Pronormality, contranormality and generalized nilpotency in infinite groups

This article is dedicated to some criteria of generalized nilpotency involving pronormality and abnormality. Also new results on groups, in which abnormality is a transitive relation, have been obtained

On the inner structure of 3-dimensional Leibniz algebras

Let $L$ be an algebra over a field $F$ with the binary operations $+$ and $[,]$. Then $L$ is called a left Leibniz algebra if $[[a,b],c]=[a,[b,c]]-[b,[a,c]]$ for all $a,b,c\in L$. We describe the inner structure of left Leibniz algebras having dimension 3

A Forecast Model of the Complex Negative Impact of Agricultural Production Technologies on Water Bodies

Introduction. The purpose of research is to develop a mathematical model for assessing and forecasting the complex negative impacts of agricultural technologies on water bodies. This problem is relevant because of the need to enlarge agricultural enterprises. The created model for forecasting is necessary to make an objective assessment, taking into account the complex effect of machine technologies applied to agricultural production and all biogenic elements that have a negative impact on water bodies. Materials and Methods. There was used the Spesivtsev – Drozdov method of logical-linguistic modeling, which allows giving expert knowledge a form mathematical model. Four experts were interviewed, and the obtained data became a subject of the regression analysis. The adequacy of the model was confirmed using the coefficient of determination and Fisher’s test. Results. A hierarchical system of 6 factors and 14 sub-factors was formed, including both the applied machine technologies and the management decisions on the matter. There was created a model containing a polynomial equation reflecting the influence of factors on the level of negative impact of technologies and equations that determine the influence of sub-factors on factors. Discussion and Conclusion. The created model can be used for practical purposes to support making decisions for planning, forecasting and selecting scenarios to modernize agricultural enterprises. The model equations make it possible to understand the significance of factors and sub-factors affecting the level of negative impact (diffuse load) on water bodies. This allows us to choose more effective ways to reduce the negative impact by choosing the most significant factors and/or sub-factors as objects of management