Elkin O. Mathematical model and solution method of decomposition and tracing with regard for the region's space form

The research object is the optimization process of decomposition and tracing variants for regions with geometric, physics and geodesic properties. The research project is aimed at construction of a mathematical model and development of structural facilities of its realization for raising the effectiveness in solving discrete problems of decomposition as well as tracing with regard for the region's space form. Research methodology and techniques: theory of choice and decision-making, geometric design, graphs theory, digital and analogo-digital equipment. A mathematical model has been constructed of a basic optimization problem of decomposition and tracing of a given region taking into account a number of technical restrictions. The characteristics of the basic mathematical model have been studied, which made it possible to reduce the problem to decomposition of the region and subsidiary tracing within the region. A mathematical model and solution method are proposed for the region decomposition into equal rectangular sub-regions taking account of the region's space form. A mathematical model and solution method are offered for the problem of laying out a subsidiary tracing network for a general case of non-orthogonal area decomposition structure. Also developed and patent registered are instrument structures for the realization of the mathematical models suggested. Introduction of dissertation results is carried out in the Research technological institute of the P. Vasilenko Kharkiv national technical university of agriculture, in the Research and operating firm "STOZI", in the educational process of the International Solomon university. Fields of application: agro-industrial sector, urban area development, veterinary science, etc.