  The dynamical symmetry limit of the two-fluid Interacting Vector Boson Model
(IVBM), defined through the chain $Sp(12,R) \supset U(3,3) \supset U_{p}(3)
\otimes \overline{U_{n}(3)} \supset SU^{\ast}(3) \supset SO(3)$, is considered
and applied for the description of nuclear collective spectra exhibiting
axially asymmetric features. The effect of the introduction of a Majorana
interaction to the $SU^{\ast}(3)$ model Hamiltonian on the $\gamma$-band
energies is studied. The theoretical predictions are compared with the
experimental data for $^{192}Os$, $^{190}Os$, and $^{112}Ru$ isotopes. It is
shown that by taking into account the full symplectic structures in the
considered dynamical symmetry of the IVBM, the proper description of the energy
spectra and the $\gamma$-band energy staggering of the nuclei under
considerations can be achieved. The obtained results show that the potential
energy surfaces for the following two nuclei $^{192}Os$ and $^{112}Ru$, possess
almost $\gamma$-flat potentials with very shallow triaxial minima, suggesting a
more complex and intermediate situation between $\gamma$-rigid and
$\gamma$-unstable structures. Additionally, the absolute $B(E2)$ intraband
transition probabilities between the states of the ground state band and
$\gamma$ band, as well as the $B(M1)$ interband transition probabilities
between the states of the ground and $\gamma$ bands for the two nuclei
$^{192}Os$ and $^{190}Os$ are calculated and compared with experiment and for
the $B(E2)$ values with the predictions of some other collective models
incorporating the $\gamma$-rigid or $\gamma$-unstable structures. The obtained
results agree well with the experimental data and reveal the relevance of the
used dynamical symmetry of IVBM in the description of nuclei exhibiting axially
asymmetric features in their spectra.
