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% body of BMS paper for LATTICE'92 proceedings, Nucl Phys B Proc Suppl
% Title: Multigrid meets neural nets
% Authors: M. Baeker, G. Mack, M. Speh
%----------------------------------------------------------------------
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%
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%-----------------------------------------------------------------------
%                           HEAD
%-----------------------------------------------------------------------
\title{Multigrid meets neural nets}
\author{M. B\"aker,
Y        G. Mack
Y        and M. Speh\\[3mm]
Y        II. Institut f\"ur Theoretische Physik,
Y        Universit\"at Hamburg, Luruper Chaussee 149, 2000 Hamburg 50
Y        }
%-----------------------------------------------------------------------
%                      Abstract
%-----------------------------------------------------------------------
\begin{abstract}
We present evidence that
multigrid (MG) works for wave equations in disordered systems, e.g. in
the presence of gauge fields, no matter how
strong the disorder. We introduce a ``neural computations''
point of view into large scale simulations: First, the system must
learn how to do the simulations efficiently, then do the simulation
(fast). The method can also
be used to provide smooth interpolation kernels which are needed in
multigrid Monte Carlo updates.
\end{abstract}
\maketitle
%-----------------------------------------------------------------------
%                      Section 1
%-----------------------------------------------------------------------
%
\section{INTRODUCTION}
%
Y   There is a stochastic multigrid method and a deterministic one.
The stochastic version is used to compute high dimensional integrals in
Euclidean quantum field theory or statistical mechanics by a Monte Carlo
method which uses updates at different length scales~\cite{1,2}. The
deterministic version~\cite{4} solves discretized partial
differential equations. One hopes to use both of them in simulations
of lattice QCD, for updating the gauge fields and for computing
fermion propagators in given gauge fields. In either case the aim is
to beat critical slowing down (CSD) in nearly critical systems.
Y
Our notation is as follows: $\L^0 $ denotes a given
``fundamental'' lattice $\L^0$ of spacing $a_0$.
Coarser (block) lattices of increasing spacings
$a_j=L_b^ja_0$ are denoted $\L^1,\L^2,..., \L^N$.
Typically, we chose $L_b=2$, and a single point as
the last layer $\L^N$. Interpolation operators
$\A^j $ are introduced to transfer functions
on coarser lattices into functions on finer lattices,
while restriction operators $C^j \equiv \A^{j \ast }$
transfer functions from finer to coarser lattices
(``variational coarsening'').
%-----------------------------------------------------------------------
%                      Section 2
%-----------------------------------------------------------------------
%
\section{IMPORTANCE OF SMOOTHNESS \label{SMOOTHNESS}}
%
A crucial problem is how to define and exhibit smooth functions
in the disordered context, i.e. when translation symmetry is strongly
violated. Other possible applications besides gauge theories are
low lying states of spin glasses,
the shape of a lightning,
waves on fractal lattices (with bond percolation), or
the localization of low lying electronic states in amorphous materials.
Y
In the case of deterministic MG,
one wants to solve a discretized elliptic differential equation on
$\L^0$:
\be D_0\xi^0 =f^0 \ .  \label{De}
\ee
It might have arisen from an eigenvalue equation
$D_0\xi^0 = \epsilon \xi^0 $ by inverse iteration.
If $D_0$ has a small
eigenvalue, then local relaxation algorithms suffer from CSD.
After some relaxation sweeps on $\L^0$ one gets an approximate
solution $\tilde{\xi }^0 $ whose error
Y  $ e^0 = \xi^0 - \tilde{\xi }^0 $
is not necessarily small but is \it smooth \rm (on length scale
$a_0$). The unknown error $e^0$
satisfies the equation
\be D_0 e^0 = r^0 . \label{Dee} \ee
%It involves the \it residual \rm
with  the residual $r^0 = f^0 -D_0\tilde{\xi }^0 $.
Given that $e^0$ is smooth, it can be obtained by smooth interpolation
of a suitable function $e^{1  } $ on $\Lambda^1$,
\be e^0 = \A^1 e^{1 }\ . \label {intp0}  \ee
That is, $e^0_z = \sum_{x \in \L^1} \A^1_{zx}e^{1  }_x $ with
$\A^1_{zx}$ which depends smoothly on $z$.
Now define a restriction operator $C^1$ such that
$C^1\A^1=1$.
Then~(\ref{intp0}) can be inverted,
Y $ e^{1  } = C^1 e^0 \ . $
Applying $C^1 $ to both sides of~(\ref{Dee}) yields an equation for
$e^{1  }$,
\be D_1 e^{1  } = r^1 \ , \label{cgrideq}\ee
with
$ r^{1  } =  C^1r^0 $
and the effective operator $ D_1 = C^1D_0\A^1 $.
Given $e^{1  }$, one obtains $e^0$ from~(\ref{intp0}), and
$\tilde{\xi }^0 + e^0$ is an
improved solution of~(\ref{De}).
Thus, \it the problem has been reduced to an equation on the lattice
$\L^1 $ which has fewer points. \rm
If necessary, one repeats the procedure, moving to $\L^2 $ etc. The
procedure stops, because an equation on a ``lattice'' $\L^N$ with only a
single point is easy to solve.
Y
The iterated interpolation
Y $ \A^{[0j]} \equiv \A^1 \A^2 \dots \A^j$
Y                           from $\L^j$ to $\L^0$ should yield functions
on $\L^0 $ which are \it
Y           smooth on length scale $a_j$\rm , i.e. which change
little over a distance $a_j$ (in the ordered case).
For reasons of practicality, one must require
$ \A^j_{zx}= 0$ unless $z$ is near $ x$.
%-----------------------------------------------------------------------
%                      Section 3
%-----------------------------------------------------------------------
%
\section{SMOOTHNESS AND DISORDER}
%
Y A successful MG scheme, whether
Y deterministic or stochastic, needs smooth interpolation kernels $\A $.
Y Thus we may ask: \it Which functions are smooth in
Y the disordered situation, for instance in an external gauge field? \rm
Y
Y A (gauge covariant) naive answer is
\ba
Y \sum_{\mu } (\nabla_{\mu }\xi , \nabla_{\mu }\xi )
Y = (\xi , -\Delta \xi ) \geq \epsilon_0 (\xi , \xi )
\ea
Y (with discretized covariant derivatives $\nabla_{\mu }$).
Y By definition,
Y the lowest eigenvalue $\epsilon_0$ of the negative
Y covariant Laplacian $-\Delta $ is not small for disordered gauge
Y fields. (It is positive and vanishes only for pure gauges.)
Y Therefore there are no smooth functions in this case.
Y
Y Nevertheless there is an answer to the question, assuming
Y a fundamental differential operator $D_0$ is specified by the problem
Y (in the stochastic case, the Hamiltonian often provides
Y $D_0$):
Y
Y  \it A function $\xi $ on $\Lambda^0$ is smooth on length
Y scale $a$ when \rm
Y $\| D_0\xi \|^2 \ll \|\xi \|^2$ in units $a=1$.
Y
Y We  found that  a deterministic multigrid which employs
Y interpolation kernels $\A^{[0j]}$ from $\L^j $ to the fundamental
lattice
Y $\L^0$ which are smooth in this sense, works for arbitrarily disordered
Y gauge fields.
Y When there are no smooth functions in this sense at length scale $a_0$,
Y then $D_0$ has no low eigenvalue, and there is no CSD
Y and no need for MG.
Y
Y The above answer appears natural, and the
``projective MG'' of~\cite{10,11} is in its spirit.
Y But to obtain kernels $\A^{[0j]}_{zx}$
Y which are smooth \it on length scale $a_j$,  \rm
Y one needs  approximate solutions of eigenvalue equations
Y \be D_0 \A^{[0j]}_{zx} = \epsilon_0(x) \A^{[0j]}_{zx} \label{EVA}
Y \ee  \rm
Y Since $\A^{[0j]} $ is required to
Y vanish for $z$ outside a neighbourhood of $x$, the  problem
Y involves Dirichlet boundary conditions.
Y For large $j$, $\A^{[0j]} $ will have a large support.
Y If there is no degeneracy
Y in the lowest eigenvalue, one can use inverse iteration combined
Y with standard relaxation algorithms for the resulting inhomogeneous
Y equation.
Y But this and other standard methods will
Y suffer from CSD again.
Y Moreover, in the standard multigrid setup, one uses basic interpolation
Y kernels $\A^j$ which interpolate from one grid $\L^{j}$ to the next
Y finer one. In this case
Y  \be \A^{[0j]} = \A^1 \A^2\dots \A^j \ , \label{FACTOR} \ee
Y and~(\ref{EVA}) becomes a very complicated set of nonlinear conditions.
Y Possible solutions are
Y \begin{description}
Y \item[{\rm (i)}] Replace~(\ref{EVA}) by minimality of a cost functional
Y        (cp. later). Use neural algorithms to find kernels $\A^j $
Y        which minimize it.  This is still under study.
Y \item[{\rm (ii)}] Give up factorization~(\ref{FACTOR}) and determine
Y        independent
Y        kernels $\A^{[0j]}$ as solutions of~(\ref{EVA}) by
Y        multigrid iteration. {\it This is done
Y        successively for $j=1,2,\dots$ One uses
Y        already determined kernels $\A^{[0k]}$ with $k<j$ for updating
Y        $\A^{[0j]}$.\/} We found that this works very well -
Y        cp. sect.~\ref{PERFORMANCE}.
Y \end{description}
Y Method (ii) will need of order $L^d \ln L$ storage space and
Y $L^d\ln^2 L$ computational work for a $d$-dimensional system
Y of linear extension $L$.
Y %Method (ii) is not quite as efficient as
Y %standard multigrid methods (MG) for ordered systems because of a large
Y %overhead for storing and computing the kernels.
%-----------------------------------------------------------------------
%                      Section 4
%-----------------------------------------------------------------------
%
\section{CRITERIA FOR OPTIMALITY\label{CRITERIA}}
%
Y Any iteration to solve~(\ref{De}) amounts to updating steps of the form
Y \be \tilde{\xi}^0 \mapsto \tilde{\xi}^{ 0\prime } = \rho\
Y \tilde{\xi}^0 + \sigma\ f^0 \ .
Y  \label{iterlin}
Y \ee
Y with the iteration matrix $\rho$ whose norm governs the convergence,
Y and $\sigma= (1-\rho) D_0^{-1}$.
Y If $\|\rho \|< 1$, the iteration converges with
Y a relaxation time $ \tau \leq -1/\ln \|\rho \|$.
Y \it Parameters \rm in the algorithm - such as operators
Y $\A^j_{zx}$, $C^j_{xz}$ and $D_j$ -
Y are \it optimal \rm if the cost functional
$ E = \|\rho\|^2 $ is at its minimum.
Y
Y As an example, consider a twogrid iteration in which a standard
Y relaxation sweep on $\L^0$ with iteration matrix $\rho_0$
Y is followed by exact solution of the
Y coarse grid equation~(\ref{cgrideq}). The second step leads to
Y an updating with some iteration matrix $\rho_1$, and
Y $\rho = \rho_1\rho_0$. Therefore one may estimate
Y $E\leq \|D_0\ \rho_0\|^2\ E_1 $ with
Y $E_1 = \|D_0^{-1}\ \rho_1\|^2 $
Y (fine grid relaxation smoothens the error
Y but does not converge fast - therefore $\|D_0\ \rho_0\|$ is
Y suppressed whereas $\|\rho_0\|$ is not much smaller than $1$)
Y and try to  optimize the parameters
Y above by minimizing $E_1$:
Y Using the trace norm, $\|\rho \|^2 = {\rm tr}\ \rho \rho^{\ast }$,
Y one finds
\ba
Y  E_1  =  {\rm Volume}^{-1}
Y          \sum_{z,w\in \L^0} |\Gamma_{zw}|^2
\ea
Y with $\Gamma  =  D_0^{-1} - \A^1\ D_1^{-1}\ C^1$.
Y Prescribing $C^1 $, and determining $D_1$ and $\A^1 $ by minimizing
Y $E_1$ yields what we call the ``ideal interpolation kernel'' $\A^1_{zx}$
Y for a given restriction map $C^1$. Since it has exponential tails
Y instead of vanishing for $z$ outside a neighbourhood of $x$, it is
Y impractical for production runs, though~\cite{12}.
%-----------------------------------------------------------------------
%                      Section 5
%-----------------------------------------------------------------------
%
\section{NEURAL MULTIGRID (NMG)}
%
Y ~ A feed-for\-ward ar\-ti\-fi\-cial neu\-ral net\-work
Y (ANN)~\cite{13} can perform the computations
Y to solve~(\ref{Dee}) by MG relaxation.
Y
Y The nodes (``neurons'') of the NMG
Y are identified with points of the MG as shown in Fig.~\ref{FIGUR1}.
