Introduction.Application of new methods, in particular, expert systems with mathematical apparatus, enables improving the recipe composition of multi-component food products in a wide range of content of components with their full or partial replacement by alternative ones, including natural functional and technological ingredients.Problem Statement. The creation and use of hybrid expert system of ice cream recipe modelling is impossible without using special mathematical apparatus.Purpose. To develop mathematical models and methods that enable to calculate the multicomponent ice cream recipes with the standard chemical composition taking into account the raw materials and functional and technological ingredients available at the manufacturer and to get the finished products of guaranteed quality.Materials and Methods. The methods of analysis and synthesis, generalization and scientific abstraction, as well as the method of mathematical modelling are used. The information base of the research is the results of laboratory studies of the quality of recipe components and ice creams of different chemical composition. Mathematical modelling with the use of tuples, systems of equations and restrictions, is made in MathCad and MathLab software packages.Results. As a result of the development of the expert system mathematical apparatus, a set-theoretical mathematical model of the finished product quality control at the stage of operative planning of new types of ice cream with increased nutritional value has been obtained; multi-component ice cream recipes have been optimized in terms of composition; and a model for determining the optimal set of control actions in the presence of technological defects in the calculation of recipes has been built.Conclusions. The created mathematical apparatus for modeling ice cream recipes has a large-scale application due to interchangeability of separate functional and technological components, which has been tested and confirmed during the trials in research laboratories. K e y w o r d s : mathematical apparatus, expert system, optimization, and ice cream recipe modelling.

PROBLEMS OF FORMING BARRIER-FREE ENVIRONMENT FOR PEOPLE WITH DISABILITIESABSTRACT. The article substantiates the need for developing municipal target-oriented programs in view of the needs of people with disabilities. It considers a municipal targetoriented program as an effective management tool, shows the features of its development. It analyzes the most essential needs of disabled people and people with limited mobility to build an accessible environment in Irkutsk Oblast. It describes the levels of development and management decision-making in the context of forming a barrier-free environment for individual with disabilities. It presents an analysis of the sociological research identifies problems in preparation of the municipal target-oriented program «Accessible Environment» in Irkutsk. This study has allowed to systematize the problems inherent in the structural subdivisions of the city, in building an accessible environment for people with disabilities. Development of municipal programs is an important mechanism in implementing governmental policy of forming a barrier-free environment for people with disabilities, thus allowing to take into account the interests of the socially vulnerable population groups and attracting to the maximum material, financial and labor resources.

Представлено математичну модель виробничої програми підприємства, у якого попит на продукцію змінюється у часі в залежності від сезону. Загальні витрати складаються з витрат на виробництво, зберігання та доставку із зовні. Можливості підприємства обмежуют

В роботі сформульована та формалізована задача розробки методу планування виконання проектів, до яких можна віднести і розробку технічних систем. Під проектом розуміють сукупність операцій, які необхідно виконати для досягнення конкретної мети за мінімаль

Chips Potato grains Bran Squeezed pumpkin seeds Regression equation Optimization The article is devoted to the development of a regression model of optimal parameters for the production of molded potato chips due to the requirements of nutritiology. Potato grits, rye bran, barley, squeezed pumpkin seeds were used to develop the technology of molded potato chips. The processing of the results was carried out by the method of a complete factor experiment, which gave the opportunity to describe mathematically the investigated process in some local area of the factor space, which lies around the selected point. Three factors were taken for the development of the regression equation: X 1-is the degree of cutting of bran, mr; X 2-temperature of baking-drying, °С; X 3-quantity of added water, ml. To verify the significance of the regression coefficients, additional parallel experiments were performed to determine the reproducibility variance. Therefore, in each point of the factor space a serie of three experiments was conducted. The homogeneity of the variance was checked by the Cochran criterion and compared to the table values. The statistical processing of experimental data consisted of calculating the coefficients of the regression equation and checking their significance. The founded coefficients of the regression equation were evaluated for statistical significance. The assessment was conducted according to Student's criterion. The obtained regression equation was checked for the adequacy of the investigated object, that is, its ability to adequately describe the surface of the response. The adequacy of the model was checked by Fischer's criterion. As a result of the experiment, regression equations were obtained in coded and natural form. On the basis of the obtained dependences graphic interpretation of mathematical model was carried out as isosurfaces of review. Application of methods of mathematical modeling allowed to obtain the parameters of production of molded potato chips with high nutritional value with given structural and mechanical parameters that will affect the strength of the final product.