\begin{table}%t2
\caption{The pulsation models.\label{puls_mods}} 
%\centerline
{\begin{tabular}{rccccrrrr}
\hline \hline 
 $L$/$L_{\odot}$ &   $M$/$M_{\odot}$ & $M_{\rm c}$/$M_{\odot}$  & $\ell$/$H_{\rm p}$  &  log~$T_{\rm eff}$ &     $P_0$   &   $P_1$    &   $P_2$    &   $P_3$   \\
\hline
\multicolumn{9}{l} {RGB - no mass loss} \\
   794 &   0.9000 &   0.4002 &   1.80  &   3.5987  &    27.6  &   18.1  &   12.5  &    9.6 \\
  1000 &   0.9000 &   0.4136 &   1.80  &   3.5906  &    36.1  &   23.2  &   15.8  &   12.3 \\
  1259 &   0.9000 &   0.4274 &   1.80  &   3.5818  &    47.7  &   29.8  &   20.1  &   16.2 \\
  1585 &   0.9000 &   0.4417 &   1.80  &   3.5724  &    64.0  &   38.2  &   25.6  &   21.8 \\
  1995 &   0.9000 &   0.4565 &   1.80  &   3.5621  &    87.3  &   49.2  &   33.1  &   29.4 \\
  2239 &   0.9000 &   0.4640 &   1.80  &   3.5567  &   102.6  &   56.0  &   38.2  &   34.0 \\
\multicolumn{9}{l} {AGB - no mass loss} \\
   794 &   0.9000 &   0.4737 &   1.80  &   3.6034  &    26.5  &   17.3  &   11.9  &    9.2 \\
  1000 &   0.9000 &   0.4783 &   1.80  &   3.5948  &    34.8  &   22.2  &   15.2  &   11.8 \\
  1259 &   0.9000 &   0.4841 &   1.80  &   3.5857  &    46.2  &   28.6  &   19.3  &   15.7 \\
  1585 &   0.9000 &   0.4913 &   1.80  &   3.5760  &    62.1  &   36.9  &   24.7  &   21.2 \\
  1995 &   0.9000 &   0.5005 &   1.80  &   3.5656  &    84.8  &   47.6  &   32.1  &   28.5 \\
  2512 &   0.9000 &   0.5120 &   1.80  &   3.5546  &   117.7  &   61.6  &   43.0  &   37.8 \\
  3162 &   0.9000 &   0.5265 &   1.80  &   3.5427  &   166.8  &   79.9  &   59.8  &   48.9 \\
  3981 &   0.9000 &   0.5448 &   1.80  &   3.5304  &   242.8  &  104.2  &   84.9  &   63.4 \\
\multicolumn{9}{l} {RGB - with mass loss} \\
   794 &   0.8441 &   0.4002 &   1.90  &   3.6034  &    27.5  &   18.1  &   12.5  &    9.6 \\
  1000 &   0.8340 &   0.4136 &   1.90  &   3.5949  &    36.5  &   23.4  &   16.0  &   12.7 \\
  1259 &   0.8166 &   0.4274 &   1.90  &   3.5853  &    49.5  &   30.5  &   20.6  &   17.3 \\
  1585 &   0.7915 &   0.4417 &   1.90  &   3.5746  &    69.2  &   40.0  &   27.2  &   24.2 \\
  1995 &   0.7679 &   0.4565 &   1.90  &   3.5629  &    98.7  &   52.7  &   37.4  &   32.7 \\
  2239 &   0.7628 &   0.4640 &   1.90  &   3.5572  &   117.7  &   60.2  &   44.3  &   37.3 \\
\multicolumn{9}{l} {AGB - with mass loss} \\
   794 &   0.7371 &   0.4737 &   1.90  &   3.6045  &    29.9  &   19.1  &   13.1  &   10.5 \\
  1000 &   0.7344 &   0.4783 &   1.90  &   3.5956  &    39.9  &   24.6  &   16.7  &   14.1 \\
  1259 &   0.7301 &   0.4841 &   1.90  &   3.5862  &    53.9  &   31.7  &   21.5  &   19.0 \\
  1585 &   0.7244 &   0.4913 &   1.90  &   3.5762  &    74.0  &   40.9  &   28.5  &   25.3 \\
  1995 &   0.7118 &   0.5005 &   1.90  &   3.5654  &   104.6  &   53.2  &   39.4  &   32.9 \\
  2512 &   0.6903 &   0.5120 &   1.90  &   3.5539  &   154.2  &   70.0  &   56.8  &   42.8 \\
  3162 &   0.6567 &   0.5265 &   1.90  &   3.5441  &   237.1  &   93.6  &   81.9  &   57.0 \\
  3981 &   0.6057 &   0.5448 &   1.90  &   3.5478  &   321.2  &  123.2  &   99.9  &   74.1 \\
  4217 &   0.5904 &   0.5500 &   1.90  &   3.5571  &   320.6  &  124.6  &   96.1  &   73.9 \\
  4467 &   0.5743 &   0.5556 &   1.90  &   3.5789  &   291.6  &  113.7  &   81.3  &   66.7 \\
  4571 &   0.5675 &   0.5579 &   1.90  &   3.6012  &   266.7  &   98.6  &   67.0  &   57.3 \\
\hline 
\end{tabular}}
\smallskip
\par
Notes:  $\ell$/$H_{\rm p}$ is the ratio of mixing-length to pressure scale height.  $P_0$,  $P_1$, $P_2$ and $P_3$ 
are the linear periods (in days) of the fundamental, 1st, 2nd and 3rd overtone modes.
\par
\end{table}