Search

Our work adds to the picture of second order differential operators with a full set of algebraic solutions, which we will call algebraic. We see algebraic Heun operators as pull-backs of algebraic hypergeometric operators via Belyi functions. We focus on the case when the hypergeometric one has a tetrahedral monodromy group. We find arithmetic conditions for the pull-back functions to exist. For each distribution of the singular points in the ramified fibers, we identify the minimal values of the exponent differences and we explicitly construct the dessin d’enfant corresponding to the pull-back function in the minimal cases. Then by allowing some parameters to vary, we find infinite families of such graphs, hence of Heun operators with tetrahedral monodromy.

Romanian forest management plans and policies, traditionally focused on timber production, need to reconsider the NWFPs (non-wood forest products) importance in the development of the socio-economic sector. Within the country’s forestry economy, the nature, quantity and weight of NWFPs are variable factors from one county to another, influenced to a large extent by the area covered by forests. The aim of this study is to unravel the most important NWFPs available in Arad County. In order to analyze the potential of NWFPs, data from the forest management plans of the ten subunits within the structure of the Arad Forest Directorate and statistical data from various institutions were used. In accordance with the purpose of the study, NWFPs were clustered into four categories as designed in the European project COST FP1203 European Non-Wood Forest Products (NWFPS) Network: mushrooms, tree products, understory plants and animal origin products. Eight different types of NWFPs were identified and analyzed using the analytic hierarchy process. Potential NWFPs were prioritized in accordance with the 19 criteria selected, and thus the most promising NWFPs were determined. Subsequently, AHP results were implemented in the Choice Expert Desktop software package. The results of the study indicate that Coturnix coturnix and Vulpes vulpes are in the top of the most promising NWFPs. More importantly, the obtained results can help to better address the management of NWFPs from Arad County.