Y The resulting NMG consists of two copies of the same MG,
Y except that the last layer $\L^N $ is not duplicated.
Y In the standard MG approach, the basic interpolation kernels
Y $\A^j $ interpolate from one layer $\L^j $ to the
Y preceding one, $\L^{j-1}$.
Y %
Y \begin{figure}[htb] % h = here, tb = top or bottom p = page
Y \epsfysize=170pt     % new y size
Y \epsfbox[85 265 498 598]{fig-1.ps}
Y \caption{A feed-forward NMG architecture.}
Y \label{FIGUR1}
Y \end{figure}
Y %
Y Each node is connected to some of the nodes in the preceding layer.
Y In the upper half, the connection strength
Y from $x\in \L^j $ to $z\in \L^{j-1}$ is $\A^j_{zx}$. In the lower half,
Y node $z \in \L^{j-1} $ is connected to $x\in \L^j $ with strength
Y $R^j_{xz}$. In addition there is a connection of strength
Y $\omega_j d_j^{-1}$
Y between the two nodes which represent the same
Y point $z$ in $\L^j$ ($j<N$).
Y
Y According to Hebb's hypothesis of synaptical learning,
Y a biological neural network learns by adjusting the
Y strength of its synaptical connections.
Y
Y The network receives as input an approximate solution
Y $\xi $ of~(2.1), from which the residual $r^0=f^0-D_0\xi $
Y is then determined.
Y It computes as output an improved
Y solution $O = \xi + \delta \xi $. The desired output (``target'') is
Y $\zeta = D_0^{-1}f^0$. $\delta \xi $ is a linear function of $r^0$.
Y Except on the bottom layer,
Y each node receives as input a weighted sum of the output of those
Y nodes below it in the diagram to which it is connected. The weights
Y are given by the connection strengths. Our neurons are linear because
Y our problem is linear. The output of each neuron
Y is a linear function of the input.
Y
Y The result of the computation is
Y \be \delta\xi = ( \omega_0\ d_0^{-1}  +
Y \sum_{k\geq 1} \A^{[0k]}\ \omega_k\  d_k^{-1} \ R^{[k0]})\ r^0 \ee
Y where $R^{[k0]}=R^k...R^2R^1$ and $\A^{[0k]}= \A^1\A^2...\A^k$.
Y The operators $C^j$ and $D_j (j>0)$,
Y and the damping parameters $\omega_j$ $(j>0)$ are not needed
Y separately since they only enter in the combination
Y $R^j = C^j(1-\omega_{j-1}D_{j-1}d_{j-1}^{-1})$.
Y The fundamental differential operator $D_0 $ and its
Y diagonal part $d_0$ are furnished as part of the problem.
Y The connection strengths (``synaptical strengths'') $\A^j_{zx}$,
Y $R^j_{xz}$ (and possibly $\omega_0$) need to be found by a learning
Y process in such a way that the actual output is as close as possible
Y to the desired output.
Y In supervised learning~\cite{13},
Y pairs  $(\xi^{\mu }, \zeta^{\mu })$ (``training patterns'')
Y are presented to an ANN.
Y Given input $\xi^{\mu }$,
Y the actual output $O^{\mu }$ is compared to the target $\zeta^{\mu }$,
Y and the connection strengths are adjusted in such a way that the
Y cost functional
Y $E = \sum_{\mu } \|O^{\mu } - \zeta^{\mu } \|^2 $
Y gets minimized. An iterative procedure to
Y achieve this minimization is called \it  learning rule. \rm
Y
Y Taking for the sequence $\xi^{\mu }$ a complete orthonormal system
Y of functions on $\L^0$, in the limit $f^0 \mapsto 0$,
Y the target is $\zeta^{\mu }=0$ for any input, and the output
Y $O^{\mu }= \rho\  \xi^{\mu }$ by~(\ref{iterlin}). The learning
Y rule for the resulting cost functional
\ba E= \sum_{\mu } \|\rho\ \xi^{\mu }\|^2= {\rm tr}\ \rho \rho_{\ast }
Y  \equiv \|\rho \|^2 \stackrel{!}{=} \mbox{min}\
\ea
Y is our previous optimality condition for multigrid relaxation
Y in sect.~\ref{CRITERIA}.
%-----------------------------------------------------------------------
%                      Section 6
%-----------------------------------------------------------------------
%
\section{LEARNING RULE PERFORMANCE\label{PERFORMANCE}}
%
Y The variant (ii) in sect.~\ref{SMOOTHNESS}
Y involves a slightly different NMG. Instead of the
Y connections between neighbouring layers of the multigrid,
Y we now have
Y connections from $\L^0$ to $\L^k$ with strength
Y $C^{[k0]}_{xz}$, and from $\L^j$ to $\L^0$ with strength
Y $\A^{[0j]}_{zx}$.
Y If we adopt variational coarsening,
Y all connection strengths are determined by
Y interpolation kernels $\A^{[0k]}$ which have to be learned.
Y The  damping factors $\omega_k$ were
Y set to $1$ and $d_k$ is the diagonal part of $D_k$ as before,
Y with
\be  D_k =
Y   \A^{[0k]\ast}D_0 \A^{[0k]}\ .
\ee
Y The learning rule (ii) requires a process of ``hard thinking''
Y by the NMG. Nodes which have learned their lesson
Y already - i.e. which have their
Y connection strengths fixed -
Y are used to instruct the rest of the neural net, adjusting the
Y strengths of the next layer of nodes in the NMG.
Y
Y A variant of this algorithm was tested in 2 dimensions, using
Y SU(2)-gauge fields which were
Y equilibrated with standard Wilson
Y action at various values of $\beta$, and
Y $D_0=-\Delta-\epsilon_0+\delta m^2 $.
Y $\epsilon_0$ is the lowest eigenvalue of the covariant
Y Laplacian $-\Delta $, and $\delta m^2 > 0$.
Y Conventional relaxation algorithms for solving~(\ref{De}) suffer
Y from CSD for such $D_0$, for any volume and
Y small $\delta m^2$.
Y
Y It turned out that it was not necessary to find accurate solutions
Y of the eigenvalue equation for the interpolation kernels $\A^{[0j]}$.
Y An approximation $\A^{[0j]}_{zx}$ to  $(-\Delta )^{-n} \delta_{zx}$ was
Y computed by multigrid iteration. It does not depend on $\delta m^2$.
Y Updating  $\xi $ at $x \in  \L^j$ changes $\xi $ by
\ba
Y \delta \xi_z=  \A^{[0j]}_{zx}d_{j,x}^{-1}r^j_x\ ,  \ \
Y r^j=\A^{[0j]\ast }r^0 .
\ea
Y The convergence rate (in units of MG iterations)
Y of the $\xi$-iteration is
Y shown in Fig.~\ref{FIGUR2} for $\beta =1.0$.
Y One MG iteration involved one
Y sweep (in checkerboard fashion) through each MG layer, starting with $j=0$.
%
Y \begin{figure}[htb]
Y \epsfxsize=215pt     % new x size
Y \epsfbox[68 94 558 408]{fig-2.ps}
Y \caption{Correlation time $\tau$ as function of the lowest eigenvalue
Y $\delta m^2$ in a representative gauge field configuration
Y equilibrated at $\beta = 1.0$. For the $64^2$ lattice, $\tau$
Y fluctuates very little with the gauge field.}
Y \label{FIGUR2}
Y \end{figure}
%-----------------------------------------------------------------------
%                      Acknowledgements
%-----------------------------------------------------------------------
%
%\subsubsection*{ACKNOWLEDGEMENTS}
Y
Y We thank the HLRZ J\" ulich for computer time and assistance.
Y
Y Support by Deutsche Forschungsgemeinschaft is gratefully
Y acknowledged.
%-----------------------------------------------------------------------
%                      References
%-----------------------------------------------------------------------
%
\begin{thebibliography}{99}
\bibitem{1}
Y      G. Mack, in: Nonperturbative quantum field theory,
Y      eds. G. 't Hooft et al. (Plenum, New York 1989).
\bibitem{2} J. Goodman and A.D. Sokal,
Y      Phys. Rev. D 40 (1989) 2035.
\bibitem{4} W. Hackbusch,
Y      Multi-Grid Methods and Applications
%      Springer Series in Computational Mathematics 4
Y      (Springer-Verlag, Berlin, 1985).
\bibitem{10} R.C. Brower, K. Moriarty,  C. Rebbi and E. Vicari,
Y      Nucl. Phys. B 20 (1991) 89.
\bibitem{11} A. Hulsebos, J. Smit and J.C. Vink,
Y      Nucl. Phys. B 368 (1992) 379.
\bibitem{12} T. Kalkreuter,
Y      Phys. Lett. B 276 (1992) 485.
\bibitem{13} J. Hertz, A. Krogh and R.G.\,Palmer,
Y      Introduction to the Theory of Neural Computation
Y      (Addison-Wesley, Redwood City CA, 1991).
\end{thebibliography}
%
\end{document}
XXX
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Y 1648 2375 d 1618 2403 r 1626 2403 d 1640 2403 r 1648 2403 d 1646 2375 r
Y 1654 2375 d 1668 2417 r 1668 2383 d 1670 2377 d 1674 2375 d 1678 2375 d
Y 1682 2377 d 1684 2381 d 1670 2417 r 1670 2383 d 1672 2377 d 1674 2375 d
Y 1662 2403 r 1678 2403 d 1698 2403 r 1698 2361 d 1700 2403 r 1700 2361 d
Y 1700 2397 r 1704 2401 d 1708 2403 d 1712 2403 d 1718 2401 d 1722 2397 d
Y 1724 2391 d 1724 2387 d 1722 2381 d 1718 2377 d 1712 2375 d 1708 2375 d
Y 1704 2377 d 1700 2381 d 1712 2403 r 1716 2401 d 1720 2397 d 1722 2391 d
Y 1722 2387 d 1720 2381 d 1716 2377 d 1712 2375 d 1692 2403 r 1700 2403 d
Y 1692 2361 r 1706 2361 d 1740 2403 r 1740 2381 d 1742 2377 d 1748 2375 d
