms of a single
Isgur-Wise function. Five relations among these six form factors have been
found to remain after $O(1/m_c)$ power corrections are
included.  We extend this result to all orders in the strong coupling
and then display the relations to $O(\bas(m_c)/m_c)$.
Such form factor relations provide a valuable means for assessing the
uncertainty in future measurements of the mixing angle $|V_{cb}|$
from semileptonic $\Lambda_b$ decay.

        Finally, we estimate and compare the numerical sizes of the scaling and
power correction expansion parameters that appear in the HQET.

% -------------------------------------------------------------------------
\newsec{Nonrenormalization at the zero recoil point}
% -------------------------------------------------------------------------

        Finite quark mass corrections enter into the HQET in two
ways.  Firstly, $O(1/m_c)$ and $O(1/m_b)$ terms appear in the Lagrangian
which break the theory's flavor and spin symmetries:
%
\eqn\Lagrangian{
\CL_v = \sum_{\Q=c,b} \Bigl\{ \hvbar (iv \ccdot \CD) \hv + a_1 O_1 + a_2 O_2
  \Bigr\}. }
%
The $O_i$ operators are built up out of two heavy quark fields and
symmetric or antisymmetric combinations of two covariant derivatives
$\CD_\mu = \partial_\mu - i g A^a_\mu T^a$:
%
\foot{A third operator $O_3=-(1/2\mQ) \hvbar (i v \ccdot \CD)^2 \hv$ could
be included with those in \Oops.  However, since it can be eliminated via
a nonlinear field redefinition, this operator has no effect and can be
neglected without loss \FGL.}
%
%However, since the lowest order equation
%of motion $(v \ccdot \CD) \hv = 0$ can be applied to matrix elements
%between physical states \Politzer,
%this operator has no effect and can be neglected without loss \FGL.}
%
\eqn\Oops{\eqalign{
O_1 &= {1 \over 2\mQ} \hvbar (i\CD)^2 \hv \cr
O_2 &= {g \over 4\mQ} \hvbar \sigma^{\mu\nu} G^a_{\mu\nu} T^a \hv .\cr}}
%
We have absorbed various numerical factors into these operators'
definitions so that their tree level coefficients equal unity:
%
\eqn\acoeffs{a_1 = a_2 = 1+O(\bas).}
%
The Ademollo-Gatto theorem indicates that corrections to the normalization of
form factors from the $O_i$ terms in \Lagrangian\ arise only at second order
in $1/m_c$ and $1/m_b$ \refs{\Boyd,\Lebed}.
The QCD corrections to the $a_i$ coefficients in \acoeffs\ do not upset this
result.

        There are also power corrections to the effective currents in the HQET
which correspond to the vector and axial currents in the underlying full
theory.  In general, the two sets of currents are related as
%
\eqn\fulltoeff{\eqalign{
V^\mu &= \overline{c} \gamma^\mu b \to \sum C^{(3)}_j P^\mu_j
  + \sum C^{(4)}_k Q^\mu_k + \cdots\cr
A^\mu &= \overline{c} \gamma^\mu\gamma^5 b \to \sum {C^{(3)}_j}' P'^\mu_j +
  \sum {C^{(4)}_k}' Q'^\mu_k +\cdots . \cr}}
%
Here $P_j^{(\prime)\mu}$ and $Q_k^{(\prime)\mu}$ denote dimension three and
four
operators with appropriate quantum numbers while the ellipses represent higher
order terms.  A convenient basis for these operators is listed below:
%
\eqna\PQops
%
\smallskip\noindent${\underline{{\rm Dimension} \; 3:}}$
%
$$ \vbox{\settabs \+ \quad\qquad\qquad & \qquad\qquad &
  $P^\mu_0$ & $=$ & $\cvp \gu \bv$
  \qquad \qquad \qquad & $P'^\mu_0$ & $=$ & $\cvp \gu \gfive \bv$ \quad \cr
\+ \quad \qquad \qquad & \qquad \qquad &
  \hfill $P^\mu_0$ & $=$ & $ \cvp \gu \bv$ \hfill &
  \hfill $P'^\mu_0$ & $=$ & $ \cvp \gu\gfive \bv$ \hfill \quad \cr
\+ \quad \qquad \qquad & \qquad \qquad &
  \hfill $P^\mu_1$ & $=$ & $ \cvp \v \bv$ \hfill &
  \hfill $P'^\mu_1$ & $=$ & $ \cvp \v \gfive \bv$ \hfill
  $\>$ \quad \qquad (2.5a)  \cr
\+ \quad \qquad \qquad & \qquad \qquad &
  \hfill $P^\mu_2$ & $=$ & $ \cvp \vp \bv$ \hfill &
  \hfill $P'^\mu_2$ & $=$ & $ \cvp \vp \gfive \bv$ \hfill \quad \cr} $$
%
\noindent${\underline{{\rm Dimension} \; 4:}}$
%
$$ \vbox{\settabs \+ \qquad\qquad \qquad &
$Q_{13}$ & $=$ &  $\> -\imc \cvp v\ccdot \Dl \vp \bv \>$
\qquad\qquad & $Q'_{13}$ & $=$ & $\> -\imc \cvp \v\ccdot \Dl \vp \gfive \bv \>$
\cr
\+ \qquad\qquad \qquad & \hfill $Q^\mu_1$ &
$=$ & $ -\imc \cvp \Dlslash \gu \bv$
 \hfill &
  \hfill $Q'^\mu_1$ & $=$ & $ -\imc \cvp \Dlslash \gu\gfive \bv$ \hfill \cr
\+ \qquad\qquad \qquad & \hfill $Q^\mu_2$ &
$=$ & $ \imb \cvp \gu \Dslash \bv$ \hfill &
  \hfill $Q'^\mu_2$ & $=$ & $ \imb \cvp \gu\gfive \Dslash \bv$ \hfill \cr
\+ \qquad\qquad \qquad & \hfill $Q^\mu_3$ &
$=$ & $ -\imc \cvp v\ccdot\Dl \gu \bv$ \hfill &
  \hfill $Q'^\mu_3$ & $=$ & $ -\imc \cvp v\ccdot\Dl \gu\gfive \bv$ \hfill \cr
\+ \qquad\qquad \qquad & \hfill $Q^\mu_4$ &
$=$ & $ \imb \cvp \gu v'\ccdot \CD \bv$ \hfill &
  \hfill $Q'^\mu_4$ & $=$ & $ \imb \cvp \gu\gfive v'\ccdot \CD \bv$ \hfill \cr
\+ \qquad\qquad \qquad & \hfill $Q^\mu_5$ & $=$ & $ -\imc \cvp \Dlslash \v \bv$
\hfill &
  \hfill $Q'^\mu_5$ & $=$ & $ -\imc \cvp \Dlslash \v \gfive \bv$ \hfill \cr
\+ \qquad\qquad \qquad & \hfill $Q^\mu_6$ &
$=$ & $ -\imc \cvp \Dlslash \vp \bv$
 \hfill &
  \hfill $Q'^\mu_6$ & $=$ & $ -\imc \cvp \Dlslash \vp \gfive \bv$ \hfill \cr
\+ \qquad\qquad \qquad & \hfill $Q^\mu_7$ &
$=$ & $ \imb \cvp \v  \Dslash \bv$ \hfill &
  \hfill $Q'^\mu_7$ & $=$ & $ \imb \cvp \v\gfive \Dslash \bv$ \hfill
  $\>$ ~~~ (2.5b)\cr
\+ \qquad\qquad \qquad & \hfill $Q^\mu_8$ &
$=$ & $ \imb \cvp \vp \Dslash \bv$ \hfill &
  \hfill $Q'^\mu_8$ & $=$ & $ \imb \cvp \vp \gfive \Dslash \bv$ \hfill \cr
\+ \qquad\qquad \qquad & \hfill $Q^\mu_9$ &
$=$ & $ -\imc \cvp \Dlmu \bv$ \hfill
 &
  \hfill $Q'^\mu_9$ & $=$ & $ -\imc \cvp \Dlmu \gfive \bv$ \hfill \cr
\+ \qquad\qquad \qquad & \hfill $Q^\mu_{10}$ &
$=$ & $ \imb \cvp \CD^\mu \bv$ \hfill &
  \hfill $Q'^\mu_{10}$ & $=$ & $ \imb \cvp \gfive \CD^\mu \bv$ \hfill \cr
%}$$
%
%\vfill\eject
%
%$$ \vbox{\settabs \+ $Q_{13}$ & $=$ &  $\> -\imc \cvp v\ccdot \Dl \vp \bv \>$
%\qquad\qquad & $Q'_{13}$ &
%$=$ & $\> -\imc \cvp \v\ccdot \Dl \vp \gfive \bv \>$%\cr
\+ \qquad\qquad \qquad & \hfill $Q^\mu_{11}$ &
$=$ & $ -\imc \cvp v\ccdot \Dl \v
 \bv$ \hfill &
  \hfill $Q'^\mu_{11}$ & $=$ & $ -\imc
 \cvp v\ccdot \Dl \v \gfive \bv$ \hfill \cr
\+ \qquad\qquad \qquad & \hfill $Q^\mu_{12}$ &
$=$ & $ -\imc \cvp v\ccdot \Dl \vp \bv$ \hfill &
  \hfill $Q'^\mu_{12}$ & $=$ &
$ -\imc \cvp v\ccdot \Dl \vp\gfive \bv$ \hfill \cr
\+ \qquad\qquad \qquad & \hfill $Q^\mu_{13}$ &
$=$ & $ \imb \cvp \v v'\ccdot \CD \bv$ \hfill &
  \hfill $Q'^\mu_{13}$ & $=$ &
$ \imb \cvp \v\gfive v'\ccdot \CD \bv$ \hfill \cr
\+ \qquad\qquad \qquad & \hfill $Q^\mu_{14}$ & $=$ & $ \imb
 \cvp \vp v'\ccdot \CD \bv$ \hfill &
  \hfill $Q'^\mu_{14}$ & $=$ & $ \imb \cvp \vp\gfive v'\ccdot \CD \bv$.\hfill
  \cr}$$
%
The operators' coefficients are determined by matching Green's functions
with single current insertions in the full and effective theories.
They are dimensionless functions of the strong coupling $\as$, the
renormalization point $\mu$, and the quark masses $m_c$ and $m_b$.
Their values can be calculated perturbatively provided
$\mu$ is large enough so that $\as(\mu)$ is small.

