The territory of the Polar Urals is characterized by significant forecast resources of natural zeolites. In case of their successful development, the resources of the zeolite deposits can provide a positive impact on the development of a number of industries in the adjacent regions of the Urals and Western Siberia. At the same time, the available data about the zeolite-bearing rocks of the Polar Urals present in published research paper and materials of geological funds is rather contradictory. The results of research performed by different scientific groups often contain opposed conclusions on the mineralogical composition, the content of the commercial component in the ore, as well as on the ore reserves calculation and the potential of commercial exploitation for the same mineral occurrences. In many respects, this situation can be explained by the complexity of the geological and geomorphological conditions of the territory under consideration, the remoteness of the promising mineral occurrences from large scientific and industrial centers, and the variety of ore occurrences. This work presents the study results of lithological–petrographic features and the material composition of the eluvial debris of the Middle–Late (Givetian–Frasnian) Devonian zeolite-bearing rocks of the volcanogenic-sedimentary origin within the Naunpe area of the Polar Urals., The main objective of the proposed research was to evaluate the economic feasibility of their development and possible directions for commercial exploitation of this type of ores. Research methods included petrographic study of samples of zeolite-bearing rocks in thin sections, SEM-EDS, determination of the total mineral composition by XRD and the chemical composition by XRF. Within the Naunpe area, the outcrops of zeolite-bearing rocks on the surface are represented by blankets and debris of small lumpy–gravel eluvial deposits with indistinct outlines. Macroscopically, zeolite-bearing eluvial deposits are represented by reddish or pinkish in color, massive and relatively homogenous rocks. The ore occurrences are well interpreted based on the remote sensing data. According to the results of petrographic, lithological, and mineralogical studies, three main rock types were distinguished among the eluvial debris deposits: zeolite-bearing crystallo–lithoclastic tuffs of the mafic, intermediate, and felsic composition, and also tuffoargillites, and siliceous rocks., and Crystallo–lithoclastic tuffs and tuffoargillites contain Ca-zeolites, represented mainly by laumontite (13.8–18.9 %), which fill small open spaces between crystallites and lithoclasts. Volcanic glass fragments and feldspars from tuffoargillites are replaced partially or completely by zeolites. The content of zeolites in these rocks is even lower (less than 10 %). The characteristic features of the studied zeolite-bearing rocks from the ores of the known deposits of the Polar and Subpolar Urals have higher contents of Fe2O3, CaO и Na2O and lower content of K2O. The obtained results show that the studied rocks are quite complex, diverse, and polygenetic, as well as their formation is a result of several stages of post-volcanic authigenic mineral formation. The rather low content of zeolite minerals in these rocks and high variability of the material composition decrease the industrial potential of that eluvial debris deposits as an object of mineral raw material base. At this, they can be considered as prospecting indicator for prospecting the areas with a similar geological structure.
This paper is inspired by recent results [15, 16] which have shown that a multiplicative generator of a strict triangular norm can be reconstructed from the first partial derivatives of the triangular norm on the segment {0} x [0,1]. The strict triangular norms to which this method is applicable have been called zero-reconstructible triangular norms. This paper shows that every continuous triangular norm can be approximated (with an arbitrary precision) by a zero-reconstructible one, and thus substantiates the significance of this subclass of strict triangular norms.
Zero-term rank of a matrix is the minimum number of lines (rows or columns) needed to cover all the zero entries of the given matrix. We characterize the linear operators that preserve zero-term rank of the
$m \times n$ real matrices. We also obtain combinatorial equivalent condition for the zero-term rank of a real matrix.