Y 1752 2375 d 1758 2377 d 1762 2381 d 1742 2403 r 1742 2381 d 1744 2377 d
Y 1748 2375 d 1762 2403 r 1762 2375 d 1764 2403 r 1764 2375 d 1734 2403 r
Y 1742 2403 d 1756 2403 r 1764 2403 d 1762 2375 r 1770 2375 d 1784 2417 r
Y 1784 2383 d 1786 2377 d 1790 2375 d 1794 2375 d 1798 2377 d 1800 2381 d
Y 1786 2417 r 1786 2383 d 1788 2377 d 1790 2375 d 1778 2403 r 1794 2403 d
Y 1860 2417 r 1844 2375 d 1860 2417 r 1876 2375 d 1860 2413 r 1874 2375 d
Y 1846 2377 r 1874 2377 d 1844 2375 r 1876 2375 d 1902 2417 r 1898 2415 d
Y 1896 2413 d 1896 2411 d 1898 2409 d 1904 2407 d 1910 2407 d 1904 2407 r
Y 1896 2405 d 1892 2403 d 1890 2399 d 1890 2395 d 1894 2391 d 1900 2389 d
Y 1906 2389 d 1904 2407 r 1898 2405 d 1894 2403 d 1892 2399 d 1892 2395 d
Y 1896 2391 d 1900 2389 d 1892 2387 d 1888 2385 d 1886 2381 d 1886 2377 d
Y 1890 2373 d 1900 2369 d 1902 2367 d 1902 2363 d 1898 2361 d 1894 2361 d
Y 1900 2389 r 1894 2387 d 1890 2385 d 1888 2381 d 1888 2377 d 1892 2373 d
Y 1900 2369 d 1566 1844 r 1570 1844 d 1570 1846 d 1566 1844 d 1562 1838 d
Y 1560 1832 d 1560 1826 d 1562 1820 d 1564 1818 d 1568 1818 d 1572 1820 d
Y 1576 1826 d 1578 1832 d 1560 1826 r 1562 1822 d 1564 1820 d 1568 1820 d
Y 1572 1822 d 1576 1826 d 1576 1832 r 1576 1826 d 1578 1820 d 1580 1818 d
Y 1584 1818 d 1588 1820 d 1592 1826 d 1594 1832 d 1594 1838 d 1592 1844 d
Y 1590 1846 d 1590 1844 d 1592 1844 d 1576 1826 r 1578 1822 d 1580 1820 d
Y 1584 1820 d 1588 1822 d 1592 1826 d 1607 1826 r 1610 1828 d 1613 1831 d
Y 1613 1806 d 1612 1830 r 1612 1806 d 1607 1806 r 1618 1806 d 1654 1860 r
Y 1654 1818 d 1656 1860 r 1656 1818 d 1654 1840 r 1650 1844 d 1646 1846 d
Y 1642 1846 d 1636 1844 d 1632 1840 d 1630 1834 d 1630 1830 d 1632 1824 d
Y 1636 1820 d 1642 1818 d 1646 1818 d 1650 1820 d 1654 1824 d 1642 1846 r
Y 1638 1844 d 1634 1840 d 1632 1834 d 1632 1830 d 1634 1824 d 1638 1820 d
Y 1642 1818 d 1648 1860 r 1656 1860 d 1654 1818 r 1662 1818 d 1673 1826 r
Y 1676 1828 d 1679 1831 d 1679 1806 d 1678 1830 r 1678 1806 d 1673 1806 r
Y 1684 1806 d 1694 1868 r 1715 1868 d 1726 1878 r 1728 1879 d 1732 1882 d
Y 1732 1857 d 1731 1881 r 1731 1857 d 1726 1857 r 1737 1857 d   1 lw 1514 1836
r
Y 1473 1836 d 1443 1842 r 1434 1836 d 1443 1830 d 1452 1851 r 1437 1836 d
Y 1452 1821 d 1437 1836 r 1488 1836 d   3 lw 1590 2144 r 1594 2144 d 1594 2146
d
Y 1590 2144 d 1586 2138 d 1584 2132 d 1584 2126 d 1586 2120 d 1588 2118 d
Y 1592 2118 d 1596 2120 d 1600 2126 d 1602 2132 d 1584 2126 r 1586 2122 d
Y 1588 2120 d 1592 2120 d 1596 2122 d 1600 2126 d 1600 2132 r 1600 2126 d
Y 1602 2120 d 1604 2118 d 1608 2118 d 1612 2120 d 1616 2126 d 1618 2132 d
Y 1618 2138 d 1616 2144 d 1614 2146 d 1614 2144 d 1616 2144 d 1600 2126 r
Y 1602 2122 d 1604 2120 d 1608 2120 d 1612 2122 d 1616 2126 d 1635 2131 r
Y 1631 2130 d 1629 2126 d 1628 2120 d 1628 2117 d 1629 2111 d 1631 2107 d
Y 1635 2106 d 1637 2106 d 1641 2107 d 1643 2111 d 1644 2117 d 1644 2120 d
Y 1643 2126 d 1641 2130 d 1637 2131 d 1635 2131 d 1632 2130 d 1631 2129 d
Y 1630 2126 d 1629 2120 d 1629 2117 d 1630 2111 d 1631 2108 d 1632 2107 d
Y 1635 2106 d 1637 2106 r 1640 2107 d 1641 2108 d 1642 2111 d 1643 2117 d
Y 1643 2120 d 1642 2126 d 1641 2129 d 1640 2130 d 1637 2131 d 1678 2160 r
Y 1678 2118 d 1680 2160 r 1680 2118 d 1678 2140 r 1674 2144 d 1670 2146 d
Y 1666 2146 d 1660 2144 d 1656 2140 d 1654 2134 d 1654 2130 d 1656 2124 d
Y 1660 2120 d 1666 2118 d 1670 2118 d 1674 2120 d 1678 2124 d 1666 2146 r
Y 1662 2144 d 1658 2140 d 1656 2134 d 1656 2130 d 1658 2124 d 1662 2120 d
Y 1666 2118 d 1672 2160 r 1680 2160 d 1678 2118 r 1686 2118 d 1701 2131 r
Y 1697 2130 d 1695 2126 d 1694 2120 d 1694 2117 d 1695 2111 d 1697 2107 d
Y 1701 2106 d 1703 2106 d 1707 2107 d 1709 2111 d 1710 2117 d 1710 2120 d
Y 1709 2126 d 1707 2130 d 1703 2131 d 1701 2131 d 1698 2130 d 1697 2129 d
Y 1696 2126 d 1695 2120 d 1695 2117 d 1696 2111 d 1697 2108 d 1698 2107 d
Y 1701 2106 d 1703 2106 r 1706 2107 d 1707 2108 d 1708 2111 d 1709 2117 d
Y 1709 2120 d 1708 2126 d 1707 2129 d 1706 2130 d 1703 2131 d 1718 2168 r
Y 1739 2168 d 1750 2178 r 1752 2179 d 1756 2182 d 1756 2157 d 1755 2181 r
Y 1755 2157 d 1750 2157 r 1761 2157 d   1 lw 1595 2179 r 1595 2264 d 1432 2264
d
Y 1408 2270 r 1399 2264 d 1408 2258 d 1417 2279 r 1402 2264 d 1417 2249 d
Y 1402 2264 r 1453 2264 d   3 lw 1965 2419 r 1950 2373 d 1965 2419 r 1980 2373
d
Y 1965 2413 r 1978 2373 d 1943 2373 r 1956 2373 d 1972 2373 r 1987 2373 d
Y 1999 2444 r 1995 2443 d 1992 2439 d 1991 2432 d 1991 2428 d 1992 2422 d
Y 1995 2418 d 1999 2416 d 2002 2416 d 2005 2418 d 2008 2422 d 2009 2428 d
Y 2009 2432 d 2008 2439 d 2005 2443 d 2002 2444 d 1999 2444 d 1996 2443 d
Y 1995 2441 d 1994 2439 d 1992 2432 d 1992 2428 d 1994 2422 d 1995 2419 d
Y 1996 2418 d 1999 2416 d 2002 2416 r 2004 2418 d 2005 2419 d 2007 2422 d
Y 2008 2428 d 2008 2432 d 2007 2439 d 2005 2441 d 2004 2443 d 2002 2444 d
Y 1965 2205 r 1950 2159 d 1965 2205 r 1980 2159 d 1965 2199 r 1978 2159 d
Y 1943 2159 r 1956 2159 d 1972 2159 r 1987 2159 d 1995 2225 r 1998 2226 d
Y 2002 2230 d 2002 2202 d 2000 2229 r 2000 2202 d 1995 2202 r 2007 2202 d
Y 1965 1990 r 1950 1944 d 1965 1990 r 1980 1944 d 1965 1984 r 1978 1944 d
Y 1943 1944 r 1956 1944 d 1972 1944 r 1987 1944 d 1992 2010 r 1994 2008 d
Y 1992 2007 d 1991 2008 d 1991 2010 d 1992 2012 d 1994 2014 d 1998 2015 d
Y 2003 2015 d 2007 2014 d 2008 2012 d 2009 2010 d 2009 2007 d 2008 2004 d
Y 2004 2002 d 1998 1999 d 1995 1998 d 1992 1995 d 1991 1991 d 1991 1987 d
Y 2003 2015 r 2005 2014 d 2007 2012 d 2008 2010 d 2008 2007 d 2007 2004 d
Y 2003 2002 d 1998 1999 d 1991 1990 r 1992 1991 d 1995 1991 d 2002 1989 d
Y 2005 1989 d 2008 1990 d 2009 1991 d 1995 1991 r 2002 1987 d 2007 1987 d
Y 2008 1989 d 2009 1991 d 2009 1994 d 1965 1776 r 1950 1730 d 1965 1776 r
Y 1980 1730 d 1965 1770 r 1978 1730 d 1943 1730 r 1956 1730 d 1972 1730 r
Y 1987 1730 d 1992 1797 r 1994 1796 d 1992 1794 d 1991 1796 d 1991 1797 d
Y 1994 1800 d 1998 1801 d 2003 1801 d 2007 1800 d 2008 1797 d 2008 1793 d
Y 2007 1790 d 2003 1789 d 1999 1789 d 2003 1801 r 2005 1800 d 2007 1797 d
Y 2007 1793 d 2005 1790 d 2003 1789 d 2005 1788 d 2008 1785 d 2009 1783 d
Y 2009 1779 d 2008 1776 d 2007 1775 d 2003 1773 d 1998 1773 d 1994 1775 d
Y 1992 1776 d 1991 1779 d 1991 1780 d 1992 1781 d 1994 1780 d 1992 1779 d
Y 2007 1787 r 2008 1783 d 2008 1779 d 2007 1776 d 2005 1775 d 2003 1773 d
Y 1965 1562 r 1950 1516 d 1965 1562 r 1980 1516 d 1965 1556 r 1978 1516 d
Y 1943 1516 r 1956 1516 d 1972 1516 r 1987 1516 d 1992 1582 r 1994 1580 d
Y 1992 1579 d 1991 1580 d 1991 1582 d 1992 1584 d 1994 1586 d 1998 1587 d
Y 2003 1587 d 2007 1586 d 2008 1584 d 2009 1582 d 2009 1579 d 2008 1576 d
Y 2004 1574 d 1998 1571 d 1995 1570 d 1992 1567 d 1991 1563 d 1991 1559 d
Y 2003 1587 r 2005 1586 d 2007 1584 d 2008 1582 d 2008 1579 d 2007 1576 d
Y 2003 1574 d 1998 1571 d 1991 1562 r 1992 1563 d 1995 1563 d 2002 1561 d
Y 2005 1561 d 2008 1562 d 2009 1563 d 1995 1563 r 2002 1559 d 2007 1559 d
Y 2008 1561 d 2009 1563 d 2009 1566 d 1965 1347 r 1950 1301 d 1965 1347 r
Y 1980 1301 d 1965 1341 r 1978 1301 d 1943 1301 r 1956 1301 d 1972 1301 r
Y 1987 1301 d 1995 1367 r 1998 1368 d 2002 1372 d 2002 1344 d 2000 1371 r
Y 2000 1344 d 1995 1344 r 2007 1344 d 1965 1133 r 1950 1087 d 1965 1133 r
Y 1980 1087 d 1965 1127 r 1978 1087 d 1943 1087 r 1956 1087 d 1972 1087 r
Y 1987 1087 d 1999 1158 r 1995 1157 d 1992 1153 d 1991 1146 d 1991 1142 d
Y 1992 1136 d 1995 1132 d 1999 1130 d 2002 1130 d 2005 1132 d 2008 1136 d
Y 2009 1142 d 2009 1146 d 2008 1153 d 2005 1157 d 2002 1158 d 1999 1158 d
Y 1996 1157 d 1995 1155 d 1994 1153 d 1992 1146 d 1992 1142 d 1994 1136 d
Y 1995 1133 d 1996 1132 d 1999 1130 d 2002 1130 r 2004 1132 d 2005 1133 d
Y 2007 1136 d 2008 1142 d 2008 1146 d 2007 1153 d 2005 1155 d 2004 1157 d
Y 2002 1158 d
e
%%Trailer
EndPSPlot
XXX
chmod 0440 fig-1.ps ||
echo 'restore of fig-1.ps failed'
Wc_c="`wc -c < 'fig-1.ps'`"
test 46782 -eq "$Wc_c" ||
        echo 'fig-1.ps: original size 46782, current size' "$Wc_c"
fi
# ============= fig-2.ps ==============
if test -f 'fig-2.ps' -a X"$1" != X"-c"; then
        echo 'x - skipping fig-2.ps (File already exists)'
else
echo 'x - extracting fig-2.ps (Text)'
sed 's/^Y//' << 'XXX' > 'fig-2.ps' &&
%!