        All of the effective current operator coefficients in \fulltoeff\
gain zero contribution from tree level matching except
%
$$ \eqalign{C^{(3)}_0 &= {C^{(3)}_0}'=1 \cr
C^{(4)}_1 &= {C^{(4)}_1}' = C^{(4)}_2 = {C^{(4)}_2}'=1/2.\cr} $$
%
In the original proof of Luke's theorem, only the
operators corresponding to these nonvanishing coefficients were
considered.  To extend the theorem's validity to arbitrary order in $\as$, one
must examine the effects from all the others listed in \PQops{}.
Therefore, consider a representative HQET matrix element of a prototype
dimension four operator between heavy $B$ and $D$ states that both move with
four-velocity $v$:
%
\eqn\firstidentity{
\vev{\widetilde D(v)|\overline{c}_{v} i\Dl{}^\alpha \Gamma b_v |
  \widetilde B(v)} = \lambda v^\alpha \Tr \overline{M}(v)\Gamma  M(v).}
%\vev{\widetilde D^*(v,\epsilon)|\overline{c}_{v} i\Dl{}^\alpha \Gamma b_v |
%  \widetilde B(v)} &= \lambda v^\alpha \Tr \overline{M}(v,\epsilon)\Gamma
%  M(v)~.}}
%
The tildes appearing on the LHS of this equation indicate that the states are
evaluated in the effective theory to zeroth order in $1/\mQ$.  On the RHS, the
meson matrices
%
$$ \eqalign{M(v) &= -{1 +\vsl \over 2} \gfive \cr
\overline{M}(v) &= \gfive {1+\vsl \over 2} \cr} $$
%\overline{M}(v,\epsilon) &= \sl{\epsilon}^* {1 +\vsl\over 2} \cr} $$
%
are contracted together in accordance with the HQET flavor and spin symmetries.
After dotting both sides of \firstidentity\ with $v_\alpha$ and applying
the equation of motion $v\ccdot \CD c_v=0$, one finds that the constant
$\lambda$ vanishes identically.  Since matrix elements between $B(v)$ and
$D(v')$ states of all the dimension four operators in \PQops{b}\
can be derived from equations like \firstidentity, they too must vanish
when $v=v'$.  An analogous argument holds for $B\to D^*$ transitions.

        Could the zeros in heavy meson matrix elements of the
$Q_k^{(\prime)\mu}$ operators be cancelled by poles in their
${C_k^{(4)}}^{(\prime)}$ coefficients?  We do not believe so.  Consider the
analytic structure of meson form factors regarded as complex functions of
the momentum transfer $q^2$.  By examining Feynman diagrams in the underlying
full QCD theory,  one sees that the physical cut which starts at the maximum
momentum transfer $q^2_{\rm max}=(m_B - m_D)^2$ originates from infrared
singularities in these graphs.  This infrared behavior must be reproduced by
the dynamics of the effective theory and should not appear in the coefficient
functions which contain only short distance information.
%Because the momentum transfer
%at zero recoil is $q^2=(m_b v + k_b - m_c v -k_c)^2 = q^2_{\rm max} +
%2(m_b - m_c) v\ccdot(k_b - k_c)+ (k_b - k_c)^2$, the analytic structure
%around $q^2_{\rm max}$ should be recovered in the HQET in terms of the
%variable $v\ccdot(k_b-k_c)$.

        Therefore, since matrix elements of the dimension four operators
vanish while their coefficients remain regular at $\vv=1$, there can
be no first order power corrections to the zero recoil current normalizations
to all orders in QCD.

% -------------------------------------------------------------------------
\newsec{Form factor relations for $\pmb{\LB\to\LC}$ transitions}
% -------------------------------------------------------------------------

        The nonrenormalization theorem discussed in the previous section
for mesons applies to $\Lambda_\Q$ baryons as well.  Vector and axial current
matrix elements between $\LB$ and $\LC$ baryon states appear in the HQET as
%
\eqn\ffsdefn{\eqalign{
\vev{\Lambdac|V^\mu|\Lambdab} &= \ubar[F_1(\vv) \gamma^\mu + F_2(\vv) v^\mu
  + F_3(\vv) v'^\mu ]\u \cr
\vev{\Lambdac|A^\mu|\Lambdab} &= \ubar [G_1(\vv) \gamma^\mu + G_2(\vv) v^\mu
  + G_3(\vv) v'^\mu ]\gfive \u. \cr}}
%
A few points about these expressions should be noted.  Firstly, the Dirac
spinors for the baryons' heavy quark constituents satisfy $\u =\vsl\u$.
Therefore when $v = v'$, the current matrix elements reduce to \Wise
%
\eqna\reducedelems
%
$$ \eqalignno{
\vev{\Lambda_c(v,s')|V^\mu|\Lambdab} &= [F_1(1)+F_2(1)+F_3(1)]
  \overline{u}(v,s')v^\mu \u &\reducedelems a \cr
\vev{\Lambda_c(v,s')|A^\mu|\Lambdab} &= G_1(1) \overline{u}(v,s')
  \gamma^\mu \gfive \u. & \reducedelems b\cr} $$
%
Secondly, the spin of a $\Lambda_\Q$ baryon comes entirely from
its heavy quark in the infinite mass limit; the light spectator degrees
of freedom carry zero angular momentum.  The form
factors $F_i$ and $G_i$ are consequently all determined from
one universal function which is normalized at zero recoil \Baryonrefs.
To avoid any confusion with the Isgur-Wise function $\xi(\vv)$ for heavy
mesons, we will denote this universal function associated with $\Lambda_\Q$
baryons as $\IW$.  Finally, an additional dimensionful constant
$\overline{\Lambda} \approx m_{\Lambda_c}-m_c \approx m_{\Lambda_b}-m_b$
must be introduced to specify the form factors when $\mQ \ne\infty$.
The parameter $\overline{\Lambda}$ may be interpreted as the baryon
state's energy above the vacuum in the HQET.

        Order $1/m_c$ power corrections to the effective vector and axial
currents arising from either local dimension four $Q_k^{(\prime)\mu}$
operators in \PQops{b}\ or time ordered products of dimension five $O_i$
operators in \Lagrangian\ and dimension three $P_j^{(\prime)\mu}$ operators
in \PQops{a}\ were considered in ref.~\GGW.
The time ordered products were shown to generally not contribute, and five
relations among the six form factors in \ffsdefn\ were found.
We now demonstrate that five relations remain even when current corrections of
order $1/m_c$, $1/m_b$ and all orders in $\as$ are retained.
We start with the identity
%
$$ \vev{\Lambdac \vert i \CD^\alpha (\cvp \Gamma \bv) \vert \Lambdab} =
  \bar{\Lambda} \IW (v^\alpha - v'^\alpha) \ubar \Gamma \u $$
%
which follows from the relation between momentum and derivative operators
in the effective theory \Georgi:
%
$$ [ {\bf P^\alpha}, \hv(x) ] = -(m v^\alpha + i \CD^\alpha) \hv(x).$$
%
With the aid of this identity, the general matrix elements
%
\eqn\secondidentity{\eqalign{
\vev{\Lambdac \vert \cvp i \Dlalpha \Gamma \bv \vert \Lambdab} &=
  \bar{\Lambda} \IW {v^\alpha - v\ccdot v' v'^\alpha \over v \ccdot v'+1}
  \ubar \Gamma \u \cr
\vev{\Lambdac \vert \cvp \Gamma i \CD^\alpha \bv \vert \Lambdab} &=
  \bar{\Lambda} \IW {\vv v^\alpha - v'^\alpha \over v\ccdot v'+1 }
  \ubar \Gamma \u \cr}}
%
are readily evaluated.  Notice that like
the meson element in \firstidentity, these expressions vanish for
$v = v'$.

        Matrix elements of all the basis operators in \PQops{b}\
are fixed by those in \secondidentity.  Since any
dimension four contribution to the effective currents can be decomposed over
this complete operator set, we see that Luke's theorem holds to all powers
in the strong coupling.  Furthermore, as no new parameters
need be introduced into the current form factors, no relations among them
are lost.
%
%
%       While this completes the proof, it is instructive to look at the matrix
%elements of some of the operators above. We will see below that in order
%$\bas(m_c)$ the operators $P_j$ with $i=0,1$ and $Q_k$ with $j=1,2,3,5,11$
%contribute to the matrix element of the vector current. Their matrix elements
%are given by
%
%\eqn\matrixelements{\eqalign{
%%
%\vev{P^\mu_0 + \half Q^\mu_1} &= \IW \ubar
%\Bigl[ \gamma^\mu+\cLambdabar \bigl( \half\gamma^\mu - {1 \over \vv+1}v^\mu
% \bigr) \Bigr] \u \cr
%\vev{\half Q^\mu_2} &= \IW \bLambdabar \ubar \Bigl[
%  \half \gamma^\mu - {1 \over \vv+1} {v'}^\mu \Bigr] \u \cr
%\vev{Q^\mu_3} &= \IW \cLambdabar (\vv-1) \ubar \gamma^\mu \u \cr
%\vev{ P^\mu_1+ \half Q^\mu_5} &=
% \IW \Bigl( 1 + \half \cLambdabar {\vv-1\over \vv+1} \Bigr) \ubar v^\mu \u \cr
%\vev{Q^\mu_{11}} &= \IW \cLambdabar (\vv-1) \ubar v^\mu \u \cr}}
%
%One sees that each of these satisfies Luke's theorem. Nevertheless, the
%normalization is the result of cancelation of terms which contribute to
%different form factors, {\it e.g.,\/} $F_1$ and $F_2$ in the first line above.
%
%
Such relations can be determined to the order at which the
effective current coefficients in \fulltoeff\ are known.  We compute these
coefficients assuming $m_b \gg m_c$, and we first work in an intermediate
HQET with a heavy $b$ quark but full theory $c$ field.  For simplicity, we
neglect the QCD running between the bottom and charm scales which has
previously been discussed in refs.~\refs{\Volopol,\FGGW,\Falk}.
We instead concentrate upon the $O(\bas(m_c)/m_c)$ matching contributions to
the current coefficients that arise
at the charm scale boundary between the intermediate and final
effective theories in which both the $c$ and $b$ are treated as heavy.

        We match 1PI two-point Green's functions with a single vector or
axial current insertion in the intermediate and final HQET's.  The one-loop
diagrams that enter into this matching computation are illustrated in
\Graphs.  The graphs contain $O(1/m_c)$ operator insertions from the
Lagrangian in \Lagrangian\ and currents in \fulltoeff.
We adopt the mass independent renormalization scheme of dimensional
regularization plus modified minimal subtraction to accommodate the
ultraviolet infinities in these diagrams.  Infrared
divergences which appear after Taylor expanding loop integrals in powers of
external residual momenta can be explicitly eliminated by judiciously
arranging integrand terms in the two theories into infrared safe
combinations.  After including the tree level $O(1/m_c)$ and $O(1/m_b)$
contributions and taking the difference between the two-point functions in the
intermediate and final HQET's, we find the following $c$-scale matching
contributions to the effective currents:
%
\eqna\matchcurrents
%
$$\eqalign{
%
V^\mu &= P^\mu_0+\half Q^\mu_1 +\half Q^\mu_2 \cr
&+ \third \coupling \biggl \{ 2(\vv+1)r \bigl[P^\mu_0+\half Q^\mu_1 \bigr]
  -2 {r-1 \over \vv-1} Q^\mu_3 \cr
&\qquad\qquad\qquad -4r \bigl[P^\mu_1+\half Q^\mu_5 \bigr]
  -{4(1-\vv r) \over \vv^2-1} Q^\mu_{11} \biggr \} \cr}\eqno\matchcurrents a $$
%
\bigskip
%
$$ \eqalign{
%
A^\mu &= P'^\mu_0+\half Q'^\mu_1 + \half Q'^\mu_2 \cr
&+ \third \coupling \biggl \{ 2(\vv-1)r \bigl[P'^\mu_0+\half Q'^\mu_1 \bigr]
  +2 {r+1 \over \vv+1} Q'^\mu_3 \cr
&\qquad\qquad\qquad -4r \bigl[P'^\mu_1+\half Q'^\mu_5 \bigr]
  -{4(1-\vv r) \over \vv^2-1} Q'^\mu_{11} \biggr \} \cr}\eqno\matchcurrents b$$
%
where
%
$$ r = {\log(\vv +\sqrt{\vv ^2-1}) \over \sqrt{\vv ^2-1}}~.$$
%
The $O(\bas(m_c))$ coefficients of the dimension three terms in these formulas
are consistent with results from previous matching computations \FGGW.
%We have also
%verified that the renormalization scale and scheme dependence of these
%results is cancelled in matrix elements between heavy hadron states by
%the implicit $\mu$-dependence of the Isgur-Wise function.

