The combined application of Singular Spectrum Analysis (SSA) and Cluster Analysis to the automatic smoothing of raw kinematic signals is an alternative to the use of traditional digital filtering and spline based methods. SSA is a non parametric technique that decomposes original time series into a number of additive time series each of which can be easily identified as being part of the noise ...

Examples are constructed of Laplace-Beltrami operators and graph Laplacians with singular continuous spectrum. In previous papers in this series [6,3,5,2,8], we have explored the occurrence of singular continuous spectrum, particularly for Schrodinger operators and Jacobi matrices. In this note, we'll construct examples of graphs whose Laplacians and Riemannian manifolds whose Laplace-Beltrami ...

The well known strombolian activity at Stromboli volcano is occasionally interrupted by rarer episodes of paroxysmal activity which can lead to considerable hazard for Stromboli inhabitants and tourists. On 5 April 2003 a powerful explosion, which can be compared in size with the latest one of 1930, covered with bombs a good part of the normally tourist-accessible summit area. This explosion wa...

The Baire category theorem implies that the family, F,of dense sets G6 in a fixed metric space, X , is a candidate for generic sets since it is closed under countable intersections; and if X is perfect (has no isolated point), then A E F has uncountable intersections with any open ball in X. There is a long tradition of soft arguments to prove that certain surprising sets are generic. For examp...

We give a mathematically rigorous analysis which confirms the surprising results in a recent paper [2] of Benilov, O’Brien and Sazonov about the spectrum of a highly singular non-self-adjoint operator that arises in a problem in fluid mechanics. MSC-class: 34Lxx, 76Rxx, 65F15, 65Q05 keywords: spectrum, non-self-adjoint, fluid mechanics, pseudospectra, eigenvalue, basis.

We prove several results showing that absolutely continuous spectrum for the Laplacian on radial trees is a rare event. In particular, we show that metric trees with unbounded edges have purely singular spectrum and that generically (in the sense of Baire) radial trees have purely singular continuous spectrum.

A bstract . For Sturm-Liouville operators on the half line, we show that the property of having singular, singular continuous, or pure point spectrum for a set of boundary conditions of positive measure depends only on the behavior of the potential at infinity. We also prove that existence of recurrent spectrum implies that of singular spectrum and that “almost sure” existence of L2-solutions i...

There are three ways to determine the spectrum of a clinical photon beam: direct measurement, modelling the source and reconstruction from ion-chamber measurements. We focus on reconstruction because the necessary equipment is readily available and it provides independent confirmation of source models for a given machine. Reconstruction methods involve measuring the dose in an ion chamber after...

In a variety of contexts, we prove that singular continuous spectrum is generic in the sense that for certain natural complete metric spaces of operators, those with singular spectrum are a dense Gδ . In the spectral analysis of various operators of mathematical physics, a key step, often the hardest, is to prove that the operator has no continuous singular spectrum, that is, that the spectral ...