Y /sp {showpage} def /gr {grestore} def /gs {gsave} def /n {newpath} def
/s {stroke} def /m {moveto} def /l {lineto} def /tl {translate} def
/sd {setdash} def /sw {setlinewidth} def /cp {closepath} def /f {fill} def
/e {eofill} def /g {setgray} def /o {show} def /ff {findfont} def
/ro {rotate} def /sf {setfont} def /cf {scalefont} def /a {arc} def
/mf {makefont} def /sc {scale} def /k {rmoveto} def /r {rlineto} def gs
0.240000 0.240000 sc 82 82 tl 0 ro 0.000 g []0 sd 1 sw n 2052 482 m -3 2 r
-4 0 r -5 -2 r -3 -5 r -2 -5 r 0 -5 r 2 -4 r 2 -1 r 3 -2 r 3 0 r 6 2 r 3 5 r
2 5 r 0 5 r -2 3 r -7 9 r -2 3 r 0 3 r 2 2 r 4 0 r 3 -2 r 3 -3 r s n 2045 484 m
-3 -2 r -3 -5 r -2 -5 r 0 -7 r 2 -3 r s n 2045 460 m 4 2 r 3 5 r 2 5 r 0 6 r
-2 4 r -3 5 r -2 3 r 0 4 r 2 1 r 3 0 r 5 -3 r s n 2071 484 m 0 -24 r s n
2072 484 m 0 -24 r s n 2072 478 m 4 4 r 5 2 r 3 0 r 5 -2 r 2 -4 r 0 -18 r s n
2084 484 m 4 -2 r 1 -4 r 0 -18 r s n 2091 478 m 3 4 r 5 2 r 4 0 r 5 -2 r 2 -4 r
0 -18 r s n 2103 484 m 3 -2 r 2 -4 r 0 -18 r s n 2066 484 m 6 0 r s n 2066 460
m
Y 11 0 r s n 2084 460 m 12 0 r s n 2103 460 m 12 0 r s n 2123 497 m 0 -2 r -2 0
r
Y 0 2 r 2 2 r 3 1 r 5 0 r 4 -1 r 2 -4 r -2 -3 r -4 -2 r -5 -1 r -3 -2 r -2 -3 r
0 -6 r s n 2131 500 m 2 -1 r 2 -4 r -2 -3 r -2 -2 r s n 2121 480 m 2 2 r 2 0 r
5 -2 r 5 0 r 2 2 r s n 2125 482 m 5 -4 r 5 0 r 2 4 r 0 2 r s n 490 1521 m
-5 -22 r s n 490 1521 m -3 -22 r s n 475 1517 m 3 4 r 5 1 r 19 0 r s n
475 1517 m 3 2 r 5 2 r 19 0 r s n 537 793 m 31 0 r s n 537 783 m 31 0 r s n
647 808 m -5 -2 r -2 -3 r 0 -5 r 2 -3 r 5 -2 r 7 0 r 5 2 r 1 3 r 0 5 r -1 3 r
-5 2 r -7 0 r cp s n 647 808 m -3 -2 r -2 -3 r 0 -5 r 2 -3 r 3 -2 r s n
654 793 m 3 2 r 2 3 r 0 5 r -2 3 r -3 2 r s n 647 793 m -5 -2 r -2 -1 r -2 -4 r
0 -6 r 2 -4 r 2 -2 r 5 -1 r 7 0 r 5 1 r 1 2 r 2 4 r 0 6 r -2 4 r -1 1 r -5 2 r
s
Y n 647 793 m -3 -2 r -2 -1 r -2 -4 r 0 -6 r 2 -4 r 2 -2 r 3 -1 r s n 654 773 m
3 1 r 2 2 r 1 4 r 0 6 r -1 4 r -2 1 r -3 2 r s n 671 810 m 0 -2 r -1 0 r 0 2 r
1 2 r 4 1 r 5 0 r 3 -1 r 2 -4 r -2 -3 r -3 -2 r -5 -2 r -4 -1 r -1 -4 r 0 -5 r
s
Y n 680 813 m 1 -1 r 2 -4 r -2 -3 r -1 -2 r s n 670 793 m 1 2 r 2 0 r 5 -2 r
5 0 r 2 2 r s n 673 795 m 5 -4 r 5 0 r 2 4 r 0 1 r s n 692 788 m 21 0 r s n
727 808 m 0 -35 r s n 729 808 m 0 -35 r s n 722 808 m 7 0 r s n 722 773 m 12 0
r
Y s n 746 793 m 0 -2 r -1 0 r 0 2 r 1 2 r 4 1 r 7 0 r 3 -1 r 2 -2 r 1 -3 r
0 -12 r 2 -4 r 2 -1 r s n 762 793 m 0 -15 r 1 -4 r 4 -1 r 1 0 r s n 762 790 m
-2 -2 r -10 -2 r -5 -1 r -2 -4 r 0 -3 r 2 -4 r 5 -1 r 5 0 r 3 1 r 4 4 r s n
750 786 m -4 -1 r -1 -4 r 0 -3 r 1 -4 r 4 -1 r s n 779 808 m 0 -28 r 2 -6 r
3 -1 r 4 0 r 3 1 r 2 4 r s n 781 808 m 0 -28 r 2 -6 r 1 -1 r s n 774 796 m
14 0 r s n 805 808 m 0 -28 r 1 -6 r 4 -1 r 3 0 r 3 1 r 2 4 r s n 806 808 m
0 -28 r 2 -6 r 2 -1 r s n 800 796 m 13 0 r s n 830 808 m -2 -2 r 2 -1 r 2 1 r
-2 2 r cp s n 830 796 m 0 -23 r s n 832 796 m 0 -23 r s n 825 796 m 7 0 r s n
825 773 m 12 0 r s n 864 791 m -2 -1 r 2 -2 r 1 2 r 0 1 r -3 4 r -3 1 r -6 0 r
-5 -1 r -3 -4 r -2 -5 r 0 -3 r 2 -5 r 3 -4 r 5 -1 r 4 0 r 5 1 r 3 4 r s n
853 796 m -3 -1 r -3 -4 r -2 -5 r 0 -3 r 2 -5 r 3 -4 r 3 -1 r s n 877 786 m
20 0 r 0 4 r -1 3 r -2 2 r -3 1 r -6 0 r -5 -1 r -3 -4 r -2 -5 r 0 -3 r 2 -5 r
3 -4 r 5 -1 r 4 0 r 5 1 r 3 4 r s n 896 786 m 0 5 r -2 4 r s n 885 796 m -3 -1
r
Y -3 -4 r -2 -5 r 0 -3 r 2 -5 r 3 -4 r 3 -1 r s n 537 740 m 31 0 r s n 537 730
m
31 0 r s n 613 748 m 4 2 r 5 5 r 0 -35 r s n 620 753 m 0 -33 r s n 613 720 m
15 0 r s n 659 750 m -2 -2 r 2 -1 r 1 1 r 0 2 r -1 3 r -4 2 r -5 0 r -5 -2 r
-3 -3 r -2 -3 r -2 -7 r 0 -10 r 2 -5 r 4 -4 r 5 -1 r 3 0 r 5 1 r 3 4 r 2 5 r
0 1 r -2 6 r -3 3 r -5 2 r -2 0 r -5 -2 r -3 -3 r -2 -6 r s n 650 755 m -3 -2 r
-3 -3 r -2 -3 r -2 -7 r 0 -10 r 2 -5 r 3 -4 r 4 -1 r s n 652 720 m 3 1 r 4 4 r
1 5 r 0 1 r -1 6 r -4 3 r -3 2 r s n 671 757 m 0 -2 r -1 0 r 0 2 r 1 1 r 4 2 r
5 0 r 3 -2 r 2 -3 r -2 -3 r -3 -2 r -5 -2 r -4 -1 r -1 -4 r 0 -5 r s n 680 760
m
Y 1 -2 r 2 -3 r -2 -3 r -1 -2 r s n 670 740 m 1 2 r 2 0 r 5 -2 r 5 0 r 2 2 r s
n
673 742 m 5 -4 r 5 0 r 2 4 r 0 1 r s n 692 735 m 21 0 r s n 727 755 m 0 -35 r s
n 729 755 m 0 -35 r s n 722 755 m 7 0 r s n 722 720 m 12 0 r s n 746 740 m
0 -2 r -1 0 r 0 2 r 1 2 r 4 1 r 7 0 r 3 -1 r 2 -2 r 1 -3 r 0 -12 r 2 -4 r 2 -1
r
Y s n 762 740 m 0 -15 r 1 -4 r 4 -1 r 1 0 r s n 762 737 m -2 -2 r -10 -2 r
-5 -2 r -2 -3 r 0 -3 r 2 -4 r 5 -1 r 5 0 r 3 1 r 4 4 r s n 750 733 m -4 -2 r
-1 -3 r 0 -3 r 1 -4 r 4 -1 r s n 779 755 m 0 -29 r 2 -5 r 3 -1 r 4 0 r 3 1 r
2 4 r s n 781 755 m 0 -29 r 2 -5 r 1 -1 r s n 774 743 m 14 0 r s n 805 755 m
0 -29 r 1 -5 r 4 -1 r 3 0 r 3 1 r 2 4 r s n 806 755 m 0 -29 r 2 -5 r 2 -1 r s n
800 743 m 13 0 r s n 830 755 m -2 -2 r 2 -1 r 2 1 r -2 2 r cp s n 830 743 m
0 -23 r s n 832 743 m 0 -23 r s n 825 743 m 7 0 r s n 825 720 m 12 0 r s n
864 738 m -2 -1 r 2 -2 r 1 2 r 0 1 r -3 4 r -3 1 r -6 0 r -5 -1 r -3 -4 r
-2 -5 r 0 -3 r 2 -5 r 3 -4 r 5 -1 r 4 0 r 5 1 r 3 4 r s n 853 743 m -3 -1 r
-3 -4 r -2 -5 r 0 -3 r 2 -5 r 3 -4 r 3 -1 r s n 877 733 m 20 0 r 0 4 r -1 3 r
-2 2 r -3 1 r -6 0 r -5 -1 r -3 -4 r -2 -5 r 0 -3 r 2 -5 r 3 -4 r 5 -1 r 4 0 r
5 1 r 3 4 r s n 896 733 m 0 5 r -2 4 r s n 885 743 m -3 -1 r -3 -4 r -2 -5 r
0 -3 r 2 -5 r 3 -4 r 3 -1 r s n 537 687 m 31 0 r s n 537 677 m 31 0 r s n
610 695 m 2 -1 r -2 -2 r -2 2 r 0 1 r 2 4 r 2 1 r 5 2 r 6 0 r 5 -2 r 2 -3 r
0 -5 r -2 -4 r -5 -1 r -5 0 r s n 623 702 m 4 -2 r 1 -3 r 0 -5 r -1 -4 r -4 -1
r
Y s n 623 687 m 4 -2 r 3 -3 r 2 -4 r 0 -5 r -2 -3 r -2 -2 r -5 -1 r -6 0 r -5 1
r
Y -2 2 r -2 3 r 0 2 r 2 2 r 2 -2 r -2 -2 r s n 628 683 m 2 -5 r 0 -5 r -2 -3 r
-1 -2 r -4 -1 r s n 640 695 m 2 -1 r -2 -2 r -2 2 r 0 1 r 2 4 r 2 1 r 5 2 r
7 0 r 5 -2 r 1 -1 r 2 -4 r 0 -3 r -2 -4 r -5 -3 r -8 -3 r -3 -2 r -4 -3 r
-2 -5 r 0 -5 r s n 654 702 m 3 -2 r 2 -1 r 1 -4 r 0 -3 r -1 -4 r -5 -3 r -7 -3
r
Y s n 638 670 m 2 2 r 4 0 r 8 -4 r 5 0 r 3 2 r 2 2 r s n 644 672 m 8 -5 r 7 0 r
1 1 r 2 4 r 0 3 r s n 671 704 m 0 -2 r -1 0 r 0 2 r 1 1 r 4 2 r 5 0 r 3 -2 r
2 -3 r -2 -3 r -3 -2 r -5 -2 r -4 -1 r -1 -4 r 0 -5 r s n 680 707 m 1 -2 r
2 -3 r -2 -3 r -1 -2 r s n 670 687 m 1 1 r 2 0 r 5 -1 r 5 0 r 2 1 r s n
673 688 m 5 -3 r 5 0 r 2 3 r 0 2 r s n 692 682 m 21 0 r s n 727 702 m 0 -35 r s
n 729 702 m 0 -35 r s n 722 702 m 7 0 r s n 722 667 m 12 0 r s n 746 687 m
0 -2 r -1 0 r 0 2 r 1 1 r 4 2 r 7 0 r 3 -2 r 2 -1 r 1 -4 r 0 -11 r 2 -4 r 2 -1
r
Y s n 762 687 m 0 -15 r 1 -4 r 4 -1 r 1 0 r s n 762 683 m -2 -1 r -10 -2 r
-5 -2 r -2 -3 r 0 -3 r 2 -4 r 5 -1 r 5 0 r 3 1 r 4 4 r s n 750 680 m -4 -2 r
-1 -3 r 0 -3 r 1 -4 r 4 -1 r s n 779 702 m 0 -29 r 2 -5 r 3 -1 r 4 0 r 3 1 r
2 4 r s n 781 702 m 0 -29 r 2 -5 r 1 -1 r s n 774 690 m 14 0 r s n 805 702 m
0 -29 r 1 -5 r 4 -1 r 3 0 r 3 1 r 2 4 r s n 806 702 m 0 -29 r 2 -5 r 2 -1 r s n
800 690 m 13 0 r s n 830 702 m -2 -2 r 2 -1 r 2 1 r -2 2 r cp s n 830 690 m
0 -23 r s n 832 690 m 0 -23 r s n 825 690 m 7 0 r s n 825 667 m 12 0 r s n
864 685 m -2 -2 r 2 -1 r 1 1 r 0 2 r -3 3 r -3 2 r -6 0 r -5 -2 r -3 -3 r
-2 -5 r 0 -3 r 2 -5 r 3 -4 r 5 -1 r 4 0 r 5 1 r 3 4 r s n 853 690 m -3 -2 r
-3 -3 r -2 -5 r 0 -3 r 2 -5 r 3 -4 r 3 -1 r s n 877 680 m 20 0 r 0 3 r -1 4 r
-2 1 r -3 2 r -6 0 r -5 -2 r -3 -3 r -2 -5 r 0 -3 r 2 -5 r 3 -4 r 5 -1 r 4 0 r
5 1 r 3 4 r s n 896 680 m 0 5 r -2 3 r s n 885 690 m -3 -2 r -3 -3 r -2 -5 r
0 -3 r 2 -5 r 3 -4 r 3 -1 r s n 537 634 m 31 0 r s n 537 624 m 31 0 r s n
628 644 m -1 -2 r 1 -2 r 2 2 r 0 2 r -2 3 r -3 2 r -5 0 r -5 -2 r -3 -3 r