        Five independent relations among the vector and axial
form factors are readily derived from the currents in
\matchcurrents{}.  We choose to express these relations as ratios relative to
the first axial form factor:
%
\def\myif#1#2{{\ifx\answ\bigans{#1}\else{#2}\fi}}
\eqna\ratios
%
\myif{$$ \eqalignno{
{F_1 \over G_1} &= 1+\Bigl[ \cLambdabar + \bLambdabar \Bigr]
  {2 \over (\vv+1)}  + \fourthirds\coupling r
  + \fourthirds\coupling\cLambdabar
  {2(1+r-\vv r) \over (\vv+1) } \quad &\ratios a \cr
%
{F_2 \over G_1} &= {G_2 \over G_1} =
  - \cLambdabar {2 \over (\vv+1) } - \fourthirds \coupling r
  - \fourthirds\coupling \cLambdabar {2(1+r-\vv r) \over (\vv+1) }
  \quad &\ratios b \cr
%
{F_3 \over G_1} &= -{G_3 \over G_1} =
  - \bLambdabar {2 \over (\vv+1) }. \quad &\ratios c \cr} $$}%
{$$ \eqalignno{
{F_1 \over G_1} &= 1+\Bigl[ \cLambdabar + \bLambdabar \Bigr]
  {2 \over (\vv+1)}  \cr
   &\qquad\qquad + \fourthirds\coupling r
  + \fourthirds\coupling\cLambdabar
  {2(1+r-\vv r) \over (\vv+1) } \quad &\ratios a \cr
%
{F_2 \over G_1} &= {G_2 \over G_1} =
  - \cLambdabar {2 \over (\vv+1) } \cr
   &\qquad\qquad - \fourthirds \coupling r
  - \fourthirds\coupling \cLambdabar {2(1+r-\vv r) \over (\vv+1) }
  \quad &\ratios b \cr
%
{F_3 \over G_1} &= -{G_3 \over G_1} =
  - \bLambdabar {2 \over (\vv+1) }. \quad &\ratios c \cr} $$}%
As a check, we have verified that these form factor relations are
renormalization scheme independent as must be the case for physical
observables.

        The ratios in \ratios{}\ imply $F_1 + F_2 + F_3 = G_1$
for all values of $\vv$.  Our enhanced version of Luke's theorem applied to
eqn.~\reducedelems{}\ guarantees that no dimension four terms disrupt the
normalization of these form factor combinations at zero recoil.
Possible normalization violations from dimension three terms are also
prohibited when $v=v'$ as can be readily verified in $v\ccdot A^a=0$
gauge.  Therefore to leading order, only calculable QCD scaling
corrections move the values
of these form factor combinations away from unity at the zero recoil
point:
%
\eqn\formcombos{
 F_1(1)+F_2(1)+F_3(1) = G_1(1) = \Bigl[ {\bas(m_b) \over
  \bas(m_c)} \Bigr]^{- 6/25} . }
%

        To conclude, we estimate the numerical sizes of the expansion
parameters that enter into HQET computations when the bottom and charm
quarks are sequentially treated as heavy and the running between them is
neglected.  Such calculations are organized as perturbative expansions in
$\bar{\Lambda}/2m_c$, $\as(m_c)/\pi$, $\bar{\Lambda}/2m_b$ and $\as(m_b)/\pi$.
Assuming the reasonable values $m_b=4.5 \GeV$, $m_c=1.5 \GeV$,
$\bar{\Lambda}=0.5 \GeV$ and $\Lambda_{\rm QCD}^{(3)}=0.2 \GeV$ and using the
leading log approximation for the strong interaction fine structure constant,
we find that the charm scale parameters $\bar{\Lambda}/2m_c=0.17$ and
$\as(m_c)/\pi=0.11$ are of comparable magnitude.  Their squares
$(\bar{\Lambda}/2m_c)^2=0.03$, $(\as(m_c)/\pi) \bar{\Lambda}/2m_c =0.02$ and
$(\as(m_c)/\pi)^2=0.01$ are not much
smaller than the bottom scale expansion parameters $\as(m_b)/\pi=0.07$ and
$\bar{\Lambda}/2m_b=0.05$.  Further corrections lie below the 1 \% level.  The
uncertainty in the relations \ratios{}\ and \formcombos\ is therefore
dominated by second order $(\bar{\Lambda}/2m_c)^2$ power corrections.  Such
terms are comparable in size to the order $(\as(m_c)/\pi)
\bar{\Lambda}/2m_c$ contributions that we have considered here.

\bigskip
\noindent{\bf Acknowledgements}
\bigskip

        It is a pleasure to acknowledge helpful discussions with Howard Georgi
and Mark Wise.  BG would like to thank the Alfred P. Sloan
Foundation for partial support. This work  was supported in part by the
National Science Foundation under grant  PHY--87--14654, by the
Texas National Research Laboratory Commission
under grant \#RGFY9106, and by the Department of Energy under contract
DE--AC35--89ER40486.

\listrefs
\listfigs
\bye


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  dup 94 /circumflex put
  dup 95 /dotaccent put
  dup 123 /endash put
  dup 124 /emdash put
  dup 125 /hungarumlaut put
  dup 126 /tilde put
  pop
} bdef

/Do-CM-tt-encoding {
  Do-standard-CM-encodings
  CMEncoding
  dup 12 /.notdef put
  dup 13 /quotesingle put
  dup 14 /exclamdown put
  dup 15 /questiondown put
  dup 94 /circumflex put
  dup 126 /tilde put
  pop
} bdef

%
% Routines to handle packing/unpacking numbers.
%
%  <target> <pos> <num> PackHW --> <new target>
%
/PackHW {
  /num xdef
  /pos xdef
  /target xdef
  num 16#0000FFFF and 1 pos sub 16 mul bitshift
    target or
} bdef

%
%  <target> <pos> <num> PackByte --> <new target>
%
/PackByte {
  /num xdef
  /pos xdef
  /target xdef
  num 16#000000FF and 3 pos sub 8 mul bitshift
    target or
} bdef

%
%  <pos> <num> UnpkHW --> <unpacked value>
%
/UnpkHW {
  /num xdef
  /pos xdef
  num 1 pos sub -16 mul bitshift 16#0000FFFF and
  dup 16#00007FFF gt {16#00010000 sub} if
} bdef

%
%  <pos> <num> UnpkByte --> <unpacked value>
%
/UnpkByte {
  /num xdef
  /pos xdef
  num 3 pos sub -8 mul bitshift 16#000000FF and
  dup 16#0000007F gt {16#00000100 sub} if
} bdef

%
%  <int-font-name> <ext-font-name> <pt-sz(pix)> <type> <loaded-fg> DefineCMFont
%
%    type 10: "as-is" PostScript font
%    type 11: CM-mapped PostScript font - roman
%    type 12: CM-mapped PostScript font - text italic
%    type 13: CM-mapped PostScript font - typewriter type
%
/int-dict-name {int (-dict) str-concat} bdef
/int-dict {int (-dict) str-concat cvx load} bdef

/DF {
  true  % signal that the font is already loaded
  DefineCMFont
} bdef

/DNF {
  false  % signal that the font is not already loaded
  DefineCMFont
} bdef

/DefineCMFont {
  /loaded xdef
  /typ xdef
  /psz xdef
  /ext xdef
  /int xdef

  typ 10 ne
    { % font_type = 11, 12, 13
    loaded not
      { /fnam ext 3 str-strip def
        fnam findfont copydict /newdict xdef
        typ DefineCMEncoding
        newdict /Encoding CMEncoding put
        ext newdict definefont pop
      } if
    int-dict-name ext findfont psz scalefont def
    currentdict int [int-dict /setfont cvx] cvx put
    }
    { % font_type = 10
    /fnam ext def
    int-dict-name fnam findfont psz scalefont def
    currentdict int [int-dict /setfont cvx] cvx put
    }
  ifelse
} bdef

%
%  <int-font-name> <ext-font-name> <pt-sz(pix)> <PXL mag> <num-chars>
%      [llx lly urx ury] <newfont-fg> DefinePXLFont
%

/PXLF {
  true  % signal that the font is already loaded
  DefinePXLFont
} bdef

/PXLNF {
  false  % signal that the font is not already loaded
  DefinePXLFont
} bdef

/PXLBuildCharDict 17 dict def

/CMEncodingArray 256 array def
0 1 255 {CMEncodingArray exch dup tempstr cvs cvn put} for

/RasterConvert {RasterScaleFactor div} bdef

/TransformBBox {
  aload pop

  /BB-ury xdef
  /BB-urx xdef
  /BB-lly xdef
  /BB-llx xdef

  [BB-llx RasterConvert BB-lly RasterConvert
   BB-urx RasterConvert BB-ury RasterConvert]
} bdef

/DefinePXLFont {
  /newfont xdef
  /bb xdef
  /num xdef
  /psz xdef
  /dsz xdef
  /pxlmag xdef
  /ext xdef
  /int xdef

  /fnam ext (-) str-concat pxlmag tempstr cvs str-concat def

  newfont not {
    int-dict-name 13 dict def

    int-dict begin
      /FontType 3 def
      /FontMatrix [1 dsz div 0 0 1 dsz div 0 0] def
      /FontBBox bb TransformBBox def
      /Encoding CMEncodingArray def
      /CharDict 1 dict def
      CharDict begin
        /Char-Info num array def
        end

