Uvarov R. Interlocation formulas of RFM and their applications in POLYE systems

Object of research is interlocation formulas of RFM and their applications in modelling the physical-mechanical fields, ecological processes, and in constructing the normalized equations of solids in problems of geometrical design. Purpose of work is development and statement of interlocation formulas and their applications in creating the methods of constructing the normalized equations of solids, blending and blending on skeleton, calculating the phisycal-mechanical phields, building mathematical and computer models for prediction of ecological situation. In work the R-functions method and interlocation formulas, methods of geometrical design (blending and blending on skeleton), computational methods are used. The Lagrange and Hermite interlocation (generalized interpolation) formulas are developed and stated The theorem on completeness of constructed interlocation sheaves are proved. The constructive apparatus of R-functions is improved. For problems of blending the new R-operation, which rounds bya circle, is constructed. For the first time interlocation formulas is applied to constructing the normalized functions, which describe blending on skeleton. The new method of constructing the solids (based on the interlocation formulas and blending on skeleton) is developed. It allows to construct the normalized equation of turbine blade. The mathematical model for prediction of ecological situation, using constructive tools of the theory of R-functions, is built (for the first time the border of Ukraine and function of atmosphere pollution are analytically built; for taking into account attenuation pattern of pollution function the Lagrange interlocation formula is modified). With the mathematical model the specialized program system was developed. The flexure problem of rigidly clamped plate with local combined loadings is solved. Sphere of use can be different areas of mechanical engineering, power-engineering industry, and program system can be of use to conservancy and sanitation services for predictionof ecological and epidemiological situations.