-2 -4 r -2 -6 r 0 -10 r 2 -6 r 3 -3 r 5 -2 r 4 0 r 5 2 r 3 3 r 2 6 r 0 1 r
-2 5 r -3 4 r -5 1 r -2 0 r -5 -1 r -3 -4 r -2 -5 r s n 620 649 m -3 -2 r
-4 -3 r -1 -4 r -2 -6 r 0 -10 r 2 -6 r 3 -3 r 3 -2 r s n 622 613 m 3 2 r 3 3 r
2 6 r 0 1 r -2 5 r -3 4 r -3 1 r s n 654 645 m 0 -32 r s n 655 649 m 0 -36 r s
n
Y 655 649 m -18 -25 r 27 0 r s n 649 613 m 11 0 r s n 671 650 m 0 -1 r -1 0 r
0 1 r 1 2 r 4 2 r 5 0 r 3 -2 r 2 -3 r -2 -4 r -3 -1 r -5 -2 r -4 -2 r -1 -3 r
0 -5 r s n 680 654 m 1 -2 r 2 -3 r -2 -4 r -1 -1 r s n 670 634 m 1 1 r 2 0 r
5 -1 r 5 0 r 2 1 r s n 673 635 m 5 -3 r 5 0 r 2 3 r 0 2 r s n 692 629 m 21 0 r
s
Y n 727 649 m 0 -36 r s n 729 649 m 0 -36 r s n 722 649 m 7 0 r s n 722 613 m
12 0 r s n 746 634 m 0 -2 r -1 0 r 0 2 r 1 1 r 4 2 r 7 0 r 3 -2 r 2 -1 r 1 -4 r
0 -12 r 2 -3 r 2 -2 r s n 762 634 m 0 -16 r 1 -3 r 4 -2 r 1 0 r s n 762 630 m
-2 -1 r -10 -2 r -5 -2 r -2 -3 r 0 -4 r 2 -3 r 5 -2 r 5 0 r 3 2 r 4 3 r s n
750 627 m -4 -2 r -1 -3 r 0 -4 r 1 -3 r 4 -2 r s n 779 649 m 0 -29 r 2 -5 r
3 -2 r 4 0 r 3 2 r 2 3 r s n 781 649 m 0 -29 r 2 -5 r 1 -2 r s n 774 637 m
14 0 r s n 805 649 m 0 -29 r 1 -5 r 4 -2 r 3 0 r 3 2 r 2 3 r s n 806 649 m
0 -29 r 2 -5 r 2 -2 r s n 800 637 m 13 0 r s n 830 649 m -2 -2 r 2 -2 r 2 2 r
-2 2 r cp s n 830 637 m 0 -24 r s n 832 637 m 0 -24 r s n 825 637 m 7 0 r s n
825 613 m 12 0 r s n 864 632 m -2 -2 r 2 -1 r 1 1 r 0 2 r -3 3 r -3 2 r -6 0 r
-5 -2 r -3 -3 r -2 -5 r 0 -3 r 2 -6 r 3 -3 r 5 -2 r 4 0 r 5 2 r 3 3 r s n
853 637 m -3 -2 r -3 -3 r -2 -5 r 0 -3 r 2 -6 r 3 -3 r 3 -2 r s n 877 627 m
20 0 r 0 3 r -1 4 r -2 1 r -3 2 r -6 0 r -5 -2 r -3 -3 r -2 -5 r 0 -3 r 2 -6 r
3 -3 r 5 -2 r 4 0 r 5 2 r 3 3 r s n 896 627 m 0 5 r -2 3 r s n 885 637 m -3 -2
r
Y -3 -3 r -2 -5 r 0 -3 r 2 -6 r 3 -3 r 3 -2 r s n 2168 729 m 0 13 r 9 9 r 6 0 r
0 6 r 0 -43 r 0 6 r -6 0 r cp e n 2168 729 m 0 13 r 9 9 r 6 0 r 0 6 r 0 -43 r
0 6 r -6 0 r -9 9 r cp s n 1873 987 m 0 13 r 8 9 r 13 0 r 9 -9 r 0 -13 r -9 -9
r
Y -13 0 r cp e n 1873 987 m 0 13 r 8 9 r 13 0 r 9 -9 r 0 -13 r -9 -9 r -13 0 r
-8 9 r cp s n 1578 1304 m 0 12 r 8 9 r 13 0 r 9 -9 r 0 -12 r -9 -9 r -13 0 r cp
e n 1578 1304 m 0 12 r 8 9 r 13 0 r 9 -9 r 0 -12 r -9 -9 r -13 0 r -8 9 r cp s
n
Y 1282 1191 m 0 13 r 9 9 r 13 0 r 9 -9 r 0 -13 r -9 -8 r -13 0 r cp e n
1282 1191 m 0 13 r 9 9 r 13 0 r 9 -9 r 0 -13 r -9 -8 r -13 0 r -9 8 r cp s n
987 1180 m 0 12 r 9 9 r 13 0 r 9 -9 r 0 -12 r -9 -9 r -13 0 r cp e n 987 1180 m
0 12 r 9 9 r 13 0 r 9 -9 r 0 -12 r -9 -9 r -13 0 r -9 9 r cp s n 692 1174 m
0 12 r 9 9 r 13 0 r 9 -9 r 0 -12 r -9 -9 r -13 0 r cp e n 692 1174 m 0 12 r
9 9 r 13 0 r 9 -9 r 0 -12 r -9 -9 r -13 0 r -9 9 r cp s n 413 1158 m 0 44 r
0 -7 r 6 0 r 9 -9 r 0 -12 r -9 -9 r -6 0 r cp e n 413 1158 m 0 44 r 0 -7 r 6 0
r
Y 9 -9 r 0 -12 r -9 -9 r -6 0 r 0 -7 r cp s n 2183 736 m -295 258 r -295 316 r
-295 -112 r -295 -12 r -295 -6 r -295 0 r s n 2171 698 m 0 23 r 12 0 r 0 -23 r
cp f n 2171 698 m 0 23 r 12 0 r 0 -23 r -12 0 r cp s n 1876 967 m 0 23 r 24 0 r
0 -23 r cp f n 1876 967 m 0 23 r 24 0 r 0 -23 r -24 0 r cp s n 1581 1345 m
0 24 r 23 0 r 0 -24 r cp f n 1581 1345 m 0 24 r 23 0 r 0 -24 r -23 0 r cp s n
1286 1369 m 0 23 r 23 0 r 0 -23 r cp f n 1286 1369 m 0 23 r 23 0 r 0 -23 r
-23 0 r cp s n 991 1357 m 0 24 r 23 0 r 0 -24 r cp f n 991 1357 m 0 24 r 23 0 r
0 -24 r -23 0 r cp s n 696 1351 m 0 24 r 23 0 r 0 -24 r cp f n 696 1351 m 0 24
r
Y 23 0 r 0 -24 r -23 0 r cp s n 413 1345 m 0 24 r 11 0 r 0 -24 r cp f n
413 1345 m 0 24 r 11 0 r 0 -24 r -11 0 r cp s n 2183 710 m -295 268 r -295 379
r
Y -295 24 r -295 -12 r -295 -6 r -295 -6 r s n 2168 738 m 0 13 r 9 9 r 6 0 r
0 6 r 0 -43 r 0 6 r -6 0 r -9 9 r cp s n 1873 918 m 0 13 r 8 9 r 13 0 r 9 -9 r
0 -13 r -9 -9 r -13 0 r -8 9 r cp s n 1578 975 m 0 12 r 8 9 r 13 0 r 9 -9 r
0 -12 r -9 -9 r -13 0 r -8 9 r cp s n 1282 988 m 0 12 r 9 9 r 13 0 r 9 -9 r
0 -12 r -9 -9 r -13 0 r -9 9 r cp s n 987 985 m 0 12 r 9 9 r 13 0 r 9 -9 r
0 -12 r -9 -9 r -13 0 r -9 9 r cp s n 413 413 m 0 21 r 0 -6 r 6 0 r 9 -9 r
0 -6 r 6 0 r -37 0 r 16 0 r cp s n 2183 744 m -295 180 r -295 57 r -295 13 r
-295 -3 r s n 2171 696 m 0 24 r 12 0 r 0 -24 r -12 0 r cp s n 1876 906 m 0 23 r
24 0 r 0 -23 r -24 0 r cp s n 1581 968 m 0 24 r 23 0 r 0 -24 r -23 0 r cp s n
1286 997 m 0 24 r 23 0 r 0 -24 r -23 0 r cp s n 991 981 m 0 24 r 23 0 r 0 -24 r
-23 0 r cp s n 696 998 m 0 24 r 23 0 r 0 -24 r -23 0 r cp s n 413 413 m 0 11 r
11 0 r 0 -11 r -11 0 r cp s n 2183 708 m -295 209 r -295 63 r -295 29 r
-295 -16 r -295 17 r s n 486 790 m 0 13 r 9 9 r 13 0 r 9 -9 r 0 -13 r -9 -9 r
-13 0 r cp e n 486 790 m 0 13 r 9 9 r 13 0 r 9 -9 r 0 -13 r -9 -9 r -13 0 r
-9 9 r cp s n 490 726 m 0 23 r 23 0 r 0 -23 r cp f n 490 726 m 0 23 r 23 0 r
0 -23 r -23 0 r cp s n 486 672 m 0 13 r 9 9 r 13 0 r 9 -9 r 0 -13 r -9 -9 r
-13 0 r -9 9 r cp s n 490 608 m 0 23 r 23 0 r 0 -23 r -23 0 r cp s n 413 1593 m
0 -1180 r 1770 0 r 0 1180 r -1770 0 r cp s n 501 425 m 0 -12 r s n 501 1581 m
0 12 r s n 553 425 m 0 -12 r s n 553 1581 m 0 12 r s n 590 425 m 0 -12 r s n
590 1581 m 0 12 r s n 619 425 m 0 -12 r s n 619 1581 m 0 12 r s n 642 425 m
0 -12 r s n 642 1581 m 0 12 r s n 662 425 m 0 -12 r s n 662 1581 m 0 12 r s n
679 425 m 0 -12 r s n 679 1581 m 0 12 r s n 694 425 m 0 -12 r s n 694 1581 m
0 12 r s n 708 436 m 0 -23 r s n 708 1570 m 0 23 r s n 796 425 m 0 -12 r s n
796 1581 m 0 12 r s n 848 425 m 0 -12 r s n 848 1581 m 0 12 r s n 885 425 m
0 -12 r s n 885 1581 m 0 12 r s n 914 425 m 0 -12 r s n 914 1581 m 0 12 r s n
937 425 m 0 -12 r s n 937 1581 m 0 12 r s n 957 425 m 0 -12 r s n 957 1581 m
0 12 r s n 974 425 m 0 -12 r s n 974 1581 m 0 12 r s n 989 425 m 0 -12 r s n
989 1581 m 0 12 r s n 1003 436 m 0 -23 r s n 1003 1570 m 0 23 r s n 1091 425 m
0 -12 r s n 1091 1581 m 0 12 r s n 1143 425 m 0 -12 r s n 1143 1581 m 0 12 r s
n
Y 1180 425 m 0 -12 r s n 1180 1581 m 0 12 r s n 1209 425 m 0 -12 r s n
1209 1581 m 0 12 r s n 1232 425 m 0 -12 r s n 1232 1581 m 0 12 r s n 1252 425 m
0 -12 r s n 1252 1581 m 0 12 r s n 1269 425 m 0 -12 r s n 1269 1581 m 0 12 r s
n
Y 1284 425 m 0 -12 r s n 1284 1581 m 0 12 r s n 1298 436 m 0 -23 r s n
1298 1570 m 0 23 r s n 1387 425 m 0 -12 r s n 1387 1581 m 0 12 r s n 1438 425 m
0 -12 r s n 1438 1581 m 0 12 r s n 1475 425 m 0 -12 r s n 1475 1581 m 0 12 r s
n
Y 1504 425 m 0 -12 r s n 1504 1581 m 0 12 r s n 1527 425 m 0 -12 r s n
1527 1581 m 0 12 r s n 1547 425 m 0 -12 r s n 1547 1581 m 0 12 r s n 1564 425 m
0 -12 r s n 1564 1581 m 0 12 r s n 1579 425 m 0 -12 r s n 1579 1581 m 0 12 r s
n
Y 1593 436 m 0 -23 r s n 1593 1570 m 0 23 r s n 1682 425 m 0 -12 r s n
1682 1581 m 0 12 r s n 1734 425 m 0 -12 r s n 1734 1581 m 0 12 r s n 1770 425 m
0 -12 r s n 1770 1581 m 0 12 r s n 1799 425 m 0 -12 r s n 1799 1581 m 0 12 r s
n
Y 1822 425 m 0 -12 r s n 1822 1581 m 0 12 r s n 1842 425 m 0 -12 r s n
1842 1581 m 0 12 r s n 1859 425 m 0 -12 r s n 1859 1581 m 0 12 r s n 1874 425 m
0 -12 r s n 1874 1581 m 0 12 r s n 1888 436 m 0 -23 r s n 1888 1570 m 0 23 r s
n
Y 1977 425 m 0 -12 r s n 1977 1581 m 0 12 r s n 2029 425 m 0 -12 r s n
2029 1581 m 0 12 r s n 2065 425 m 0 -12 r s n 2065 1581 m 0 12 r s n 2094 425 m
0 -12 r s n 2094 1581 m 0 12 r s n 2117 425 m 0 -12 r s n 2117 1581 m 0 12 r s
n
Y 2137 425 m 0 -12 r s n 2137 1581 m 0 12 r s n 2154 425 m 0 -12 r s n
2154 1581 m 0 12 r s n 2169 425 m 0 -12 r s n 2169 1581 m 0 12 r s n 2183 436 m
0 -23 r s n 2183 1570 m 0 23 r s n 436 413 m -23 0 r s n 2159 413 m 24 0 r s n
