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Purpose of work. Development of proposals for desirability function calculation by interval arithmetic method. Obtained results. A connection was shown between multiple-criterial (vector) optimization problem and calculation of Harrington function (desirability function) values. Generalized desirability function was shown to be treated as a multiplicative convolution of partial desirabilities. Using golden section properties, a connection was discerned between hierarchy analysis methods and calculation of desirability function values. In this case the distribution of probable desirability function values among intervals determined in accordance with golden mean rule does coincide with values obtained by expert method. Application of golden proportion enables increasing the number of intervals; thus, it may prove convenient in improvement of Harrington function sensitivity. Conclusions. For partial desirability function in its explicit form such geometric characteristics were determined as values of tangent, curvature of curve and center of curvature coordinates. For a necessary averaged desirability system obtaining process control, such characteristics were determined in general and explicit form as partial desirability elasticity, generalized desirability elasticity relative to partial desirability, generalized desirability elasticity relative to a variable that has physical sense and respective dimension depending on particular subject area and affects partial desirability value. To determine the boundary value of one partial desirability being substituted for another partial desirability, the rate of substitution function and boundary rate of substitution elasticity function were established. Due to errors emerging in determination of desirability function values application of interval analysis methods was proposed. Application of interval numbers as presented in hyperbolic form was shown for calcutaion of partial and generalized desirability, A partial power series sum was determined relative to a variable presented in hyperbolic form. Suggestions. The method of calculation of Harrington function (desirability function) values at interval determination of arguments was shown to be eventually used in development of specifications and preliminary design of complicated engineering аnd organizational systems.

Purpose of work. Development of algorithms and software support of EXCEL-oriented methods for arraying of regression equations, using Chebyshev polynomials. Results. The work shows how aggravating geopolitical instability and effect of other pressure factors on the condition of economic systems in numerous countries leads to severe vulnerability of their financial systems. The result is slowing down of world economic growth, accelerated inflation pressure and business uncertainty. Under these circumstances the diagnostics of changes in directions, amounts, rates, regularity of business financial flows becomes quite important. Temporal variation of financial system influential parameters may be presented in the form of regression polynomials. In the present work Chebyshev polynomials were applied for their determination. This method was implemented in software products whose usage is limited by licensing restrictions. Therefore, the development of EXCEL-oriented software product applicable to formulation of regression equations using Chebyshev polynomials may be considered an urgent task. The work specifies calculation algorithms for Chebyshev regression polynomials up to fifth power inclusive, as well as transcribes block diagrams of their implementing algorithms. The determination of data packet, its index and data flows are also described. In order to compare the quality of Chebyshev polynomials in different powers a concept was introduced of relative error chain decilog. The work assumes that any discrepancy between indices of two adjacent flows means violation of process stability. The moment of stability violation corresponds to the highest number in pair of packets. Algorithm block diagram and numerical application example of our proposed method are shown.

Поставлена задача определения численного значения энтропии функции квантилей (энтропии Васичека) для непрерывной случайной величины. Для показательного распределения, распределения Чампернауна, логистического распределения, распределения арксинуса, распределения Рэлея, распределения Парето, распределения Лапласа получены в явном виде выражения для определения численных значений энтропии функции квантилей (энтропии Васичека). Для распределения Коши, распределения минимального значения, распределения максимального значения, двойного показательного распределения и распределения Вейбулла описана процедура решения поставленной задачи численными методами. Предложена единица измерения энтропии Васичека - вит.

The article is devoted to the problem of the crisis of personal and social identities as significant components of the “existential crisis” in the context of social transformation. Based on the ideas of existential phenomenology, the authors reveal the changing nature of the teacher identification system, suggest highlighting the notion of the “teacher identity” and consider the crisis nature of its formation. The authors revealed that the process of identifying future teachers is carried out in stages through the subsequent change of academic, educational, professional and professional identity. The transition from one type of identity to another occurs on the basis of identity crises.