Fast and stable contour integration for high order divided differences via elliptic functions

In this paper, we will present a new method for evaluating high order divided differences for certain classes of analytic, possibly, operator valued functions. This is a classical problem in numerical mathematics but also arises in new applications such as, e.g., the use of generalized convolution quadrature to solve retarded potential integral equations. The functions which we will consider are allowed to grow exponentially to the left complex half plane, polynomially to the right half plane and have an oscillatory behaviour with increasing imaginary part. The interpolation points are scattered in a large real interval. Our approach is based on the representation of divided differences as contour integral and we will employ a subtle parameterization of the contour in combination with a quadrature approximation by the trapezoidal rule

Treatment dilemmas in a young man presenting with narcolepsy and psychotic symptoms.

Psychotic features can be present in both narcolepsy and psychosis, which can result in challenges in diagnosis and management. The prevalence of both conditions is low and the reports in young people are scarce. Our report illustrates the relevance of a thorough differential diagnosis as well as the need to explore treatment avenues based on the evidence available for both narcolepsy and psychosis symptoms to try and maximise the therapeutic impact

Flood risk assessment in an urban area: Vila Nova de Gaia

This paper proposes a methodology for flood risk assessment in a non fluvial urban flood. Two hazard classifications were considered; one with water depth and flow velocity classes and other with the product of water depth and flow velocity. The vulnerability assessment resulted in five classes obtained by cluster and principal components analysis. Flood risk maps were achieved by hazard and vulnerability classes’ crossover. The methodology is applied to a case study in the city of Vila Nova de Gaia. DTM with one meter resolution; HEC-HMS and HEC-RAS was applied to an urban catch- ment with one hour temporal scale; the 2001 statistical census tracts provide the demographic and social information. This methodology can be considered a straightforward and successful way to assess flood risk maps. However, the differences attained by the two hazard methods point out the need of further developments in the assessment of flood risk in stepped urban areas

Commutator methods for unitary operators

We present an improved version of commutator methods for unitary operators under a weak regularity condition. Once applied to a unitary operator, the method typically leads to the absence of singularly continuous spectrum and to the local finiteness of point spectrum. Large families of locally smooth operators are also exhibited. Half of the paper is dedicated to applications, and a special emphasize is put on the study of cocycles over irrational rotations. It is apparently the first time that commutator methods are applied in the context of rotation algebras, for the study of their generators.Comment: 15 page