424 472 m -11 0 r s n 2171 472 m 12 0 r s n 424 531 m -11 0 r s n 2171 531 m
12 0 r s n 424 590 m -11 0 r s n 2171 590 m 12 0 r s n 424 649 m -11 0 r s n
2171 649 m 12 0 r s n 436 708 m -23 0 r s n 2159 708 m 24 0 r s n 424 767 m
-11 0 r s n 2171 767 m 12 0 r s n 424 826 m -11 0 r s n 2171 826 m 12 0 r s n
424 885 m -11 0 r s n 2171 885 m 12 0 r s n 424 944 m -11 0 r s n 2171 944 m
12 0 r s n 436 1003 m -23 0 r s n 2159 1003 m 24 0 r s n 424 1062 m -11 0 r s n
2171 1062 m 12 0 r s n 424 1121 m -11 0 r s n 2171 1121 m 12 0 r s n 424 1180 m
-11 0 r s n 2171 1180 m 12 0 r s n 424 1239 m -11 0 r s n 2171 1239 m 12 0 r s
n
Y 436 1298 m -23 0 r s n 2159 1298 m 24 0 r s n 424 1357 m -11 0 r s n
2171 1357 m 12 0 r s n 424 1416 m -11 0 r s n 2171 1416 m 12 0 r s n 424 1475 m
-11 0 r s n 2171 1475 m 12 0 r s n 424 1534 m -11 0 r s n 2171 1534 m 12 0 r s
n
Y 436 1593 m -23 0 r s n 2159 1593 m 24 0 r s n 361 353 m 3 2 r 5 5 r 0 -36 r s
n
Y 368 358 m 0 -34 r s n 361 324 m 15 0 r s n 396 360 m -5 -2 r -3 -5 r -2 -9 r
0 -5 r 2 -8 r 3 -5 r 5 -2 r 4 0 r 5 2 r 3 5 r 2 8 r 0 5 r -2 9 r -3 5 r -5 2 r
-4 0 r cp s n 396 360 m -3 -2 r -2 -2 r -2 -3 r -1 -9 r 0 -5 r 1 -8 r 2 -3 r
2 -2 r 3 -2 r s n 400 324 m 3 2 r 2 2 r 1 3 r 2 8 r 0 5 r -2 9 r -1 3 r -2 2 r
-3 2 r s n 418 353 m 20 0 r s n 461 361 m 0 -1 r 2 0 r 0 1 r -2 2 r -3 2 r
-4 0 r -3 -2 r -2 -2 r -1 -5 r 0 -8 r 1 -4 r 4 -1 r 5 0 r 3 1 r 2 4 r 0 3 r
-2 4 r -3 1 r -5 0 r -5 -3 r s n 454 365 m -3 -4 r -2 -5 r 0 -8 r 2 -4 r 2 -1 r
s n 458 343 m 1 1 r 2 4 r 0 3 r -2 4 r -1 1 r s n 656 353 m 3 2 r 5 5 r 0 -36 r
s n 663 358 m 0 -34 r s n 656 324 m 15 0 r s n 691 360 m -5 -2 r -3 -5 r -2 -9
r
Y 0 -5 r 2 -8 r 3 -5 r 5 -2 r 4 0 r 5 2 r 3 5 r 2 8 r 0 5 r -2 9 r -3 5 r -5 2
r
-4 0 r cp s n 691 360 m -3 -2 r -2 -2 r -1 -3 r -2 -9 r 0 -5 r 2 -8 r 1 -3 r
2 -2 r 3 -2 r s n 695 324 m 3 2 r 2 2 r 1 3 r 2 8 r 0 5 r -2 9 r -1 3 r -2 2 r
-3 2 r s n 713 353 m 20 0 r s n 744 365 m -1 -10 r s n 744 365 m 12 0 r s n
744 363 m 7 0 r 5 2 r s n 743 355 m 1 1 r 4 2 r 5 0 r 3 -2 r 2 -3 r 0 -5 r
-2 -4 r -3 -1 r -5 0 r -4 1 r -1 2 r 0 2 r 1 0 r 0 -2 r s n 753 358 m 1 -2 r
2 -3 r 0 -5 r -2 -4 r -1 -1 r s n 951 353 m 3 2 r 5 5 r 0 -36 r s n 958 358 m
0 -34 r s n 951 324 m 15 0 r s n 986 360 m -5 -2 r -3 -5 r -2 -9 r 0 -5 r 2 -8
r
Y 3 -5 r 5 -2 r 4 0 r 5 2 r 3 5 r 2 8 r 0 5 r -2 9 r -3 5 r -5 2 r -4 0 r cp s
n
986 360 m -3 -2 r -2 -2 r -1 -3 r -2 -9 r 0 -5 r 2 -8 r 1 -3 r 2 -2 r 3 -2 r s
n
Y 990 324 m 3 2 r 2 2 r 1 3 r 2 8 r 0 5 r -2 9 r -1 3 r -2 2 r -3 2 r s n
1008 353 m 20 0 r s n 1046 361 m 0 -18 r s n 1048 365 m 0 -22 r s n 1048 365 m
-12 -16 r 19 0 r s n 1043 343 m 8 0 r s n 1246 353 m 3 2 r 5 5 r 0 -36 r s n
1253 358 m 0 -34 r s n 1246 324 m 15 0 r s n 1281 360 m -5 -2 r -3 -5 r -2 -9 r
0 -5 r 2 -8 r 3 -5 r 5 -2 r 4 0 r 5 2 r 3 5 r 2 8 r 0 5 r -2 9 r -3 5 r -5 2 r
-4 0 r cp s n 1281 360 m -3 -2 r -2 -2 r -1 -3 r -2 -9 r 0 -5 r 2 -8 r 1 -3 r
2 -2 r 3 -2 r s n 1285 324 m 3 2 r 2 2 r 1 3 r 2 8 r 0 5 r -2 9 r -1 3 r -2 2 r
-3 2 r s n 1303 353 m 21 0 r s n 1334 361 m 0 -1 r -1 0 r 0 1 r 1 2 r 4 2 r
5 0 r 3 -2 r 2 -3 r -2 -4 r -3 -1 r s n 1343 365 m 2 -2 r 1 -3 r -1 -4 r -2 -1
r
Y s n 1340 355 m 3 0 r 3 -2 r 2 -4 r 0 -1 r -2 -4 r -3 -1 r -5 0 r -4 1 r -1 2
r
0 2 r 1 0 r 0 -2 r s n 1343 355 m 2 -2 r 1 -4 r 0 -1 r -1 -4 r -2 -1 r s n
1541 353 m 3 2 r 5 5 r 0 -36 r s n 1548 358 m 0 -34 r s n 1541 324 m 15 0 r s n
1576 360 m -5 -2 r -3 -5 r -2 -9 r 0 -5 r 2 -8 r 3 -5 r 5 -2 r 4 0 r 5 2 r 3 5
r
Y 2 8 r 0 5 r -2 9 r -3 5 r -5 2 r -4 0 r cp s n 1576 360 m -3 -2 r -2 -2 r
-1 -3 r -2 -9 r 0 -5 r 2 -8 r 1 -3 r 2 -2 r 3 -2 r s n 1580 324 m 3 2 r 2 2 r
2 3 r 1 8 r 0 5 r -1 9 r -2 3 r -2 2 r -3 2 r s n 1598 353 m 21 0 r s n
1630 361 m 0 -1 r -2 0 r 0 1 r 2 2 r 3 2 r 5 0 r 3 -2 r 2 -3 r -2 -4 r -3 -1 r
-5 -2 r -3 -2 r -2 -3 r 0 -5 r s n 1638 365 m 2 -2 r 1 -3 r -1 -4 r -2 -1 r s n
1628 344 m 2 2 r 1 0 r 5 -2 r 5 0 r 2 2 r s n 1631 346 m 5 -3 r 5 0 r 2 3 r
0 2 r s n 1836 353 m 3 2 r 5 5 r 0 -36 r s n 1843 358 m 0 -34 r s n 1836 324 m
15 0 r s n 1871 360 m -5 -2 r -3 -5 r -2 -9 r 0 -5 r 2 -8 r 3 -5 r 5 -2 r 4 0 r
5 2 r 3 5 r 2 8 r 0 5 r -2 9 r -3 5 r -5 2 r -4 0 r cp s n 1871 360 m -3 -2 r
-2 -2 r -1 -3 r -2 -9 r 0 -5 r 2 -8 r 1 -3 r 2 -2 r 3 -2 r s n 1875 324 m 3 2 r
2 2 r 2 3 r 1 8 r 0 5 r -1 9 r -2 3 r -2 2 r -3 2 r s n 1893 353 m 21 0 r s n
1926 360 m 5 5 r 0 -22 r s n 1930 363 m 0 -20 r s n 1925 343 m 11 0 r s n
2144 353 m 3 2 r 5 5 r 0 -36 r s n 2150 358 m 0 -34 r s n 2144 324 m 15 0 r s n
2179 360 m -5 -2 r -4 -5 r -1 -9 r 0 -5 r 1 -8 r 4 -5 r 5 -2 r 3 0 r 5 2 r 4 5
r
Y 1 8 r 0 5 r -1 9 r -4 5 r -5 2 r -3 0 r cp s n 2179 360 m -3 -2 r -2 -2 r
-2 -3 r -2 -9 r 0 -5 r 2 -8 r 2 -3 r 2 -2 r 3 -2 r s n 2182 324 m 4 2 r 1 2 r
2 3 r 2 8 r 0 5 r -2 9 r -2 3 r -1 2 r -4 2 r s n 2205 365 m -3 -2 r -2 -5 r
0 -9 r 2 -5 r 3 -1 r 5 0 r 3 1 r 2 5 r 0 9 r -2 5 r -3 2 r -5 0 r cp s n
2205 365 m -2 -2 r -1 -5 r 0 -9 r 1 -5 r 2 -1 r s n 2210 343 m 2 1 r 1 5 r 0 9
r
Y -1 5 r -2 2 r s n 220 430 m -5 -1 r -3 -5 r -2 -9 r 0 -5 r 2 -8 r 3 -5 r 5 -2
r
Y 4 0 r 5 2 r 3 5 r 2 8 r 0 5 r -2 9 r -3 5 r -5 1 r -4 0 r cp s n 220 430 m
-3 -1 r -2 -2 r -1 -3 r -2 -9 r 0 -5 r 2 -8 r 1 -4 r 2 -1 r 3 -2 r s n 224 395
m
Y 3 2 r 2 1 r 1 4 r 2 8 r 0 5 r -2 9 r -1 3 r -2 2 r -3 1 r s n 246 398 m -2 -1
r
Y 2 -2 r 1 2 r -1 1 r cp s n 268 430 m -5 -1 r -4 -5 r -2 -9 r 0 -5 r 2 -8 r
4 -5 r 5 -2 r 3 0 r 5 2 r 3 5 r 2 8 r 0 5 r -2 9 r -3 5 r -5 1 r -3 0 r cp s n
268 430 m -4 -1 r -1 -2 r -2 -3 r -2 -9 r 0 -5 r 2 -8 r 2 -4 r 1 -1 r 4 -2 r s
n
Y 271 395 m 3 2 r 2 1 r 2 4 r 1 8 r 0 5 r -1 9 r -2 3 r -2 2 r -3 1 r s n
220 726 m -5 -2 r -3 -5 r -2 -9 r 0 -5 r 2 -8 r 3 -5 r 5 -2 r 4 0 r 5 2 r 3 5 r
2 8 r 0 5 r -2 9 r -3 5 r -5 2 r -4 0 r cp s n 220 726 m -3 -2 r -2 -2 r -1 -3
r
Y -2 -9 r 0 -5 r 2 -8 r 1 -3 r 2 -2 r 3 -2 r s n 224 690 m 3 2 r 2 2 r 1 3 r
2 8 r 0 5 r -2 9 r -1 3 r -2 2 r -3 2 r s n 246 694 m -2 -2 r 2 -2 r 1 2 r
-1 2 r cp s n 261 726 m -4 -17 r s n 257 709 m 4 3 r 5 2 r 5 0 r 5 -2 r 3 -3 r
2 -5 r 0 -4 r -2 -5 r -3 -3 r -5 -2 r -5 0 r -5 2 r -2 2 r -2 3 r 0 2 r 2 1 r
2 -1 r -2 -2 r s n 271 714 m 3 -2 r 4 -3 r 1 -5 r 0 -4 r -1 -5 r -4 -3 r -3 -2
r
Y s n 261 726 m 17 0 r s n 261 724 m 8 0 r 9 2 r s n 215 1014 m 4 2 r 5 5 r
0 -36 r s n 222 1019 m 0 -34 r s n 215 985 m 15 0 r s n 246 989 m -2 -2 r 2 -2
r
Y 1 2 r -1 2 r cp s n 268 1021 m -5 -2 r -4 -5 r -2 -8 r 0 -6 r 2 -8 r 4 -5 r
5 -2 r 3 0 r 5 2 r 3 5 r 2 8 r 0 6 r -2 8 r -3 5 r -5 2 r -3 0 r cp s n
268 1021 m -4 -2 r -1 -2 r -2 -3 r -2 -8 r 0 -6 r 2 -8 r 2 -3 r 1 -2 r 4 -2 r s
n 271 985 m 3 2 r 2 2 r 2 3 r 1 8 r 0 6 r -1 8 r -2 3 r -2 2 r -3 2 r s n
215 1309 m 4 2 r 5 5 r 0 -36 r s n 222 1314 m 0 -34 r s n 215 1280 m 15 0 r s n
246 1284 m -2 -2 r 2 -2 r 1 2 r -1 2 r cp s n 261 1316 m -4 -17 r s n 257 1299
m
Y 4 3 r 5 2 r 5 0 r 5 -2 r 3 -3 r 2 -5 r 0 -3 r -2 -6 r -3 -3 r -5 -2 r -5 0 r
-5 2 r -2 2 r -2 3 r 0 2 r 2 2 r 2 -2 r -2 -2 r s n 271 1304 m 3 -2 r 4 -3 r
1 -5 r 0 -3 r -1 -6 r -4 -3 r -3 -2 r s n 261 1316 m 17 0 r s n 261 1314 m 8 0
r
Y 9 2 r s n 212 1604 m 2 -1 r -2 -2 r -2 2 r 0 1 r 2 4 r 2 1 r 5 2 r 6 0 r 5 -2
r
Y 2 -1 r 2 -4 r 0 -3 r -2 -4 r -5 -3 r -8 -3 r -4 -2 r -3 -3 r -2 -5 r 0 -5 r s
n
Y 225 1611 m 4 -2 r 1 -1 r 2 -4 r 0 -3 r -2 -4 r -5 -3 r -6 -3 r s n 210 1579 m
2 2 r 3 0 r 9 -4 r 5 0 r 3 2 r 2 2 r s n 215 1581 m 9 -5 r 6 0 r 2 1 r 2 4 r
0 3 r s n 246 1579 m -2 -2 r 2 -1 r 1 1 r -1 2 r cp s n 268 1611 m -5 -2 r
-4 -5 r -2 -8 r 0 -5 r 2 -9 r 4 -5 r 5 -1 r 3 0 r 5 1 r 3 5 r 2 9 r 0 5 r -2 8
