The interpolation of small datasets is challenging problem regarding the selection of interpolation methods and type of datasets. Here, for such analysis, the analysed data was taken in two hydrocarbon fields (“A” and “B”), located in the western part of the Sava Depression (in Northern Croatia). The selected reservoirs “L” (in the “A” Field) and “K” (“B”) are of Lower Pontian (Upper Miocene) age and belong to the Kloštar-Ivanić Formation. Due to strong tectonics, there are numerous tectonic blocks, each sampled with only a few wells. We selected two variables for interpolation—reservoirs permeabilities and injected volumes of field water. The following interpolation methods are described, compared and applied: Nearest Neighbourhood, Natural Neighbour (for the first time in the Sava Depression) and Inverse Distance Weighting. The last one has been recommended as the most appropriate in this study. Also, the presented research can be repeated in similar clastic environments at the same level hydrocarbon of exploration.

The semivariogram and the ordinary kriging analyses of porosity data from the Sava Depression (Northern Croatia), are presented relative to the Croatian part of the Pannonian Basin system. The data are taken from hydrocarbon reservoirs of the Lower Pontian (Upper Miocene) age, which belong to the Kloštar Ivanić Formation. The original datasets had been jack-knifed with the purpose of re-sampling and calculating the more reliable semivariograms. The results showed that such improvements can assist in the interpolation of more reliable maps. Both sets, made by the original and re-sampled data, need to be compared using geological recognition of isoline’s shapes (such as “bull-eye” or “butterfly” effects) as well as cross-validation results. This comparison made it possible to select the most appropriate porosity interpolation.

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In this paper we introduce a strong version of the Birkhoff-James orthogonality in Hilbert C * -modules. More precisely, we consider elements x and y of a Hilbert C * -module V over a C * -algebra A which satisfy x ≤ x + ya for all a ∈ A. We show that this relation can be described as the Birkhoff-James orthogonality of appropriate elements of V, and characterized in terms of states acting on the underlying C * -algebra A. Some analogous relations of this type are considered as well.

Abstract. In this paper we establish a generalization of the Dunkl-Williams inequality for finitely many elements in a normed linear space. As a consequence, we get some recently obtained results on the generalized triangle inequality and its reverse inequality. The case of equality for elements of a strictly convex normed linear space is also considered. (2000): 26D15. Mathematics subject classification