The singularity categories of the Cluster-tilted algebras of Dynkin type

In this paper, we use the stable categories of some selfinjective algebras to describe the singularity categories of the cluster-tilted algebras of Dynkin type. Furthermore, in this way, we settle the problem of singularity equivalence classification of the cluster-tilted algebra of type $A$, $D$ and $E$ respectively.Comment: 16 pages. arXiv admin note: substantial text overlap with arXiv:1012.4661 by other author

Dark radiation from a unified dark fluid model

We present a unified dark fluid model to describe the possible evolutionary behavior of $\Delta N_\mathrm{eff}$ in dark radiation. This model can be viewed as an interacting model for the dark sectors, in which dark matter interacts with dark radiation. We show that the evolution of $\Delta N_\mathrm{eff}$ can be nicely explained without some drawbacks, such as the blowup of $\Delta N_\mathrm{eff}$ and the non-vanishing interaction at the late time.Comment: 12 pages, 4 figures, revised version accepted by PTE

CP Violation in Predictive Neutrino Mass Structures

We study the CP violation effects from two types of neutrino mass matrices with (i) $(M_\nu)_{ee}=0$, and (ii) $(M_\nu)_{ee}=(M_\nu)_{e\mu}=0$, which can be realized by the high dimensional lepton number violating operators $\bar \ell_R^c\gamma^\mu L_L (D_\mu \Phi)\Phi^2$ and $\bar \ell_R^c l_R (D_\mu{\Phi})^2\Phi^2$, respectively. In (i), the neutrino mass spectrum is in the normal ordering with the lightest neutrino mass within the range $0.002\,{\rm eV}\lesssim m_0\lesssim 0.007\,{\rm eV}$. Furthermore, for a given value of $m_0$, there are two solutions for the two Majorana phases $\alpha_{21}$ and $\alpha_{31}$, whereas the Dirac phase $\delta$ is arbitrary. For (ii), the parameters of $m_0$, $\delta$, $\alpha_{21}$, and $\alpha_{31}$ can be completely determined. We calculate the CP violating asymmetries in neutrino-antineutrino oscillations for both mass textures of (i) and (ii), which are closely related to the CP violating Majorana phases.Comment: 17 pages, 4 figures, revised version accepted by EPJ