This paper gives a criterion for the non-vanishing of Dirac cohomology $\mathcal{L}_S(Z)$, where $\mathcal{L}_S(\cdot)$ is cohomological induction functor, while inducing module $Z$ irreducible, unitarizable, and in good range. As an application, we give formula counting number strings series. Using this formula, classify all irreducible unitary representations $E_{6(2)}$ with non-zero cohomolo...

We prove a vector-valued version of Muić's integral non-vanishing criterion for Poincaré series on the upper half-plane H. Moreover, we give an accompanying result construction modular forms in form series. As application these results, construct and study classical elliptic

For slowly rotating fluids, we establish the existence of a critical point similar to the one found for non-rotating systems. As the fluid approaches the critical point, the effective inertial mass of any fluid element decreases, vanishing at that point and changing of sign beyond it. This result implies that first order perturbative method is not always reliable to study dissipative processes ...

We show that Ambro–Kawamata’s non-vanishing conjecture holds true for a quasi-smooth WCI X which is Fano or Calabi-Yau, i.e. we prove that, if H is an ample Cartier divisor on X , then |H | is not empty. If X is smooth, we further show that the general element of |H | is smooth. We then verify Ambro–Kawamata’s conjecture for any quasi-smooth weighted hypersurface. We also verify Fujita’s freene...