      /BuildChar
        {
          PXLBuildCharDict begin
            /char xdef
            /fontdict xdef

            fontdict /CharDict get /Char-Info get char get aload pop

            /rasters xdef
            /PackedWord1 xdef

            0 PackedWord1 UnpkHW 16#7FFF ne
              { /PackedWord2 xdef
                /wx 0 PackedWord1 UnpkHW def
                /rows 2 PackedWord1 UnpkByte def
                /cols 3 PackedWord1 UnpkByte def
                /llx 0 PackedWord2 UnpkByte def
                /lly 1 PackedWord2 UnpkByte def
                /urx 2 PackedWord2 UnpkByte def
                /ury 3 PackedWord2 UnpkByte def }
              { /PackedWord2 xdef
                /PackedWord3 xdef
                /PackedWord4 xdef
                /wx 1 PackedWord1 UnpkHW def
                /rows 0 PackedWord2 UnpkHW def
                /cols 1 PackedWord2 UnpkHW def
                /llx 0 PackedWord3 UnpkHW def
                /lly 1 PackedWord3 UnpkHW def
                /urx 0 PackedWord4 UnpkHW def
                /ury 1 PackedWord4 UnpkHW def }
               ifelse

            rows 0 lt
              { /rows rows neg def
                /runlength 1 def }
              { /runlength 0 def }
             ifelse

            wx 0
            llx RasterConvert lly RasterConvert
            urx RasterConvert ury RasterConvert setcachedevice
            rows 0 ne
              {
              gsave
                cols rows true
                RasterScaleFactor 0 0 RasterScaleFactor neg llx neg ury
                  tempmatrix astore
                {GenerateRasters} imagemask
              grestore
              } if
            end
        } def
      end

      fnam int-dict definefont pop
    } if

  int-dict-name fnam findfont psz scalefont def
  currentdict int [int-dict /setfont cvx] cvx put
} bdef

%
%  <int-font-name> <code> <wx> <llx> <lly> <urx> <ury> <rows> <cols>
% <runlength> <rasters> PXLC
%
/PXLC {

  /rasters xdef
  /runlength xdef
  /cols xdef
  /rows xdef
  /ury xdef
  /urx xdef
  /lly xdef
  /llx xdef
  /wx xdef
  /code xdef
  /int xdef

  % See if the long or short format is required
  true cols CKSZ rows CKSZ ury CKSZ urx CKSZ lly CKSZ llx CKSZ
    TackRunLengthToRows
    { int-dict /CharDict get /Char-Info get code
        [0 0 llx PackByte 1 lly PackByte 2 urx PackByte 3 ury PackByte
         0 0 wx PackHW 2 rows PackByte 3 cols PackByte
         rasters] put}
    { int-dict /CharDict get /Char-Info get code
        [0 0 urx PackHW 1 ury PackHW
         0 0 llx PackHW 1 lly PackHW
         0 0 rows PackHW 1 cols PackHW
         0 0 16#7FFF PackHW 1 wx PackHW
         rasters] put}
    ifelse
} bdef

/CKSZ {abs 127 le and} bdef
/TackRunLengthToRows {runlength 0 ne {/rows rows neg def} if} bdef

%
%  <wx> <dsz> <psz> <llx> <lly> <urx> <ury> <rows> <cols> <runlength> <rasters>
% PLOTC
%
/PLOTC {
  /rasters xdef
  /runlength xdef
  /cols xdef
  /rows xdef
  /ury xdef
  /urx xdef
  /lly xdef
  /llx xdef
  /psz xdef
  /dsz xdef
  /wx xdef

  % "Plot" a character's raster pattern.
  rows 0 ne
    {
    gsave
      currentpoint translate
      psz dsz div dup scale
      cols rows true
      RasterScaleFactor 0 0 RasterScaleFactor neg llx neg ury
        tempmatrix astore
      {GenerateRasters} imagemask
    grestore
    } if
  wx x
} bdef

% Routine to generate rasters for "imagemask".
/GenerateRasters {
  rasters
  runlength 1 eq {RunLengthToRasters} if
} bdef

% Routine to convert from runlength encoding back to rasters.
/RunLengthToRasters {
  % ...not done yet...
} bdef

%
%  These procedures handle bitmap processing.
%
%  <bitmap columns> <bitmap rows> <bitmap pix/inch> <magnification> BMbeg
%
/BMbeg {
  /BMmagnification xdef
  /BMresolution xdef
  /BMrows xdef
  /BMcols xdef

  /BMcurrentrow 0 def
  gsave
    0.0 setgray
    Resolution BMresolution div dup scale
    currentpoint translate
    BMmagnification 1000.0 div dup scale
    0.0 BMrows moveto
    BMrows dup scale
    currentpoint translate
    /BMCheckpoint save def
  } bdef

/BMend {
  BMCheckpoint restore
  grestore
  } bdef

%
%  <hex raster bitmap> <rows> BMswath
%
/BMswath {
  /rows xdef
  /rasters xdef

  BMcols rows true
  [BMrows 0 0 BMrows neg 0 BMcurrentrow neg]
  {rasters}
  imagemask

  /BMcurrentrow BMcurrentrow rows add def
  BMcurrentrow % save this on the stack around a restore...
  BMCheckpoint restore
  /BMcurrentrow xdef
  /BMCheckpoint save def
  } bdef

%
%  Procedures for implementing the "rotate <theta>" special:
%  <theta> ROTB -
%        - ROTE -

/ROTB {
  XP
  gsave
  Xpos Ypos translate
  rotate % using <theta> from the stack
  Xpos neg Ypos neg translate
  RP
  } bdef

/ROTE {XP grestore RP} bdef

%
%  Procedures for implementing the "epsfile <filename> [<mag>]" special:
%  <llx> <lly> <mag> EPSB -
%  - EPSE -

/EPSB {
  0 SPB
  save
  4 1 roll % push the savelevel below the parameters
  /showpage {} def
  Xpos Ypos translate
  1000 div dup scale % using <mag> from the stack
  neg exch neg exch translate % using <llx> <lly> from the stack
  } bdef

/EPSE {restore 0 SPE} bdef

%
%  Procedure for implementing revision bars:
%  <bary1> <bary2> <barx> <barw> REVB -
%  The bar is a line of width barw drawn from (barx,bary1) to (barx,bary2).

/REVB {
  /barw xdef
  /barx xdef
  /bary2 xdef
  /bary1 xdef
  gsave
    barw setlinewidth
    barx bary1 Yadjust moveto
    barx bary2 Yadjust lineto
    stroke
  grestore
  } bdef

%
%  A small array and two procedures to facilitate The Publisher's
%  implementation of gray table cells:
%                               <ptnum> GRSP -
%  <ultpnum> <lrptnum> <graylev> <freq> GRFB -
%
%  GRSP saves the current DVI location so that it can be retrieved later
%  by the index <ptnum>.  GRFB fills a box whose corners are given by the
%  indexes <ultpnum> and <lrptnum> with a halftone gray with the given
%  level and frequency.  The array GRPM holds the coordinates of points
%  marking the corners of gray table cells.

/GRPM 40 dict def

/GRSP {GRPM exch [Xpos Ypos] put} bdef

/GRFB {
  /GRfreq xdef
  /GRgraylev xdef
  GRPM exch get aload pop /GRlry xdef /GRlrx xdef
  GRPM exch get aload pop /GRuly xdef /GRulx xdef
  gsave
    % set the screen frequency if it isn't zero
    GRfreq 0 ne
      {currentscreen
      3 -1 roll pop GRfreq 3 1 roll
      setscreen}
    if
    % set the gray level
    GRgraylev setgray
    % draw and fill the path
    GRulx GRuly moveto
    GRlrx GRuly lineto
    GRlrx GRlry lineto
    GRulx GRlry lineto
    closepath
    fill
  grestore
  } bdef


%
%  Procedures for implementing the "paper <source>" option:
%  <name> <eop> SPS          -
%         <eop> paper-manual -
%  etc.  The boolean <eop> is passed so that a paper source procedure
%  knows if it is being called at the beginning (false) or end
%  (true) of a page.

/SPS {
  /eop xdef
  /name xdef
  name where {pop eop name cvx exec} if
  } bdef

/paper-manual {
    {statusdict /manualfeed known
      {statusdict /manualfeed true put}
    if}
  if
  } bdef

/paper-automatic {
    {statusdict /manualfeed known
      {statusdict /manualfeed false put}
    if}
  if
  } bdef

/paper-top-tray {
    {}
    {statusdict /setpapertray known
      {statusdict begin gsave 0 setpapertray grestore end}
    if}
  ifelse
  } bdef

/paper-bottom-tray {
    {}
    {statusdict /setpapertray known
      {statusdict begin gsave 1 setpapertray grestore end}
    if}
  ifelse
  } bdef

/paper-both-trays {
    {}
    {statusdict /setpapertray known
      {statusdict begin gsave 2 setpapertray grestore end}
    if}
  ifelse
  } bdef