r
Y -3 5 r -5 2 r -3 0 r cp s n 268 1611 m -4 -2 r -1 -1 r -2 -4 r -2 -8 r 0 -5 r
2 -9 r 2 -3 r 1 -2 r 4 -1 r s n 271 1576 m 3 1 r 2 2 r 2 3 r 1 9 r 0 5 r -1 8 r
-2 4 r -2 1 r -3 2 r s sp gr
XXX
chmod 0444 fig-2.ps ||
echo 'restore of fig-2.ps failed'
Wc_c="`wc -c < 'fig-2.ps'`"
test 22349 -eq "$Wc_c" ||
        echo 'fig-2.ps: original size 22349, current size' "$Wc_c"
fi
# ============= epsf.sty ==============
if test -f 'epsf.sty' -a X"$1" != X"-c"; then
        echo 'x - skipping epsf.sty (File already exists)'
else
echo 'x - extracting epsf.sty (Text)'
sed 's/^Y//' << 'XXX' > 'epsf.sty' &&
%   EPSF.TEX macro file:
%   Written by Tomas Rokicki of Radical Eye Software, 29 Mar 1989.
%   Revised by Don Knuth, 3 Jan 1990.
%   Revised by Tomas Rokicki to accept bounding boxes with no
%      space after the colon, 18 Jul 1990.
%
%   TeX macros to include an Encapsulated PostScript graphic.
%   Works by finding the bounding box comment,
%   calculating the correct scale values, and inserting a vbox
%   of the appropriate size at the current position in the TeX document.
%
%   To use with the center environment of LaTeX, preface the \epsffile
%   call with a \leavevmode.  (LaTeX should probably supply this itself
%   for the center environment.)
%
%   To use, simply say
%   \input epsf           % somewhere early on in your TeX file
%   \epsfbox{filename.ps} % where you want to insert a vbox for a figure
%
%   Alternatively, you can type
%
%   \epsfbox[0 0 30 50]{filename.ps} % to supply your own BB
%
%   which will not read in the file, and will instead use the bounding
%   box you specify.
%
%   The effect will be to typeset the figure as a TeX box, at the
%   point of your \epsfbox command. By default, the graphic will have its
%   `natural' width (namely the width of its bounding box, as described
%   in filename.ps). The TeX box will have depth zero.
%
%   You can enlarge or reduce the figure by saying
%     \epsfxsize=<dimen> \epsfbox{filename.ps}
%   (or
%     \epsfysize=<dimen> \epsfbox{filename.ps})
%   instead. Then the width of the TeX box will be \epsfxsize and its
%   height will be scaled proportionately (or the height will be
%   \epsfysize and its width will be scaled proportiontally).  The
%   width (and height) is restored to zero after each use.
%
%   A more general facility for sizing is available by defining the
%   \epsfsize macro.    Normally you can redefine this macro
%   to do almost anything.  The first parameter is the natural x size of
%   the PostScript graphic, the second parameter is the natural y size
%   of the PostScript graphic.  It must return the xsize to use, or 0 if
%   natural scaling is to be used.  Common uses include:
%
%      \epsfxsize  % just leave the old value alone
%      0pt         % use the natural sizes
%      #1          % use the natural sizes
%      \hsize      % scale to full width
%      0.5#1       % scale to 50% of natural size
%      \ifnum#1>\hsize\hsize\else#1\fi  % smaller of natural, hsize
%
%   If you want TeX to report the size of the figure (as a message
%   on your terminal when it processes each figure), say `\epsfverbosetrue'.
%
\newread\epsffilein    % file to \read
\newif\ifepsffileok    % continue looking for the bounding box?
\newif\ifepsfbbfound   % success?
\newif\ifepsfverbose   % report what you're making?
\newdimen\epsfxsize    % horizontal size after scaling
\newdimen\epsfysize    % vertical size after scaling
\newdimen\epsftsize    % horizontal size before scaling
\newdimen\epsfrsize    % vertical size before scaling
\newdimen\epsftmp      % register for arithmetic manipulation
\newdimen\pspoints     % conversion factor
%
\pspoints=1bp          % Adobe points are `big'
\epsfxsize=0pt         % Default value, means `use natural size'
\epsfysize=0pt         % ditto
%
\def\epsfbox#1{\global\def\epsfllx{72}\global\def\epsflly{72}%
Y   \global\def\epsfurx{540}\global\def\epsfury{720}%
Y   \def\lbracket{[}\def\testit{#1}\ifx\testit\lbracket
Y   \let\next=\epsfgetlitbb\else\let\next=\epsfnormal\fi\next{#1}}%
%
\def\epsfgetlitbb#1#2 #3 #4 #5]#6{\epsfgrab #2 #3 #4 #5 .\\%
Y   \epsfsetgraph{#6}}%
%
\def\epsfnormal#1{\epsfgetbb{#1}\epsfsetgraph{#1}}%
%
\def\epsfgetbb#1{%
%
%   The first thing we need to do is to open the
%   PostScript file, if possible.
%
\openin\epsffilein=#1
\ifeof\epsffilein\errmessage{I couldn't open #1, will ignore it}\else
%
%   Okay, we got it. Now we'll scan lines until we find one that doesn't
%   start with %. We're looking for the bounding box comment.
%
Y   {\epsffileoktrue \chardef\other=12
Y    \def\do##1{\catcode`##1=\other}\dospecials \catcode`\ =10
Y    \loop
Y       \read\epsffilein to \epsffileline
Y       \ifeof\epsffilein\epsffileokfalse\else
%
%   We check to see if the first character is a % sign;
%   if not, we stop reading (unless the line was entirely blank);
%   if so, we look further and stop only if the line begins with
%   `%%BoundingBox:'.
%
Y          \expandafter\epsfaux\epsffileline:. \\%
Y       \fi
Y   \ifepsffileok\repeat
Y   \ifepsfbbfound\else
Y    \ifepsfverbose\message{No bounding box comment in #1; using
defaults}\fi\fi
Y   }\closein\epsffilein\fi}%
%
%   Now we have to calculate the scale and offset values to use.
%   First we compute the natural sizes.
%
\def\epsfsetgraph#1{%
Y   \epsfrsize=\epsfury\pspoints
Y   \advance\epsfrsize by-\epsflly\pspoints
Y   \epsftsize=\epsfurx\pspoints
Y   \advance\epsftsize by-\epsfllx\pspoints
%
%   If `epsfxsize' is 0, we default to the natural size of the picture.
%   Otherwise we scale the graph to be \epsfxsize wide.
%
Y   \epsfxsize\epsfsize\epsftsize\epsfrsize
Y   \ifnum\epsfxsize=0 \ifnum\epsfysize=0
Y      \epsfxsize=\epsftsize \epsfysize=\epsfrsize
%
%   We have a sticky problem here:  TeX doesn't do floating point arithmetic!
%   Our goal is to compute y = rx/t. The following loop does this reasonably
%   fast, with an error of at most about 16 sp (about 1/4000 pt).
%
Y     \else\epsftmp=\epsftsize \divide\epsftmp\epsfrsize
Y       \epsfxsize=\epsfysize \multiply\epsfxsize\epsftmp
Y       \multiply\epsftmp\epsfrsize \advance\epsftsize-\epsftmp
Y       \epsftmp=\epsfysize
Y       \loop \advance\epsftsize\epsftsize \divide\epsftmp 2
Y       \ifnum\epsftmp>0
Y          \ifnum\epsftsize<\epsfrsize\else
Y             \advance\epsftsize-\epsfrsize \advance\epsfxsize\epsftmp \fi
Y       \repeat
Y     \fi
Y   \else\epsftmp=\epsfrsize \divide\epsftmp\epsftsize
Y     \epsfysize=\epsfxsize \multiply\epsfysize\epsftmp
Y     \multiply\epsftmp\epsftsize \advance\epsfrsize-\epsftmp
Y     \epsftmp=\epsfxsize
Y     \loop \advance\epsfrsize\epsfrsize \divide\epsftmp 2
Y     \ifnum\epsftmp>0
Y        \ifnum\epsfrsize<\epsftsize\else
Y           \advance\epsfrsize-\epsftsize \advance\epsfysize\epsftmp \fi
Y     \repeat
Y   \fi
%
%  Finally, we make the vbox and stick in a \special that dvips can parse.
%
Y   \ifepsfverbose\message{#1: width=\the\epsfxsize, height=\the\epsfysize}\fi
Y   \epsftmp=10\epsfxsize \divide\epsftmp\pspoints
Y   \vbox to\epsfysize{\vfil\hbox to\epsfxsize{%
Y      \special{PSfile=#1 llx=\epsfllx\space lly=\epsflly\space
Y          urx=\epsfurx\space ury=\epsfury\space rwi=\number\epsftmp}%
Y      \hfil}}%
\epsfxsize=0pt\epsfysize=0pt}%
Y
%
%   We still need to define the tricky \epsfaux macro. This requires
%   a couple of magic constants for comparison purposes.
