An extension of the theory of Fredholm determinants

David Ruelle

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We give a survey of results concerning various classes of bounded linear operators in a Banach space defined by means of kernels and ranges. We show that many of these classes define a spectrum that satisfies the spectral mapping property.

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It is shown, that the function $\begin{matrix} H (x) & = \sum_{k = - \infty}^{\infty} e^{- k^{2} x} \\ satisfies the relation \\ H (x) & = \sum_{n = 0}^{\infty} \frac{{(2 π)}^{2 n}}{(2 n)!} H^{(n)} (x) . \end{matrix}$

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CAPS in Z(2,n)

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We consider point sets in (Z^2,n) where no three points are on a line – also called caps or arcs. For the determination of caps with maximum cardinality and complete caps with minimum cardinality we provide integer linear programming formulations and identify some values for small n.

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Weighting quantitative and qualitative variables in clustering methods.

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Description of individuals in ill-structured domains produces messy data matrices. In this context, automated classification requires the management of those kind of matrices. One of the features involved in clustering is the evaluation of distances between individuals. Then, a special function to calculate distances between individuals partially simultaneously described by qualitative and quantitative variables is required. In this paper properties and details of the metrics...