We review the way the BTZ black hole relaxes back to thermal equilibrium after a small perturbation and how it is seen in the boundary (finite volume) CFT. The unitarity requires the relaxation to be quasi-periodic. It is preserved in the CFT but is not obvious in the case of the semiclassical black hole the relaxation of which is driven by complex quasi-normal modes. We discuss two ways of mod...

A basis B of a finite dimensional Hopf algebra H is said to be positive if all the structure constants of H relative to B are non-negative. A quasi triangular structure R ∈ H ⊗ H is said to be positive with respect to B if it has non-negative coefficients in the basis B ⊗ B of H ⊗ H. In our earlier work, we have classified all finite dimensional Hopf algebras with positive bases. In this paper,...

Data obtained by scanning 3D models typically contains missing pieces and holes. These can be caused due to scanning artifacts or artifacts in the surface due to wear and tear. We provide a method based on the Moving Least Squares projection to fill holes in triangular meshes obtained during the process of surface reconstruction . Our method can be applied to holes with non-planar geometry as w...

We present explicit wavefunctions for quasi-hole excitations over a variety of nonabelian quantum Hall states: the Read-Rezayi states with k ≥ 3 clustering properties and a paired spin-singlet quantum Hall state. Quasi-holes over these states constitute a topological quantum register, which can be addressed by braiding quasi-holes. We obtain the braid properties by direct inspection of the quas...

We have studied theoretically the effect of a tuneable lateral confinement on two-dimensional hole systems realised in III-V semiconductor heterostructures. Based on the 4 × 4 Luttinger description of the valence band, we have calculated quasi-onedimensional (quasi-1D) hole subband energies and anisotropic Landé g-factors. Confinement-induced band mixing results in the possibility to manipulate...

A preform sleeving technique is demonstrated that allows the fabrication of single-mode polymer microstructured fiber with the smallest core and hole dimensions yet reported to our knowledge. For a fixed triangular hole pattern a range of fibers is produced by adjustment to the operating conditions of the draw tower. Numerical modeling is carried out for one of the fibers produced with a 570-mi...

We present in this paper some properties of k-Lipschitz quasi-arithmetic means. The Lipschitz aggregation operations are stable with respect to input inaccuracies, what is a very important property for applications. Moreover, we provide sufficient conditions to determine when a quasi–arithemetic mean holds the k-Lipschitz property and allow us to calculate the Lipschitz constant k. Keywords— k-...

We show how any finite-dimensional algebra can be realized as an idempotent subquotient of some symmetric quasihereditary algebra. In the special case of rigid symmetric algebras, we show that they can be realized as centralizer subalgebras of symmetric quasi-hereditary algebras. We also show that the infinite-dimensional symmetric quasi-hereditary algebras we construct admit quasi-hereditary s...