(end of common prolog) VMSDebug

end

systemdict /setpacking known
  {savepackingmode setpacking}
  if

%
% End of included prolog section.
%

%%EndProlog
%%BeginSetup
BeginDviLaserDoc
300 300 RES
%%EndSetup


%%PageBoundingBox: (atend)
%%BeginPageSetup
1000 BP 3300 2550 PM /paper-automatic false SPS 269 0 XY
%%EndPageSetup
XP /F25 /cmr10 300 41.5 41.5 128 [-3 -11 41 31] PXLNF RP
XP /F25 73 15 1 0 13 28 28 16 0
<FFF0 0F00 0F00 0F00 0F00 0F00 0F00 0F00 0F00 0F00 0F00 0F00 0F00
 0F00 0F00 0F00 0F00 0F00 0F00 0F00 0F00 0F00 0F00 0F00 0F00 0F00
 0F00 FFF0>
PXLC RP
269 448 XY F25(I)S
XP /F25 110 23 1 0 21 18 18 24 0
<FC7C00 1C8700 1D0300 1E0380 1C0380 1C0380 1C0380 1C0380 1C0380
 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 FF9FF0>
PXLC RP
284 448 XY F25(n)S
XP /F25 116 16 1 0 13 26 26 16 0
<0400 0400 0400 0400 0C00 0C00 1C00 3C00 FFE0 1C00 1C00 1C00 1C00
 1C00 1C00 1C00 1C00 1C00 1C10 1C10 1C10 1C10 1C10 0C10 0E20 03C0>
PXLC RP
306 448 XY F25(t)S
XP /F25 101 18 1 0 16 18 18 16 0
<03E0 0C30 1818 300C 700E 6006 E006 FFFE E000 E000 E000 E000 6000
 7002 3002 1804 0C18 03E0>
PXLC RP
322 448 XY F25(e)S
XP /F25 114 16 1 0 14 18 18 16 0
<FCE0 1D30 1E78 1E78 1C30 1C00 1C00 1C00 1C00 1C00 1C00 1C00 1C00
 1C00 1C00 1C00 1C00 FFC0>
PXLC RP
341 448 XY F25(r)S
XP /F25 109 35 1 0 34 18 18 40 0
<FC7E07E000 10 10 1E01E01C00 1C01C01C00 1C01C01C00
 1C01C01C00 1C01C01C00 1C01C01C00 1C01C01C00 1C01C01C00 1C01C01C00
 1C01C01C00 1C01C01C00 1C01C01C00 1C01C01C00 1C01C01C00 FF8FF8FF80>
PXLC RP
357 448 XY F25(me)S
XP /F25 100 23 2 0 21 29 29 24 0
<003F00 000700 000700 000700 000700 000700 000700 000700 000700
 000700 000700 03E700 0C1700 180F00 300700 700700 600700 E00700
 E00700 E00700 E00700 E00700 E00700 600700 700700 300700 180F00
 0C3700 07C7E0>
PXLC RP
410 448 XY F25(d)S
XP /F25 105 12 1 0 10 29 29 16 0
<1800 3C00 3C00 1800 0000 0000 0000 0000 0000 0000 0000 FC00 1C00
 1C00 1C00 1C00 1C00 1C00 1C00 1C00 1C00 1C00 1C00 1C00 1C00 1C00
 1C00 1C00 FF80>
PXLC RP
433 448 XY F25(i)S
XP /F25 97 21 2 0 20 18 18 24 0
<1FC000 307000 783800 781C00 301C00 001C00 001C00 01FC00 0F1C00
 381C00 701C00 601C00 E01C40 E01C40 E01C40 603C40 304E80 1F8700>
PXLC RP
445 448 XY F25(ate)S
XP /F25 72 31 2 0 28 28 28 32 0
<FFF3FFC0 0F003C00 0F003C00 0F003C00 0F003C00 0F003C00 0F003C00
 0F003C00 0F003C00 0F003C00 0F003C00 0F003C00 0F003C00 0FFFFC00
 0F003C00 0F003C00 0F003C00 0F003C00 0F003C00 0F003C00 0F003C00
 0F003C00 0F003C00 0F003C00 0F003C00 0F003C00 0F003C00 FFF3FFC0>
PXLC RP
514 448 XY F25(H)S
XP /F25 81 32 2 -8 29 29 37 32 0
<003F8000 00E0E000 03803800 07001C00 0E000E00 1C000700 3C000780
 38000380 780003C0 780003C0 700001C0 F00001E0 F00001E0 F00001E0
 F00001E0 F00001E0 F00001E0 F00001E0 F00001E0 700001C0 780003C0
 780003C0 38000380 3C0E0780 1C110700 0E208E00 07205C00 03A07800
 00F0E020 003FE020 00006020 00003060 000038E0 00003FC0 00003FC0
 00001F80 00000F00>
PXLC RP
545 448 XY F25(Q)S
XP /F25 69 28 2 0 26 28 28 24 0
<FFFFFC 0F003C 0F000C 0F0004 0F0004 0F0006 0F0002 0F0002 0F0202
 0F0200 0F0200 0F0200 0F0600 0FFE00 0F0600 0F0200 0F0200 0F0200
 0F0201 0F0001 0F0002 0F0002 0F0002 0F0006 0F0006 0F000C 0F003C
 FFFFFC>
PXLC RP
577 448 XY F25(E)S
XP /F25 84 30 1 0 28 28 28 32 0
<7FFFFFC0 700F01C0 600F00C0 400F0040 400F0040 C00F0020 800F0020
 800F0020 800F0020 000F0000 000F0000 000F0000 000F0000 000F0000
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PXLC RP
606 448 XY F25(T)S
XP /F25 103 21 1 -9 19 19 28 24 0
<000380 03C4C0 0C38C0 1C3880 181800 381C00 381C00 381C00 381C00
 181800 1C3800 0C3000 13C000 100000 300000 180000 1FF800 1FFF00
 1FFF80 300380 6001C0 C000C0 C000C0 C000C0 600180 300300 1C0E00
 07F800>
PXLC RP
650 448 XY F25(gra)S
XP /F25 112 23 1 -8 20 18 26 24 0
<FC7C00 1D8600 1E0300 1C0180 1C01C0 1C00C0 1C00E0 1C00E0 1C00E0
 1C00E0 1C00E0 1C00E0 1C01C0 1C01C0 1C0180 1E0300 1D0600 1CF800
 1C0000 1C0000 1C0000 1C0000 1C0000 1C0000 1C0000 FF8000>
PXLC RP
707 448 XY F25(p)S
XP /F25 104 23 1 0 21 29 29 24 0
<FC0000 1C0000 1C0000 1C0000 1C0000 1C0000 1C0000 1C0000 1C0000
 1C0000 1C0000 1C7C00 1C8700 1D0300 1E0380 1C0380 1C0380 1C0380
 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380 1C0380
 1C0380 FF9FF0>
PXLC RP
730 448 XY F25(h)S
XP /F25 102 13 0 0 15 29 29 16 0
<00F8 018C 071E 061E 0E0C 0E00 0E00 0E00 0E00 0E00 0E00 FFE0 0E00
 0E00 0E00 0E00 0E00 0E00 0E00 0E00 0E00 0E00 0E00 0E00 0E00 0E00
 0E00 0E00 7FE0>
PXLC RP
767 448 XY F25(f)S
XP /F25 111 21 1 0 19 18 18 24 0
<03F000 0E1C00 180600 300300 700380 600180 E001C0 E001C0 E001C0
 E001C0 E001C0 E001C0 600180 700380 300300 180600 0E1C00 03F000>
PXLC RP
780 448 XY F25(or)S
XP /F26 /cmmi10 300 41.5 41.5 128 [-1 -10 43 31] PXLNF RP
XP /F26 109 36 2 0 34 18 18 32 0
<381F81F0 4E20C618 4640E81C 4680F01C 8F00F01C 8E00E01C 0E00E01C
 0E00E01C 1C01C038 1C01C038 1C01C038 1C01C070 38038071 38038071
 380380E1 380380E2 70070064 30030038>
PXLC RP
831 448 XY F26(m)S
XP /F9 /cmmi7 300 29.1 29.1 128 [-1 -7 32 22] PXLNF RP
XP /F9 99 15 2 0 13 13 13 16 0
<0780 0C40 10E0 31C0 6000 6000 6000 C000 C000 4020 4040 2180 1E00>
PXLC RP
867 454 XY F9(c)S
XP /F26 60 32 3 -2 28 22 24 32 0
<00000380 00000F00 00003C00 0000F000 0003C000 000F0000 003C0000
 00F00000 03C00000 0F000000 3C000000   3C000000
 0F000000 03C00000 00F00000 003C0000 000F0000 0003C000 0000F000
 00003C00 00000F00 00000380>
PXLC RP
896 448 XY F26(<)S
XP /F26 22 25 1 -9 22 18 27 24 0
<018030 038070 038070 038070 0700E0 0700E0 0700E0 0700E0 0E01C0
 0E01C0 0E01C0 0E01C0 1C0388 1C0388 1C0388 1E0788 3E1990 3BE0E0
 380000 380000 700000 700000 700000 700000 E00000 E00000 C00000>
PXLC RP
939 448 XY F26(\026)S 12 x(<)S 12 x(m)S
XP /F9 98 15 2 0 12 20 20 16 0
<7C00 0C00 1800 1800 1800 1800 3000 3700 3880 30C0 60C0 60C0 60C0
 60C0 C180 C180 C100 4300 6600 3800>
PXLC RP
1056 454 XY F9(b)S
XP /F25 58 12 4 0 8 18 18 8 0
<60 F0 F0 60 00 00 00 00 00 00 00 00 00 00 60 F0 F0 60>
PXLC RP
1073 448 XY F25(:)S
XP /F68 /line10 300 41.5 41.5 127 [-6 -6 43 43] PXLNF RP
XP /F68 0 42 -1 -1 43 43 44 48 0
<000000000030 000000000070 0000000000E0 0000000001C0 000000000380
 000000000700 000000000E00 000000001C00 000000003800 000000007000
 00000000E000 00000001C000 000000038000 000000070000 0000000E0000
 0000001C0000 000000380000 000000700000 000000E00000 000001C00000
 000003800000 000007000000 00000E000000 00001C000000 000038000000
 000070000000 0000 0001 000380000000 000700000000
 0000 0010 003800000000 007000000000 0000
 0100 038000000000 070000000000 0000 1000
 380000000000 700000000000 0000 0000>
PXLC RP
1006 920 XY F68(\000)S -39 y -3 x(\000)S -39 y -3 x(\000)S -39 y
