Vera Abzianidze

With the intensive development of industry and population growth, environmental protection and the correct use of natural resources are of great importance. For a proper assessment, monitoring and management of the environmental situation, it is necessary to possess cartographic, environmental and other information about all its components, analyze this information and make the right decisions. There are various ways to solve this problem. The article provides a brief description of the method that we applied to assess the ecological state in one of the sections of the Mtkvari (Kura), in particular, the content of heavy metals in the waters of the Mtkvari (Kura) River in the Zagesi – Red Bridge section. The degree of anthropogenic impact was assessed by methods of mathematical modeling and modern technologies of the geographic information system. In the mathematical processing of information, a whole range of mathematical modeling tools were used - starting with mathematical statistics and ending with a complex model. The main functions of the geographic information system were also used: information organization, its processing, analysis, verification, visualization, and etc. As a result, thematic maps were created, that clearly show the degree of pollution of the river section, as well as the dynamics of changes in the concentration of heavy metals. This method can be used for environmental assessment of various objects. With its help, it is possible to carry out environmental monitoring simply and at low cost.

The author of this article considered the question of the effectiveness of the application of mathematical methods in the analysis of ecological processes in the fourth issue of this journal in 2018. In the proposed article, the authors continue to develop this idea, considering this time the human interaction with the environment. The main focus of the authors is on showing the important role of mathematics in human interaction with the environment. It is known that anthropogenic objects (populated points, various industrial enterprises, transport, etc.) as a result of their functioning have different effects on a person. For the study of these processes, there is a need to develop sciences to forecast the state of the environment and manage the processes of ecological balance in the geological environment, between nature and the technosphere (technological activity of people). In the study of these processes, mathematics is assigned a decisive role. However, the subject of research is invariably complicated, because the study requires the combination of interrelated processes of the most diverse nature. We notice that the organization of these studies is very difficult, because The study of human anthropogenic influence on the environment requires the integration of the activities of a number of specialists in various fields.

For the description and classification of geological objects and ecological systems, for the forecasting of its actions it’s needed to be developed appropriate mathematical models. The process of such model creation is quite difficult and consists of several stages. Data obtained from the observations or experiments are processed by using of statistical analysis. The development of computer technologies made it possible to apply new technologies in geology and ecology. The article describes usage of software package Excel's tools and a number of functions in the statistical analysis. Basic statistical indicators, such as the mean value, dispersion, asymmetry, square root dispersion, excess, etc. are located in one option, some other essential statistical characteristics can be defined by the corresponding functions (mainly by statistical and mathematical), which is described in the article in detail. 

The paper examines the fossilized trees of the Goderdze fossil forest based on visual, polarization-microscopic descriptions, X-ray phase and X-ray fluorescence analysis. Formation of petrified trees of Goderdze fossil forest is the result of crystallization of solutions of low-temperature hydrothermal process after the volcanism activity of Goderdze series. Horizontal (transverse) and vertical (radial and tangential) sections of petrified wood samples can be visually (macroscopically) observed on the surface of the plate with annual light and dark parallel bands of wood growth, and with the gemological and polarizing microscope, the thinnest white can be clearly seen along with the annual light and dark parallel bands of wood growth. and dark parallel lines that are completely filled with quartz group minerals crystallized at different temperatures. Petrification of wood in Goderdze was carried out in several stages. At the initial stage, the formation of fully crystalline quartz took place, at the intermediate stage, fibrous quartz and chalcedony were formed, and at the last stage of crystallization, low-temperature microcrystalline -cristobalite and -tridymite were separated.