Simple examples of non-Hermitian Hamiltonians with purely real spectra defined in L(R) having spectral singularities inside the continuous spectrum are given. It is shown that such Hamiltonians may appear by shifting the independent variable of a real potential into the complex plane. Also they may be created as SUSY partners of Hermitian Hamiltonians. In the latter case spectral singularities ...

The Lyapunov-Schmidt reduction is generalized to the case of imperfect singularities. The results presented neither need very precise information about the location of the (near) singularities nor a precise knowledge of (near) null spaces.

In this article we characterize the ideal unimodular singularities in terms of their invariants. On the basis of this characterization we give an implementation of a classifier for ideal unimodular singularities in the computer algebra system SINGULAR.

In this article, we prove that any Q-Calabi-Yau 3-fold with only ordinary terminal singularities and any Q-Fano 3-fold of Fano index 1 with only terminal singularities have Q-smoothings.