-3 x(\000)S -39 y -3 x(\000)S -39 y -4 x(\000)S 920 Y 1018 X(\000)S
-37 y -6 x(\000)S -36 y -5 x(\000)S -37 y -6 x(\000)S -36 y -5 x
(\000)S -37 y -6 x(\000)S
XP /F68 64 42 -1 -1 43 43 44 48 0
<0000 0000 700000000000 380000000000 1000
 0000 070000000000 038000000000 0100 0000
 007000000000 003800000000 0010 0000 000700000000
 000380000000 0001 0000 000070000000 000038000000
 00001C000000 00000E000000 000007000000 000003800000 000001C00000
 000000E00000 000000700000 000000380000 0000001C0000 0000000E0000
 000000070000 000000038000 00000001C000 00000000E000 000000007000
 000000003800 000000001C00 000000000E00 000000000700 000000000380
 0000000001C0 0000000000E0 000000000070 000000000030>
PXLC RP
1242 737 XY F68(@)S 37 y -5 x(@)S 36 y -6 x(@)S 37 y -5 x(@)S 36 y
-6 x(@)S 37 y -5 x(@)S
XP /F26 98 18 2 0 16 29 29 16 0
<3F00 0700 0700 0E00 0E00 0E00 0E00 1C00 1C00 1C00 1C00 39E0 3A30
 3C18 3818 7018 701C 701C 701C E038 E038 E038 E030 E070 E060 E0C0
 61C0 2300 1E00>
PXLC RP
1006 967 XY F26(b)S
XP /F9 118 17 1 0 13 13 13 16 0
<3810 4C30 4C10 8C10 9810 1810 1810 3020 3020 3040 3040 1880 0F00>
PXLC RP
1024 973 XY F9(v)S
XP /F26 99 18 2 0 17 18 18 16 0
<01F0 030C 0E0C 1C1E 383C 3018 7000 7000 E000 E000 E000 E000 E000
 E004 6008 6010 3060 1F80>
PXLC RP
1449 967 XY F26(c)S 1232 701 XY 18 18 R
XP /F25 126 21 3 24 17 28 4 16 0
<1C04 3F08 43F0 80E0>
PXLC RP
1229 638 XY F25(~)S
XP /F26 80 27 2 0 30 28 28 32 0
<01FFFF00 003C03C0 003800E0 003800F0 00380070 00380070 007000F0
 007000F0 007000F0 007000E0 00E001E0 00E003C0 00E00780 00E01E00
 01FFF000 01C00000 01C00000 01C00000 03800000 03800000 03800000
 03800000 07000000 07000000 07000000 07000000 0F000000 FFE00000>
PXLC RP
1219 648 XY F26(P)S
XP /F8 /cmr7 300 29.1 29.1 128 [-2 -8 32 22] PXLNF RP
XP /F8 48 17 2 0 14 19 19 16 0
<0F00 30C0 6060 6060 4020 C030 C030 C030 C030 C030 C030 C030 C030
 C030 4020 6060 6060 30C0 0F00>
PXLC RP
1246 655 XY F8(0)S
XP /F70 /lcircle10 300 41.5 41.5 127 [-83 -83 85 85] PXLNF RP
XP /F70 2 17 0 0 11 10 10 16 0
<C000 C000 C000 E000 6000 7000 3800 1E00 07E0 01E0>
PXLC RP
1135 811 XY F70(\002)S
XP /F70 1 17 -8 0 2 10 10 16 0
<00C0 00C0 00C0 01C0 0180 0380 0700 1E00 F800 E000>
PXLC RP
1147 811 XY F70(\001)S -5 x(\002)S -6 x(\001)S -5 x(\002)S -5 x
(\001)S -5 x(\002)S -5 x(\001)S -6 x(\002)S -5 x(\001)S -5 x(\002)S
-5 x(\001)S -5 x(\002)S -6 x(\001)S -5 x(\002)S -5 x(\001)S -5 x
(\002)S -5 x(\001)S
XP /F70 3 17 0 -8 11 2 10 16 0
<01E0 07E0 1E00 3800 7000 6000 E000 C000 C000 C000>
PXLC RP
1147 797 XY F70(\003)S
XP /F70 0 17 -8 -8 2 2 10 16 0
<E000 F800 1E00 0700 0380 0180 01C0 00C0 00C0 00C0>
PXLC RP
1159 797 XY F70(\000)S -6 x(\003)S -5 x(\000)S -5 x(\003)S -5 x
(\000)S -5 x(\003)S -6 x(\000)S -5 x(\003)S -5 x(\000)S -5 x(\003)S
-5 x(\000)S -6 x(\003)S -5 x(\000)S -5 x(\003)S -5 x(\000)S -5 x
(\003)S -6 x(\000)S
XP /F26 112 21 -1 -8 20 18 26 24 0
<070780 09C860 08D030 08E030 11C030 11C038 01C038 01C038 038070
 038070 038070 038060 0700E0 0700C0 070180 078300 0E8600 0E7800
 0E0000 0E0000 1C0000 1C0000 1C0000 1C0000 3C0000 FF8000>
PXLC RP
744 896 XY F26(p)S
XP /F25 61 32 2 4 29 16 12 32 0
<7FFFFFC0 FFFFFFE0 00000000 00000000 00000000 00000000 00000000
 00000000 00000000 00000000 FFFFFFE0 7FFFFFC0>
PXLC RP
776 896 XY F25(=)S 12 x F26(m)S 7 y F9(b)S
XP /F26 118 20 2 0 18 18 18 16 0
<1C02 2707 4707 4703 8701 8701 0E01 0E01 1C02 1C02 1C02 1C04 1804
 1808 1808 1C10 0C20 07C0>
PXLC RP
873 896 XY F26(v)S
XP /F25 43 32 2 -4 29 24 28 32 0
<00060000 00060000 00060000 00060000 00060000 00060000 00060000
 00060000 00060000 00060000 00060000 00060000 00060000 FFFFFFE0
 FFFFFFE0 00060000 00060000 00060000 00060000 00060000 00060000
 00060000 00060000 00060000 00060000 00060000 00060000 00060000>
PXLC RP
904 896 XY F25(+)S
XP /F26 107 22 2 0 20 29 29 24 0
<0FC000 01C000 01C000 038000 038000 038000 038000 070000 070000
 070000 070000 0E0700 0E1880 0E21C0 0E23C0 1C4780 1C8300 1D0000
 1E0000 3F8000 39C000 38E000 38E000 70E100 70E100 70E100 70E200
 E06200 603C00>
PXLC RP
946 896 XY F26(k)S 7 y F9(b)S -7 y 1500 X F26(p)S
XP /F10 /cmsy7 300 29.1 29.1 128 [-1 -28 35 23] PXLNF RP
XP /F10 48 10 1 1 8 16 15 8 0
<04 0E 0E 1C 1C 1C 38 38 30 70 70 60 60 C0 C0>
PXLC RP
1521 881 XY F10(0)S 15 y 13 x F25(=)S 12 x F26(m)S 7 y F9(c)S -7 y
2 x F26(v)S -15 y 1 x F10(0)S 15 y 12 x F25(+)S 9 x F26(k)S 7 y F9
(c)S
XP /F25 70 27 2 0 24 28 28 24 0
<FFFFF8 0F0078 0F0018 0F0008 0F0008 0F000C 0F0004 0F0004 0F0204
 0F0200 0F0200 0F0200 0F0600 0FFE00 0F0600 0F0200 0F0200 0F0200
 0F0200 0F0000 0F0000 0F0000 0F0000 0F0000 0F0000 0F0000 0F8000
 FFF800>
PXLC RP
269 1156 XY F25(Fina)S
XP /F25 108 12 1 0 10 29 29 16 0
<FC00 1C00 1C00 1C00 1C00 1C00 1C00 1C00 1C00 1C00 1C00 1C00 1C00
 1C00 1C00 1C00 1C00 1C00 1C00 1C00 1C00 1C00 1C00 1C00 1C00 1C00
 1C00 1C00 FF80>
PXLC RP
352 1156 XY F25(l)S 13 x(HQET)S 15 x(graph)S
XP /F25 115 16 1 0 14 18 18 16 0
<1F90 3070 4030 C010 C010 E010 F800 7F80 3FE0 0FF0 00F8 8038 8018
 C018 C018 E010 D060 8FC0>
PXLC RP
617 1156 XY F25(s)S 14 x(for)S 13 x F26(\026)S 12 x(<)S 12 x(m)S
6 y F9(c)S -6 y 2 x F25(:)S 1629 Y 1006 X F68(\000)S -39 y -3 x
(\000)S -39 y -3 x(\000)S -39 y -3 x(\000)S -39 y -3 x(\000)S -39 y
-4 x(\000@)S 39 y -3 x(@)S 39 y -3 x(@)S 39 y -3 x(@)S 39 y -3 x(@)S
39 y -3 x(@)S 1018 X(\000)S -37 y -6 x(\000)S -37 y -5 x(\000)S -36 y
-6 x(\000)S -37 y -5 x(\000)S -36 y -6 x(\000@)S 36 y -5 x(@)S 37 y
-6 x(@)S 36 y -5 x(@)S 37 y -6 x(@)S 37 y -5 x(@)S 47 y 1006 X F26
(b)S 6 y F9(v)S -6 y 1438 X F26(c)S 6 y F9(v)S
XP /F2 /cmsy5 300 20.8 20.8 128 [0 -20 29 16] PXLNF RP
XP /F2 48 9 2 1 7 12 11 8 0
<18 18 18 30 30 30 60 60 60 C0 C0>
PXLC RP
1474 1674 XY F2(0)S 1235 1404 XY 18 18 R -47 y -31 x F26(P)S 6 y F8
(0)S 1520 Y 1135 X F70(\002)S -5 x(\001)S -5 x(\002)S -6 x(\001)S
-5 x(\002)S -5 x(\001)S -5 x(\002)S -5 x(\001)S -6 x(\002)S -5 x
(\001)S -5 x(\002)S -5 x(\001)S -5 x(\002)S -6 x(\001)S -5 x(\002)S
-5 x(\001)S -5 x(\002)S -5 x(\001)S -15 y 1147 X(\003)S -5 x(\000)S
-6 x(\003)S -5 x(\000)S -5 x(\003)S -5 x(\000)S -5 x(\003)S -6 x
(\000)S -5 x(\003)S -5 x(\000)S -5 x(\003)S -5 x(\000)S -6 x(\003)S
-5 x(\000)S -5 x(\003)S -5 x(\000)S -5 x(\003)S -6 x(\000)S 2101 Y
711 X F68(\000)S -39 y -4 x(\000)S -39 y -3 x(\000)S -39 y -3 x
(\000)S -39 y -3 x(\000)S -39 y -3 x(\000@)S 39 y -3 x(@)S 39 y -3 x
(@)S 39 y -3 x(@)S 39 y -3 x(@)S 39 y -4 x(@)S 722 X(\000)S -36 y
-5 x(\000)S -37 y -6 x(\000)S -37 y -5 x(\000)S -36 y -5 x(\000)S
-37 y -6 x(\000@)S 37 y -6 x(@)S 36 y -5 x(@)S 37 y -6 x(@)S 37 y
-5 x(@)S 36 y -5 x(@)S 47 y 711 X F26(b)S 7 y F9(v)S -7 y 1143 X F26
