In Extreme Value statistics we often encounter testing procedures for assessing the presence of the Gumbel domain, attached to the simple null hypothesis of shape parameter γ = 0, thus praising the selection of extreme domains of attraction. However, the problem of assessing for light tailed distributions with finite or infinite right endpoint is seldom referred. The latter is an impending problem of practical importance, particularly at the enrollment of subsequent estimation of extremal features such as small exceedance probabilities. In this paper, we present two test statistics whose asymptotic behavior, albeit under some restrictive yet reasonable conditions, enables to distinguish light tailed distribution functions with finite right endpoint from those with infinite endpoint lying in the Gumbel domain. An illustrative example is provided via application to significant wave height data recorded at Figueira da Foz, Portugal, from 1958 until 2001

In this short note, we provide a brief proof for a recent determinantal formula involving a particular family of banded matrices.

The distance geometry problem (DGP) consists in finding an embedding in a metric space of a given weighted undirected graph such that for each edge in the graph, the corresponding distance in the embedding belongs to a given distance interval. We discuss the relationship between the existence of a graph embedding in a Euclidean space and the existence of a graph embedding in a lattice. Different approaches, including two integer programming (IP) models and a constraint programming (CP) approach, are presented to test the feasibility of the DGP. The two IP models are improved with the inclusion of valid inequalities, and the CP approach is improved using an algorithm to perform a domain reduction. The main motivation for this work is to derive new pruning devices within branch-and-prune algorithms for instances occurring in real applications related to determination of molecular conformations, which is a particular case of the DGP. A computational study based on a set of small-sized instances from molecular conformations is reported. This study compares the running times of the different approaches to check feasibility.

In this paper, a new tridiagonal matrix, whose eigenvalues are the same as the Sylvester-Kac matrix of the same order, is provided. The interest of this matrix relies also in that the spectrum of a principal submatrix is also of a Sylvester-Kac matrix given rise to an interesting spectral interlacing property. It is proved alternatively that the initial matrix is similar to the Sylvester-Kac matrix.

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