this paper is devoted to the spectral theory (more precisely, tothe variational theory of the spectrum) of guided waves in anelastic half cylinder.  we use variational methods to investigateseveral aspects of propagating waves, including localization (seefigure 1), existence criteria and the formulas to find them. weapproach the problem using two complementary methods: thevariational methods fo...

this paper is devoted to the spectral theory (more precisely, tothe variational theory of the spectrum) of guided waves in anelastic half cylinder.  we use variational methods to investigateseveral aspects of propagating waves, including localization (seefigure 1), existence criteria and the formulas to find them. weapproach the problem using two complementary methods: thevariational methods fo...

The clustering problem is to assign labels to points in order to group them in a structurally meaningful way. This is often accomplished by defining cluster centroids in the vector space and assigning points to the cluster with the nearest centroid, as the k-means algorithm does. But this approach does not work for clusters that have unusual shapes, particularly if the clusters are interwoven o...

We describe the development and implementation of an eecient spectral element code for simulating transitional ows in complex three-dimensional domains. Critical to this eeort is the use of geometrically nonconforming elements that allow localized reenement in regions of interest, coupled with a stabilized high-order time-split formulation of the semi-discrete Navier-Stokes equations. Simulatio...

Traditionally, popular synonym acquisition methods are based on the distributional hypothesis, and a metric such as Jaccard coefficients is used to evaluate the similarity between the contexts of words to obtain synonyms for a query. On the other hand, when one tries to compile and clean a thesaurus, one often already has a modest number of synonym relations at hand. Could something be done wit...

Equations arising in general relativity are usually too complicated to be solved analytically and one must rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses on a class called spectral methods in which, typically, the various functions are expanded in sets of orthogonal polynomials or functions. First, a theoretical ...

We discuss the impact of modal filtering in Legendre spectral methods, both on accuracy and stability. For the former, we derive sufficient conditions on the filter to recover high order accuracy away from points of discontinuity. Computational results confirm that less strict necessary conditions appear to be adequate. We proceed to discuss a instability mechanism in polynomial spectral method...