(c)S 7 y F9(v)S -9 y 1 x F2(0)S 940 1877 XY 18 18 R
XP /F70 115 17 -9 -9 9 9 18 24 0
<01E000 07F800 1FFE00 3FFF00 7FFF80 7FFF80 FFFFC0 FFFFC0 FFFFC0
 FFFFC0 FFFFC0 FFFFC0 7FFF80 7FFF80 3FFF00 1FFE00 07F800 01E000>
PXLC RP
999 1924 XY F70(s)S 1829 Y 927 X F26(P)S 7 y F8(0)S 1992 Y 840 X F70
(\002)S -6 x(\001)S -5 x(\002)S -5 x(\001)S -5 x(\002)S -5 x(\001)S
-6 x(\002)S -5 x(\001)S -5 x(\002)S -5 x(\001)S -5 x(\002)S -5 x
(\001)S -6 x(\002)S -5 x(\001)S -5 x(\002)S -5 x(\001)S -5 x(\002)S
-6 x(\001)S -14 y 851 X(\003)S -5 x(\000)S -5 x(\003)S -5 x(\000)S
-5 x(\003)S -6 x(\000)S -5 x(\003)S -5 x(\000)S -5 x(\003)S -5 x
(\000)S -5 x(\003)S -6 x(\000)S -5 x(\003)S -5 x(\000)S -5 x(\003)S
-5 x(\000)S -6 x(\003)S -5 x(\000)S 2101 Y 1301 X F68(\000)S -39 y
-3 x(\000)S -39 y -3 x(\000)S -39 y -3 x(\000)S -39 y -3 x(\000)S
-39 y -3 x(\000)S -1 x(@)S 39 y -3 x(@)S 39 y -3 x(@)S 39 y -3 x(@)S
39 y -3 x(@)S 39 y -3 x(@)S 1313 X(\000)S -36 y -6 x(\000)S -37 y
-5 x(\000)S -37 y -5 x(\000)S -36 y -6 x(\000)S -37 y -5 x(\000)S
-1 x(@)S 37 y -5 x(@)S 36 y -6 x(@)S 37 y -5 x(@)S 37 y -5 x(@)S
36 y -6 x(@)S 47 y 1301 X F26(b)S 7 y F9(v)S -7 y 1733 X F26(c)S
7 y F9(v)S -9 y 1 x F2(0)S 1530 1877 XY 18 18 R 1983 Y 1649 X F70
(s)S 1829 Y 1518 X F26(P)S 7 y F8(0)S 1992 Y 1430 X F70(\002)S -5 x
(\001)S -5 x(\002)S -5 x(\001)S -6 x(\002)S -5 x(\001)S -5 x(\002)S
-5 x(\001)S -5 x(\002)S -6 x(\001)S -5 x(\002)S -5 x(\001)S -5 x
(\002)S -5 x(\001)S -5 x(\002)S -6 x(\001)S -5 x(\002)S -5 x(\001)S
-14 y 1442 X(\003)S -5 x(\000)S -5 x(\003)S -6 x(\000)S -5 x(\003)S
-5 x(\000)S -5 x(\003)S -5 x(\000)S -6 x(\003)S -5 x(\000)S -5 x
(\003)S -5 x(\000)S -5 x(\003)S -5 x(\000)S -6 x(\003)S -5 x(\000)S
-5 x(\003)S -5 x(\000)S 2574 Y 415 X F68(\000)S -39 y -3 x(\000)S
-39 y -3 x(\000)S -39 y -3 x(\000)S -39 y -3 x(\000)S -39 y -3 x
(\000)S -1 x(@)S 39 y -3 x(@)S 39 y -3 x(@)S 39 y -3 x(@)S 39 y -3 x
(@)S 39 y -3 x(@)S 427 X(\000)S -37 y -5 x(\000)S -37 y -6 x(\000)S
-36 y -5 x(\000)S -37 y -6 x(\000)S -36 y -5 x(\000)S -1 x(@)S 36 y
-5 x(@)S 37 y -5 x(@)S 36 y -6 x(@)S 37 y -5 x(@)S 37 y -6 x(@)S
47 y 415 X F26(b)S 6 y F9(v)S -6 y 848 X F26(c)S 6 y F9(v)S -8 y
1 x F2(0)S 644 2349 XY 18 18 R 486 2513 XY 3 3 R 488 2512 XY
3 3 R 489 2510 XY 3 3 R 491 2509 XY 3 3 R 491 2509 XY 3 3 R
493 2510 XY 3 3 R 495 2511 XY 3 3 R 495 2511 XY 3 3 R 497 2512 XY
3 3 R 498 2513 XY 3 3 R 499 2514 XY 3 3 R 500 2516 XY 3 3 R
501 2517 XY 3 3 R 501 2517 XY 3 3 R 503 2517 XY 3 3 R 504 2518 XY
3 3 R 506 2518 XY 3 3 R 506 2518 XY 3 3 R 507 2517 XY 3 3 R
508 2516 XY 3 3 R 509 2514 XY 3 3 R 510 2513 XY 3 3 R 510 2513 XY
3 3 R 511 2511 XY 3 3 R 511 2509 XY 3 3 R 512 2508 XY 3 3 R
513 2506 XY 3 3 R 513 2506 XY 3 3 R 515 2505 XY 3 3 R 517 2505 XY
3 3 R 517 2505 XY 3 3 R 519 2506 XY 3 3 R 520 2507 XY 3 3 R
522 2508 XY 3 3 R 523 2509 XY 3 3 R 523 2509 XY 3 3 R 525 2510 XY
3 3 R 526 2510 XY 3 3 R 528 2511 XY 3 3 R 529 2512 XY 3 3 R
529 2512 XY 3 3 R 531 2511 XY 3 3 R 532 2510 XY 3 3 R 533 2509 XY
3 3 R 533 2509 XY 3 3 R 534 2507 XY 3 3 R 534 2505 XY 3 3 R
535 2503 XY 3 3 R 535 2502 XY 3 3 R 535 2502 XY 3 3 R 537 2499 XY
3 3 R 538 2497 XY 3 3 R 538 2497 XY 3 3 R 540 2497 XY 3 3 R
542 2498 XY 3 3 R 544 2498 XY 3 3 R 544 2498 XY 3 3 R 546 2499 XY
3 3 R 547 2500 XY 3 3 R 549 2501 XY 3 3 R 551 2502 XY 3 3 R
551 2502 XY 3 3 R 553 2502 XY 3 3 R 556 2501 XY 3 3 R 556 2501 XY
3 3 R 556 2499 XY 3 3 R 557 2497 XY 3 3 R 558 2495 XY 3 3 R
558 2495 XY 3 3 R 558 2493 XY 3 3 R 558 2491 XY 3 3 R 558 2489 XY
3 3 R 559 2487 XY 3 3 R 559 2487 XY 3 3 R 561 2486 XY 3 3 R
563 2485 XY 3 3 R 563 2485 XY 3 3 R 565 2486 XY 3 3 R 568 2487 XY
3 3 R 570 2488 XY 3 3 R 570 2488 XY 3 3 R 572 2488 XY 3 3 R
574 2489 XY 3 3 R 576 2489 XY 3 3 R 576 2489 XY 3 3 R 578 2487 XY
3 3 R 579 2484 XY 3 3 R 579 2484 XY 3 3 R 579 2483 XY 3 3 R
579 2481 XY 3 3 R 579 2479 XY 3 3 R 579 2477 XY 3 3 R 579 2477 XY
3 3 R 579 2475 XY 3 3 R 580 2473 XY 3 3 R 581 2471 XY 3 3 R
581 2471 XY 3 3 R 583 2472 XY 3 3 R 585 2472 XY 3 3 R 587 2472 XY
3 3 R 587 2472 XY 3 3 R 589 2472 XY 3 3 R 590 2472 XY 3 3 R
592 2473 XY 3 3 R 594 2473 XY 3 3 R 594 2473 XY 3 3 R 596 2472 XY
3 3 R 598 2471 XY 3 3 R 598 2471 XY 3 3 R 598 2469 XY 3 3 R
598 2467 XY 3 3 R 598 2465 XY 3 3 R 598 2464 XY 3 3 R 598 2464 XY
3 3 R 598 2461 XY 3 3 R 598 2459 XY 3 3 R 597 2457 XY 3 3 R
597 2457 XY 3 3 R 599 2455 XY 3 3 R 601 2454 XY 3 3 R 601 2454 XY
3 3 R 603 2454 XY 3 3 R 605 2454 XY 3 3 R 607 2454 XY 3 3 R
609 2455 XY 3 3 R 609 2455 XY 3 3 R 611 2454 XY 3 3 R 613 2454 XY
3 3 R 615 2454 XY 3 3 R 615 2454 XY 3 3 R 615 2452 XY 3 3 R
615 2450 XY 3 3 R 616 2448 XY 3 3 R 616 2448 XY 3 3 R 615 2446 XY
3 3 R 614 2444 XY 3 3 R 614 2442 XY 3 3 R 613 2440 XY 3 3 R
613 2440 XY 3 3 R 614 2438 XY 3 3 R 614 2435 XY 3 3 R 614 2435 XY
3 3 R 616 2435 XY 3 3 R 618 2435 XY 3 3 R 620 2434 XY 3 3 R
620 2434 XY 3 3 R 622 2434 XY 3 3 R 624 2434 XY 3 3 R 626 2434 XY
3 3 R 628 2433 XY 3 3 R 628 2433 XY 3 3 R 629 2431 XY 3 3 R
631 2429 XY 3 3 R 631 2429 XY 3 3 R 630 2427 XY 3 3 R 629 2425 XY
3 3 R 628 2423 XY 3 3 R 628 2423 XY 3 3 R 627 2420 XY 3 3 R
626 2418 XY 3 3 R 626 2416 XY 3 3 R 626 2416 XY 3 3 R 627 2415 XY
3 3 R 628 2414 XY 3 3 R 629 2413 XY 3 3 R 629 2413 XY 3 3 R
631 2413 XY 3 3 R 633 2412 XY 3 3 R 635 2412 XY 3 3 R 637 2411 XY
3 3 R 637 2411 XY 3 3 R 638 2410 XY 3 3 R 640 2409 XY 3 3 R
642 2408 XY 3 3 R 642 2408 XY 3 3 R 641 2407 XY 3 3 R 641 2405 XY
3 3 R 640 2403 XY 3 3 R 640 2403 XY 3 3 R 639 2401 XY 3 3 R
638 2399 XY 3 3 R 637 2398 XY 3 3 R 636 2396 XY 3 3 R 636 2396 XY
3 3 R 636 2394 XY 3 3 R 636 2391 XY 3 3 R 636 2391 XY 3 3 R
638 2390 XY 3 3 R 640 2389 XY 3 3 R 642 2388 XY 3 3 R 642 2388 XY
3 3 R 644 2388 XY 3 3 R 647 2387 XY 3 3 R 649 2386 XY 3 3 R
649 2386 XY 3 3 R 649 2383 XY 3 3 R 650 2381 XY 3 3 R 650 2381 XY
3 3 R 648 2379 XY 3 3 R 647 2378 XY 3 3 R 646 2376 XY 3 3 R
645 2375 XY 3 3 R 645 2375 XY 3 3 R 644 2374 XY 3 3 R 643 2372 XY
3 3 R 642 2371 XY 3 3 R 641 2370 XY 3 3 R 641 2370 XY 3 3 R
643 2368 XY 3 3 R 644 2366 XY 3 3 R 644 2366 XY 3 3 R 646 2365 XY
3 3 R 648 2364 XY 3 3 R 650 2363 XY 3 3 R 651 2362 XY 3 3 R
651 2362 XY 3 3 R 652 2360 XY 3 3 R 654 2359 XY 3 3 R 655 2357 XY
3 3 R 655 2357 XY 3 3 R 654 2356 XY 3 3 R 653 2355 XY 3 3 R
652 2354 XY 3 3 R 651 2352 XY 3 3 R 651 2352 XY 3 3 R 650 2351 XY
3 3 R 648 2350 XY 3 3 R 647 2349 XY 3 3 R 645 2347 XY 3 3 R
645 2347 XY 3 3 R 645 2345 XY 3 3 R 644 2343 XY 3 3 R 644 2343 XY
3 3 R 646 2342 XY 3 3 R 647 2341 XY 3 3 R 649 2339 XY 3 3 R
650 2338 XY 3 3 R
XP /F26 81 33 2 -8 30 29 37 32 0
