We develop a spectral factorization algorithm based on linear fractional transformations and on the Nevanlinna-Pick interpolation theory. The algorithm is recursive and depends on a choice of points (Zk, k 1, 2, ") inside the unit disk. Under a mild condition on the distribution of the zk's, the convergence of the algorithm is established. The algorithm is flexible and convergence can be influe...

We consider distribution properties of two-dimensional hybrid sequences (zk)k in the unit square of the form zk = ({kα}, xk), where α ∈ (0, 1) is irrational and (xk)k denotes a digital Niederreiter sequence. By definition, the construction of the sequence (xk)k relies on an infinite matrix C with entries in {0, 1}. Two special cases of such matrices were studied by Niederreiter (2009) and by Ai...

It is well known that Zk,m(t) is related to the virial coefficients of a quantum system of obstacles K at inverse temperature t. For example, G. E. Uhlenbeck [15] calculated the asymptotic behaviour of Zk,m(t) as t → ∞ in the special case where k = 1, m = 3, and K is a ball. I. McGillivray [14] obtained the full asymptotic series as t → ∞ for k = 1, m ≥ 3, and K an arbitrary, non-polar compact ...

We describe an explicit chain map from the standard resolution to the minimal resolution for the finite cyclic group Zk of order k. We then demonstrate how such a chain map induces a “Zk-combinatorial Stokes theorem”, which in turn implies “Dold’s theorem” that there is no equivariant map from an n-connected to an n-dimensional free Zk-complex. Thus we build a combinatorial access road to probl...

A prominent class of model FQH ground states is those realized as correlation function Zk(r)-algebras. In this paper, we study the interplay between these algebras and their corresponding wavefunctions. hopes realizing wavefunctions a unique densest zero energy state, propose generalization for projection Hamiltonians. Finally, using techniques from invariants binary forms, an ansatz computatio...

Proofs of security protocols are known to be error-prone and, owing to the distributed-system aspects of multiple interleaved protocol runs, awkward for humans to make. Hence work towards the automation of such proofs started soon after the first protocols were developed. The actual cryptographic operations in such proofs were idealized into so-called symbolic models. While symbolic models trad...