  This paper studies the nonterminal complexity of weakly conditional grammars,
and it proves that every recursively enumerable language can be generated by a
weak conditional grammar with no more than \textit{seven} nonterminals.
Moreover, it is shown that the number of nonterminals in weakly conditional
grammars without erasing rules leads to an infinite hierarchy of families of
languages generated by weakly conditional grammars.
  Energy levels and the reduced probability of $E2$-- transitions for Ytterbium
isotopes with proton number $Z=70$ and neutron numbers between 100 and 106 have
been calculated through phenomenological ($PhM$) and interacting boson
($IBM-1$) models. The predicted low-lying levels (energies, spins and parities)
and the reduced probability for $E2$-- transitions results are reasonably
consistent with the available experimental data. The predicted low-lying levels
($gr$--, $\beta_1$-- and $\gamma_1$-- band) by produced in the $PhM$ are in
good agreement with the experimental data comparison with those by $IBM-1$ for
all nuclei of interest. In addition, the phenomenological model was successful
in predicted the $\beta_2$--, $\beta_3$--, $\beta_4$--, $\gamma_2$-- and
$1^+$-- band while it was a failure with $IBM-1$. Also, the $3^+$-- band is
predicted by the $IBM-1$ model for $^{172}Yb$ and $^{174}Yb$ nuclei. All
calculations are compared with the available experimental data.