%
{\catcode`\%=12 \global\let\epsfpercent=%\global\def\epsfbblit{%BoundingBox}}%
%
%   So we're ready to check for `%BoundingBox:' and to grab the
%   values if they are found.
%
\long\def\epsfaux#1#2:#3\\{\ifx#1\epsfpercent
Y   \def\testit{#2}\ifx\testit\epsfbblit
Y      \epsfgrab #3 . . . \\%
Y      \epsffileokfalse
Y      \global\epsfbbfoundtrue
Y   \fi\else\ifx#1\par\else\epsffileokfalse\fi\fi}%
%
%   Here we grab the values and stuff them in the appropriate definitions.
%
\def\epsfgrab #1 #2 #3 #4 #5\\{%
Y   \global\def\epsfllx{#1}\ifx\epsfllx\empty
Y      \epsfgrab #2 #3 #4 #5 .\\\else
Y   \global\def\epsflly{#2}%
Y   \global\def\epsfurx{#3}\global\def\epsfury{#4}\fi}%
%
%   We default the epsfsize macro.
%
\def\epsfsize#1#2{\epsfxsize}
%
%   Finally, another definition for compatibility with older macros.
%
\let\epsffile=\epsfbox
Y
XXX
chmod 0444 epsf.sty ||
echo 'restore of epsf.sty failed'
Wc_c="`wc -c < 'epsf.sty'`"
test 7576 -eq "$Wc_c" ||
        echo 'epsf.sty: original size 7576, current size' "$Wc_c"
fi
# ============= espcrc2.sty ==============
if test -f 'espcrc2.sty' -a X"$1" != X"-c"; then
        echo 'x - skipping espcrc2.sty (File already exists)'
else
echo 'x - extracting espcrc2.sty (Text)'
sed 's/^Y//' << 'XXX' > 'espcrc2.sty' &&
%%%%%%%%%% espcrc2.sty %%%%%%%%%%
% C(amera) R(eady) C(opy) document-style option. (two-column format).
% Version 2.0: 5 May 1992
% To be used with LaTeX version 2.09 (14 January 1992).
%
%
% Copyright (C) 1992 by ESP. All rights reserved.
%
% IMPORTANT NOTICE:
%
% You are NOT allowed to distribute or change this file.
% Error reports in case of UNCHANGED versions to
%
%   Dr. Nico A.F.M. Poppelier
%   Elsevier Science Publishers
%   APD, R&D Department
%
%
% Usage: \documentstyle[twoside,espcrc2]{article}
%
\def\fileversion{v2.0}
\def\filedate{5 May 1992}
Y
\typeout{Document style option `espcrc2' \fileversion \space\space
Y         <\filedate>}
Y
% SIDE MARGINS:
\oddsidemargin  -4mm              % Left margin on odd-numbered pages.
\evensidemargin  4mm              % Left margin on even-numbered pages.
Y
% VERTICAL SPACING:
\topmargin      16mm              % Nominal distance from top of page to top
Y                                  % of box containing running head.
\headheight      0mm              % No running headline, and no
\headsep         0mm              % space between running headline and text.
\footskip        30pt             % Baseline-baseline distance between
Y                                  % running footline and last line of text.
Y
% DIMENSION OF TEXT:
\textheight 202mm                 % Height of text part of page
\textwidth 160mm                  % Width of text part of page, i.e of line
Y
\columnsep 10mm                   % Horizontal space between columns
\columnseprule 0pt                % No vertical rule between columns
Y
% PARAGRAPHING
\parskip 0pt                      % No extra vertical space between paragraphs.
\parindent 1em                    % Width of paragraph indentation.
Y
% SECTIONAL UNITS:
\newdimen\@bls                    % \@b(ase)l(ine)s(kip)
\@bls=\baselineskip               % \@bls ~= \baselineskip for \normalsize
\advance\@bls -1ex                % (fudge term)
\newdimen\@eps                    %
\@eps=0.0001pt                    % \eps = very small positive quantity
Y
\def\section{\@startsection{section}{1}{\z@}
Y  {2\@bls plus 0.5\@bls}{1\@bls}{\normalsize\bf}}
\def\subsection{\@startsection{subsection}{2}{\z@}
Y  {1\@bls plus 0.25\@bls}{\@eps}{\normalsize\bf}}
\def\subsubsection{\@startsection{subsubsection}{3}{\z@}
Y  {1\@bls plus 0.25\@bls}{\@eps}{\normalsize\bf}}
\def\paragraph{\@startsection{paragraph}{4}{\parindent}
Y  {1\@bls plus 0.25\@bls}{0.5em}{\normalsize\bf}}
\def\subparagraph{\@startsection{subparagraph}{4}{\parindent}
Y  {1\@bls plus 0.25\@bls}{0.5em}{\normalsize\bf}}
Y
\def\@sect#1#2#3#4#5#6[#7]#8{\ifnum #2>\c@secnumdepth
Y  \def\@svsec{}\else
Y  \refstepcounter{#1}\edef\@svsec{\csname the#1\endcsname.\hskip0.5em}\fi
Y  \@tempskipa #5\relax
Y  \ifdim \@tempskipa>\z@
Y    \begingroup
Y      #6\relax
Y      \@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\par}%
Y    \endgroup
Y    \csname #1mark\endcsname{#7}\addcontentsline
Y      {toc}{#1}{\ifnum #2>\c@secnumdepth \else
Y        \protect\numberline{\csname the#1\endcsname}\fi #7}%
Y  \else
Y    \def\@svsechd{#6\hskip #3\@svsec #8\csname #1mark\endcsname
Y      {#7}\addcontentsline{toc}{#1}{\ifnum #2>\c@secnumdepth \else
Y        \protect\numberline{\csname the#1\endcsname}\fi #7}}%
Y  \fi \@xsect{#5}}
Y
% FIGURES AND TABLES
\long\def\@makefigurecaption#1#2{\vskip 10mm #1. #2\par}
Y
\long\def\@maketablecaption#1#2{\hbox to \hsize{\parbox[t]{\hsize}
Y  {#1 \\ #2}}\vskip 0.3ex}
Y
\def\fnum@figure{Figure \thefigure}
\def\figure{\let\@makecaption\@makefigurecaption \@float{figure}}
\@namedef{figure*}{\let\@makecaption\@makefigurecaption \@dblfloat{figure}}
Y
% \def\fnum@table{Table \thetable}
\def\table{\let\@makecaption\@maketablecaption \@float{table}}
\@namedef{table*}{\let\@makecaption\@maketablecaption \@dblfloat{table}}
Y
\floatsep 10mm plus 4pt minus 4pt % Space between adjacent floats moved
Y                                  % to top or bottom of text page.
\textfloatsep=\floatsep           % Space between main text and floats
Y                                  % at top or bottom of page.
\intextsep=\floatsep              % Space between in-text figures and
Y                                  % text.
Y
% FOOTNOTE
\long\def\@makefntext#1{\parindent 1em\noindent\hbox{${}^{\@thefnmark}$}#1}
Y
% EQUATION
\mathindent=0em
Y
% TITLE
\def\maketitle{\begingroup        % Initialize generation of front-matter
%   \let\thanks\@gobble
Y    \def\thefootnote{\fnsymbol{footnote}}%
Y    \newpage \global\@topnum\z@
Y    \@maketitle \thispagestyle{plain}\@thanks
Y  \endgroup
Y  \let\maketitle\relax \let\@maketitle\relax
Y  \gdef\@thanks{}\let\thanks\relax
Y  \gdef\@address{}\gdef\@author{}\gdef\@title{}\let\address\relax}
Y
\def\justify@on{\let\\=\@normalcr
Y  \leftskip\z@ \@rightskip\z@ \rightskip\@rightskip}
Y
\newbox\fm@box                    % Box to capture front-matter in
Y
\def\@maketitle{%                 % Actual formatting of \maketitle
Y  \global\setbox\fm@box=\vbox\bgroup
Y    \raggedright                  % Front-matter text is ragged right
Y    \hyphenpenalty\@M             % and is not hyphenated.
Y    {\Large \@title \par}         % Title set in larger font.
Y    \vskip\@bls                   % One line of vertical space after title.
Y    {\normalsize                  % each author set in the normal
Y     \@author \par}               % typeface size
Y    \vskip\@bls                   % One line of vertical space after
% author(s).
Y    \@address                     % all addresses
Y  \egroup
Y  \twocolumn[%                    % Front-matter text is over 2 columns.
Y    \unvbox\fm@box                % Unwrap contents of front-matter box
Y    \vskip\@bls                   % add 1 line of vertical space,
Y    \unvbox\abstract@box          % unwrap contents of abstract boxes,
Y    \vskip 2pc]}                  % and add 2pc of vertical space
Y
\newcounter{address}
\def\theaddress{\alph{address}}
\def\@makeadmark#1{\hbox{$^{\rm #1}$}}
Y
\def\address#1{\addressmark\begingroup
Y  \xdef\@tempa{\theaddress} \let\\=\relax
Y  \def\protect{\noexpand\protect\noexpand}\xdef\@address{\@address
Y  \protect\addresstext{\@tempa}{#1}}\endgroup}
\def\@address{}
Y
\def\addressmark{\stepcounter{address}%
Y  \xdef\@tempa{\theaddress}\@makeadmark{\@tempa}}
Y
\def\addresstext#1#2{\leavevmode \begingroup
Y  \raggedright \hyphenpenalty\@M \@makeadmark{#1}#2\par \endgroup
Y  \vskip\@bls}
Y
% ABSTRACT:
\newbox\abstract@box              % Box to capture abstract in
Y
\def\abstract{%
Y  \global\setbox\abstract@box=\vbox\bgroup
Y  \small\rm
Y  \ignorespaces}
\def\endabstract{\par \egroup}
Y
% BIBLIOGRAPHY
\def\thebibliography#1{\section*{REFERENCES}\list{\arabic{enumi}}
Y  {\settowidth\labelwidth{#1}\leftmargin=1.67em
Y   \labelsep\leftmargin \advance\labelsep-\labelwidth
Y   \itemsep\z@ \parsep\z@
Y   \usecounter{enumi}}\def\makelabel##1{\rlap{##1}\hss}%
Y   \def\newblock{\hskip 0.11em plus 0.33em minus -0.07em}
Y   \sloppy \clubpenalty=4000 \widowpenalty=4000 \sfcode`\.=1000\relax}
Y
% Collapse citation numbers to ranges.
\newcount\@tempcntc
\def\@citex[#1]#2{\if@filesw\immediate\write\@auxout{\string\citation{#2}}\fi
Y  \@tempcnta\z@\@tempcntb\m@ne\def\@citea{}\@cite{\@for\@citeb:=#2\do
Y    {\@ifundefined
Y       {b@\@citeb}{\@citeo\@tempcntb\m@ne\@citea
Y        \def\@citea{,\penalty\@m\ }{\bf ?}\@warning
Y       {Citation `\@citeb' on page \thepage \space undefined}}%
Y    {\setbox\z@\hbox{\global\@tempcntc0\csname b@\@citeb\endcsname\relax}%
Y     \ifnum\@tempcntc=\z@ \@citeo\@tempcntb\m@ne
Y       \@citea\def\@citea{,\penalty\@m\ }
Y       \hbox{\csname b@\@citeb\endcsname}%
Y     \else
Y      \advance\@tempcntb\@ne
Y      \ifnum\@tempcntb=\@tempcntc
Y      \else\advance\@tempcntb\m@ne\@citeo
Y      \@tempcnta\@tempcntc\@tempcntb\@tempcntc\fi\fi}}\@citeo}{#1}}
Y
\def\@citeo{\ifnum\@tempcnta>\@tempcntb\else\@citea
Y  \def\@citea{,\penalty\@m\ }%
Y  \ifnum\@tempcnta=\@tempcntb\the\@tempcnta\else
Y   {\advance\@tempcnta\@ne\ifnum\@tempcnta=\@tempcntb \else \def\@citea{--}\fi
Y    \advance\@tempcnta\m@ne\the\@tempcnta\@citea\the\@tempcntb}\fi\fi}
Y
% INITIALIZATION
% \ps@plain                     % 'plain' page style
% \twocolumn                    % Formatting is in 2 columns, with
\sloppy                         % paragraphs that can be loosely set,
\emergencystretch=1pc           % (with 1 pc extra for emergencies),
\flushbottom                    % and pages of equal length
Y
XXX
chmod 0444 espcrc2.sty ||
echo 'restore of espcrc2.sty failed'
Wc_c="`wc -c < 'espcrc2.sty'`"
test 8364 -eq "$Wc_c" ||
        echo 'espcrc2.sty: original size 8364, current size' "$Wc_c"
fi
exit 0
%-Eprint Note: End of File etc/eprints/hep-lat/papers/9211/9211031.Z
.
