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Giving the proper citations, it is shown that, except of Lemma 2.4 and Theorem 2.6, almost all the results of the paper in the title have been previously published for ordered hypersemigroups in Eur. J. Pure Appl. Math. and they are not new. There are also two results obtained from ordered semigroups just putting a "o" instead of "o" (that isn't a correct way to work), without reference to ordered semigroups on which the results on ordered hypersemigroups are based. One of them can be obtained as corollary to a theorem in Eur. J. Pure Appl. Math. as well, and it is not new. [ABSTRACT FROM AUTHOR]

Ecoregionalization is the process by which a territory is classified in similar areas according to specific environmental and climatic factors. The climate and the environment strongly influence the presence and distribution of vectors responsible for significant human and animal diseases worldwide. In this paper, we developed a map of the eco-climatic regions of Italy adopting a data-driven spatial clustering approach using recent and detailed spatial data on climatic and environmental factors. We selected seven variables, relevant for a broad set of human and animal vector-borne diseases (VBDs): standard deviation of altitude, mean daytime land surface temperature, mean amplitude and peak timing of the annual cycle of land surface temperature, mean and amplitude of the annual cycle of greenness value, and daily mean amount of rainfall. Principal Component Analysis followed by multivariate geographic clustering using the k-medoids technique were used to group the pixels with similar characteristics into different ecoregions, and at different spatial resolutions (250 m, 1 km and 2 km). We showed that the spatial structure of ecoregions is generally maintained at different spatial resolutions and we compared the resulting ecoregion maps with two datasets related to Bluetongue vectors and West Nile Disease (WND) outbreaks in Italy. The known characteristics of Culicoides imicola habitat were well captured by 2/22 specific ecoregions (at 250 m resolution). Culicoides obsoletus/scoticus occupy all sampled ecoregions, according to its known widespread distribution across the peninsula. WND outbreak locations strongly cluster in 4/22 ecoregions, dominated by human influenced landscape, with intense cultivations and complex irrigation network. This approach could be a supportive tool in case of VBDs, defining pixel-based areas that are conducive environment for VBD spread, indicating where surveillance and prevention measures could be prioritized in Italy. Also, ecoregions suitable to specific VBDs vectors could inform entomological surveillance strategies. [ABSTRACT FROM AUTHOR]

This paper outlines the results of a study aimed at charting the spread and development of the mathematical sciences in Sardinia over the period from 1720, the year in which the island was awarded to the Savoy dynasty following the Treaty of The Hague, to 1848, the year in which King Charles Albert of Sardinia placed Sardinia on a level political and administrative footing with the Kingdom's mainland territory. In particular, the paper analyses the role played in the transmission and spread of mathematics by the Savoy educational institutions. [ABSTRACT FROM AUTHOR]