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The study includes an analysis and evaluation of the time series of expenses of the research subject. The distribution of the analyzed data was examined with the use of graphs, such as: a histogram, normality and the Shapiro-Wilk test. The existence of outliers and extreme values was then searched for with a box plot. Chernoff Faces were then used to detect the monthly seasonality in the time series of the expenses under consideration. The regularities in the form of trend and seasonality detected during the data analyzes were confirmed by the binary model of multiple regression. The study includes forecasting of the time series of expenses with the use of the Klein model. The last stage of the research was the analysis and evaluation of the remainder of forecasts. The forecast of expenses for 2021 is an amount of PLN 575 248 346. In 2022, it increased to PLN 676 989 270.

In recent years, the evolution plan in the educational system and curriculum has been one of the most important topics in educational circles. This implies that the programs implemented in higher educational system have not been fully achieved for various reasons. One of the most important reasons is "not paying attention to the localization approach in the curriculum". Curriculum planning is one of the interdisciplines that can play an important role in influencing the curriculum process of humanities. However, the lack of a suitable native curriculum model has made it increasingly dependent on foreign sources and plenty of used terms are imported and translated, resulting in little attention to customs, culture, social, economic and political conditions of society. Although our culture and civilization derive from the most complete and highest order of divine teaching, the educational system has failed to provide an appropriate educational model that is appropriate to cultural conditions throughout the country. The present study has evaluated localization approach of Master's Degree in Curriculum Planning from the viewpoints of faculty members of public universities in Tehran in 2017-2018 academic year. To achieve the research purpose, the main question is "How is desirable of consideration the curriculum localization approach in curriculum planning field based on nine elements of Klein"? This research is descriptive-survey research. The questionnaire has been used for data collection. The statistical population of this study consists faculty members of educational sciences field and have been used Krejcie and Morgan sampling method. Descriptive and inferential statistical methods were used for data analysis. The results of evaluated elements showed that faculty members of Tehran state university ranked elements learning activities, teaching methods, time, materials and resources, grouping, place, and evaluation at a relatively desirable level and target and content elements as undesirable level. [ABSTRACT FROM AUTHOR]

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Abstract: V.I. Arnold [V. I. Arnold, Lobachevsky triangle altitudes theorem as the Jacobi identity in the Lie algebra of quadratic forms on symplectic plane, Journal of Geometry and Physics, 53 (4) (2005), 421–427] gave an alternative proof to the Lobachevsky triangle altitudes theorem by using a Poisson bracket for quadratic forms and its Jacobi identity, and showed that the orthocenter theorem can be extended on . In this paper, we find a new identity in the Poisson algebra of quadratic forms. Following Arnold’s idea, the goal of this article is to give alternative proofs to theorems, of Desargues, Pascal, and Brianchon, in , by using the Poisson bracket and the identity. [Copyright &y& Elsevier]

Abstract: An isomorphism between the Lobachevsky and de Sitter’s world geometries with the symplectic geometry and the Lie algebra of binary quadratic forms is used to derive the altitudes concurrence for the Lobachevsky and de Sitter triangles. [Copyright &y& Elsevier]

We consider a real analytic dynamical system G×M→M with nonempty fixed point subset M G . Using symmetries of G×M→M, we give some conditions which imply the existence of transitive Lie transformation group with G as isotropy subgroup. [ABSTRACT FROM AUTHOR]