We extend the standard theory of cosmological perturbations to homogeneous but anisotropic universes. We present an exhaustive computation for the case of a Bianchi I model, with a residual isotropy between two spatial dimensions, which is undergoing complete isotropization at the onset of inflation; we also show how the computation can be further extended to more general backgrounds. In presen...

In this paper we present a review of some of the methods currently used for solving the absorbing boundary problem for the two-dimensional scalar wave equation. We show the relationship between the methods of Lindman and Clayton and Engquist. Through this relationship we can derive discretizations of any rational approximation to the one-way wave equation. We prove that, for all the cases consi...

We define a sparse hermitian lattice Dirac matrix, H, coupling 2n+ 1 Dirac fermions. When 2n fermions are integrated out the induced action for the last fermion is a rational approximation to the hermitian overlap Dirac operator. We provide rigorous bounds on the condition number of H and compare them to bounds for the higher dimensional Dirac operator of domain wall fermions. Our main conclusi...

Country-wide data from the 2008-2009 cholera epidemic in Zimbabwe came from the authors of Reyburn et al.4 Country-level data was used in this exercise due to the unavailability of adequate city-level data, as in the other illustrative examples. We fit this model with maximum-likelihood via iterated filtering (using the mif2 algorithm, an improved version of that described in Ionides et al5) st...

Abstract The aim of this paper is to prove the theorem which generates many examples functions belonging a geometrically defined class uniformly starlike introduced by Goodman in 1991. Only very few explicit were known until now. Next we obtain inclusion relations between some subclasses convex and functions.