<0003F800 000E0E00 00380380 00E001C0 01C001C0 038000E0 070000E0
 0F0000F0 1E0000F0 1C0000F0 3C0000F0 3C0000F0 780000F0 780000F0
 780000F0 F00001E0 F00001E0 F00001E0 F00003C0 F00003C0 
  F0000F00 703C0E00 70421C00 38823800 38827000 1C83C000
 07878100 01FF0100 00030300 00030200 00038E00 0003FC00 0003F800
 0001F800 0001E000>
PXLC RP
626 2302 XY F26(Q)S
XP /F8 49 17 3 0 13 19 19 16 0
<0C00 1C00 EC00 0C00 0C00 0C00 0C00 0C00 0C00 0C00 0C00 0C00 0C00
 0C00 0C00 0C00 0C00 0C00 FFC0>
PXLC RP
659 2308 XY F8(1)S 2574 Y 1006 X F68(\000)S -39 y -3 x(\000)S -39 y
-3 x(\000)S -39 y -3 x(\000)S -39 y -3 x(\000)S -39 y -4 x(\000@)S
39 y -3 x(@)S 39 y -3 x(@)S 39 y -3 x(@)S 39 y -3 x(@)S 39 y -3 x
(@)S 1018 X(\000)S -37 y -6 x(\000)S -37 y -5 x(\000)S -36 y -6 x
(\000)S -37 y -5 x(\000)S -36 y -6 x(\000@)S 36 y -5 x(@)S 37 y -6 x
(@)S 36 y -5 x(@)S 37 y -6 x(@)S 37 y -5 x(@)S 47 y 1006 X F26(b)S
6 y F9(v)S -6 y 1438 X F26(c)S 6 y F9(v)S -8 y 1 x F2(0)S
1235 2349 XY 18 18 R -47 y -37 x F26(Q)S 6 y F8(1)S 2465 Y 1135 X
F70(\002)S -5 x(\001)S -5 x(\002)S -6 x(\001)S -5 x(\002)S -5 x
(\001)S -5 x(\002)S -5 x(\001)S -6 x(\002)S -5 x(\001)S -5 x(\002)S
-5 x(\001)S -5 x(\002)S -6 x(\001)S -5 x(\002)S -5 x(\001)S -5 x
(\002)S -5 x(\001)S -15 y 1147 X(\003)S -5 x(\000)S -6 x(\003)S -5 x
(\000)S -5 x(\003)S -5 x(\000)S -5 x(\003)S -6 x(\000)S -5 x(\003)S
-5 x(\000)S -5 x(\003)S -5 x(\000)S -6 x(\003)S -5 x(\000)S -5 x
(\003)S -5 x(\000)S -5 x(\003)S -6 x(\000)S 2574 Y 1596 X F68(\000)S
-39 y -3 x(\000)S -39 y -3 x(\000)S -39 y -3 x(\000)S -39 y -3 x
(\000)S -39 y -3 x(\000@)S 39 y -4 x(@)S 39 y -3 x(@)S 39 y -3 x(@)S
39 y -3 x(@)S 39 y -3 x(@)S 1608 X(\000)S -37 y -5 x(\000)S -37 y
-6 x(\000)S -36 y -5 x(\000)S -37 y -6 x(\000)S -36 y -5 x(\000@)S
36 y -6 x(@)S 37 y -5 x(@)S 36 y -6 x(@)S 37 y -5 x(@)S 37 y -6 x
(@)S 47 y 1596 X F26(b)S 6 y F9(v)S -6 y 2029 X F26(c)S 6 y F9(v)S
-8 y 1 x F2(0)S 1825 2349 XY 18 18 R 1831 2338 XY 3 3 R
1830 2340 XY 3 3 R 1828 2341 XY 3 3 R 1827 2342 XY 3 3 R
1826 2343 XY 3 3 R 1826 2343 XY 3 3 R 1826 2345 XY 3 3 R
1827 2348 XY 3 3 R 1827 2348 XY 3 3 R 1828 2349 XY 3 3 R
1830 2350 XY 3 3 R 1832 2351 XY 3 3 R 1833 2352 XY 3 3 R
1833 2352 XY 3 3 R 1835 2353 XY 3 3 R 1836 2355 XY 3 3 R
1838 2356 XY 3 3 R 1838 2356 XY 3 3 R 1837 2359 XY 3 3 R
1835 2361 XY 3 3 R 1835 2361 XY 3 3 R 1834 2362 XY 3 3 R
1833 2363 XY 3 3 R 1832 2364 XY 3 3 R 1831 2366 XY 3 3 R
1830 2367 XY 3 3 R 1830 2367 XY 3 3 R 1829 2368 XY 3 3 R
1829 2370 XY 3 3 R 1828 2372 XY 3 3 R 1828 2372 XY 3 3 R
1830 2373 XY 3 3 R 1831 2374 XY 3 3 R 1832 2375 XY 3 3 R
1834 2375 XY 3 3 R 1834 2375 XY 3 3 R 1835 2376 XY 3 3 R
1837 2377 XY 3 3 R 1839 2378 XY 3 3 R 1841 2379 XY 3 3 R
1841 2379 XY 3 3 R 1841 2381 XY 3 3 R 1842 2383 XY 3 3 R
1842 2383 XY 3 3 R 1841 2384 XY 3 3 R 1840 2386 XY 3 3 R
1839 2387 XY 3 3 R 1838 2389 XY 3 3 R 1838 2389 XY 3 3 R
1837 2390 XY 3 3 R 1836 2392 XY 3 3 R 1835 2393 XY 3 3 R
1834 2395 XY 3 3 R 1834 2395 XY 3 3 R 1835 2396 XY 3 3 R
1836 2397 XY 3 3 R 1837 2399 XY 3 3 R 1837 2399 XY 3 3 R
1839 2399 XY 3 3 R 1841 2400 XY 3 3 R 1843 2400 XY 3 3 R
1845 2401 XY 3 3 R 1845 2401 XY 3 3 R 1847 2402 XY 3 3 R
1850 2404 XY 3 3 R 1850 2404 XY 3 3 R 1849 2406 XY 3 3 R
1849 2408 XY 3 3 R 1849 2409 XY 3 3 R 1849 2409 XY 3 3 R
1848 2411 XY 3 3 R 1847 2413 XY 3 3 R 1846 2415 XY 3 3 R
1845 2416 XY 3 3 R 1845 2416 XY 3 3 R 1845 2419 XY 3 3 R
1845 2421 XY 3 3 R 1845 2421 XY 3 3 R 1848 2422 XY 3 3 R
1850 2423 XY 3 3 R 1852 2423 XY 3 3 R 1852 2423 XY 3 3 R
1854 2423 XY 3 3 R 1856 2424 XY 3 3 R 1857 2424 XY 3 3 R
1859 2424 XY 3 3 R 1859 2424 XY 3 3 R 1860 2426 XY 3 3 R
1861 2428 XY 3 3 R 1861 2428 XY 3 3 R 1860 2431 XY 3 3 R
1859 2433 XY 3 3 R 1859 2436 XY 3 3 R 1859 2436 XY 3 3 R
1858 2438 XY 3 3 R 1858 2440 XY 3 3 R 1857 2442 XY 3 3 R
1857 2442 XY 3 3 R 1860 2443 XY 3 3 R 1862 2445 XY 3 3 R
1862 2445 XY 3 3 R 1864 2445 XY 3 3 R 1866 2444 XY 3 3 R
1868 2444 XY 3 3 R 1870 2444 XY 3 3 R 1870 2444 XY 3 3 R
1872 2445 XY 3 3 R 1873 2446 XY 3 3 R 1875 2446 XY 3 3 R
1875 2446 XY 3 3 R 1875 2448 XY 3 3 R 1875 2450 XY 3 3 R
1875 2452 XY 3 3 R 1875 2452 XY 3 3 R 1874 2454 XY 3 3 R
1874 2456 XY 3 3 R 1874 2458 XY 3 3 R 1873 2460 XY 3 3 R
1873 2460 XY 3 3 R 1874 2462 XY 3 3 R 1876 2464 XY 3 3 R
1876 2464 XY 3 3 R 1878 2464 XY 3 3 R 1879 2464 XY 3 3 R
1881 2464 XY 3 3 R 1883 2464 XY 3 3 R 1883 2464 XY 3 3 R
1885 2463 XY 3 3 R 1888 2463 XY 3 3 R 1890 2463 XY 3 3 R
1890 2463 XY 3 3 R 1891 2465 XY 3 3 R 1893 2467 XY 3 3 R
1893 2467 XY 3 3 R 1892 2469 XY 3 3 R 1892 2471 XY 3 3 R
1892 2473 XY 3 3 R 1892 2474 XY 3 3 R 1892 2474 XY 3 3 R
1892 2477 XY 3 3 R 1893 2479 XY 3 3 R 1893 2481 XY 3 3 R
1893 2481 XY 3 3 R 1895 2481 XY 3 3 R 1897 2481 XY 3 3 R
1899 2481 XY 3 3 R 1899 2481 XY 3 3 R 1900 2481 XY 3 3 R
1902 2480 XY 3 3 R 1904 2479 XY 3 3 R 1906 2479 XY 3 3 R
1906 2479 XY 3 3 R 1909 2479 XY 3 3 R 1911 2480 XY 3 3 R
1911 2480 XY 3 3 R 1912 2482 XY 3 3 R 1912 2484 XY 3 3 R
1912 2486 XY 3 3 R 1912 2486 XY 3 3 R 1913 2488 XY 3 3 R
1913 2490 XY 3 3 R 1913 2492 XY 3 3 R 1913 2493 XY 3 3 R
1913 2493 XY 3 3 R 1915 2495 XY 3 3 R 1917 2496 XY 3 3 R
1917 2496 XY 3 3 R 1919 2495 XY 3 3 R 1922 2494 XY 3 3 R
1924 2494 XY 3 3 R 1924 2494 XY 3 3 R 1926 2493 XY 3 3 R
1928 2492 XY 3 3 R 1930 2491 XY 3 3 R 1930 2491 XY 3 3 R
1931 2492 XY 3 3 R 1932 2494 XY 3 3 R 1934 2495 XY 3 3 R
1934 2495 XY 3 3 R 1934 2497 XY 3 3 R 1934 2499 XY 3 3 R
1935 2500 XY 3 3 R 1935 2502 XY 3 3 R 1935 2502 XY 3 3 R
1936 2504 XY 3 3 R 1937 2506 XY 3 3 R 1938 2507 XY 3 3 R
1938 2507 XY 3 3 R 1940 2507 XY 3 3 R 1942 2506 XY 3 3 R
1944 2506 XY 3 3 R 1944 2506 XY 3 3 R 1945 2505 XY 3 3 R
1947 2504 XY 3 3 R 1949 2503 XY 3 3 R 1950 2502 XY 3 3 R
1950 2502 XY 3 3 R 1953 2502 XY 3 3 R 1955 2502 XY 3 3 R
1955 2502 XY 3 3 R 1956 2504 XY 3 3 R 1957 2506 XY 3 3 R
1958 2508 XY 3 3 R 1958 2508 XY 3 3 R 1959 2510 XY 3 3 R
1960 2512 XY 3 3 R 1961 2514 XY 3 3 R 1961 2514 XY 3 3 R
1963 2515 XY 3 3 R 1966 2515 XY 3 3 R 1966 2515 XY 3 3 R
1967 2514 XY 3 3 R 1969 2513 XY 3 3 R 1970 2512 XY 3 3 R
1972 2510 XY 3 3 R 1972 2510 XY 3 3 R 1973 2510 XY 3 3 R
1974 2509 XY 3 3 R 1976 2508 XY 3 3 R 1977 2507 XY 3 3 R
1977 2507 XY 3 3 R 1979 2508 XY 3 3 R 1981 2510 XY 3 3 R
1981 2510 XY 3 3 R 1982 2512 XY 3 3 R 1983 2513 XY 3 3 R
1984 2515 XY 3 3 R 1985 2517 XY 3 3 R 1985 2517 XY 3 3 R
1986 2518 XY 3 3 R 1988 2519 XY 3 3 R 1989 2520 XY 3 3 R
1989 2520 XY 3 3 R 1990 2519 XY 3 3 R 1992 2519 XY 3 3 R
1993 2518 XY 3 3 R 1994 2517 XY 3 3 R 2302 Y 1807 X F26(Q)S 6 y F8
(1)S
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