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The aim of this paper is to propose a new methodology in the construction of spaces of test functions used in a weak formulation of the Boundary Value Problem. The proposed construction is based on the so called "two dimensional" approach where at first, we select a partition of a domain and second, a dimension of an approximating functional subspace on each partition element. The main advantage consists in the independent selection of the key parameters, aiming at achieving a requested quality of approximation with a reasonable complexity. We give theoretical justification and illustration on examples that confirm our methodology.

This paper presents a spatiotemporal analysis of hotspot areas based on the Extended Fuzzy C-Means method implemented in a geographic information system. This method has been adapted for detecting spatial areas with high concentrations of events and tested to study their temporal evolution. The data consist of georeferenced patterns corresponding to the residence of patients in the district of Naples (Italy) to whom a surgical intervention to the oto-laryngopharyngeal apparatus was carried out between the years 2008 and 2012.

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