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Abstract. The example of the mean statistical costs in a classical transportation model with restrictions on cargo supply is proposed.It is considered such restrictions on cargo supplies as: interdicted supplies; inferiorly restricted volume of supple; superiorly restricted volume of supple; obligatory volume of supply. It is performed calculations of the mean statistical costs on freight hauling in transportation model optimization with specified probabilities of the restrictions on supplies, and besides the actually arising or the of the concrete supplies are known for the supplies by the moment cargo is dispatching from them. For source data every appearing combinatorial variants represent solvable transportation tasks, which optimum solutions were found after inserting concrete extra restrictions on the volume supplies in the model.Problems of a similar nature solving in educational process during «Operations Research» course studying with computer technology and suitable software tools application will ensure on the basis of interdisciplinary connections implementation more effective development of competencies, essential for expectant professional activity of students.Keywords: educational process, interdisciplinary approach, transportation model, «generalized» supplier, restrictions on cargo supply, objective value, probability, statistical costs. Введение.В практике реализации оптимальных решений часто следует учитывать, что на состояние изучаемой системы и на значения ее параметров могут оказывать влияние различные случайные факторы. В таких задачах выбираемые управления становятся недетерминированными. При этом возникают проблемы, связанные с адекватным математико-инструментальным моделированием изучаемой системы [1][2]. Вероятностные схемы в исследовании операций используются, например, при использовании марковских моделей принятия решения; при решении парных матричных задач с нулевой суммой и статистической игры с «природой»; при построении дерева решений многоэтапного принятия решения в условиях риска и неопределенности; при имитационном моделировании технологических процессов и состояний экономических систем; при анализе рисков инвестиционных проектов; при планировании сроков завершения проекта в условиях недетерминированного времени выполнения предусмотренных в этом проекте работ [3][4][5][6][7]. В [7] приведены решения задачи распределения ресурсов и задачи

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It is shown that a recently conjectured form for the critical scaling function for planar self-avoiding polygons weighted by their perimeter and area also follows from an exact renormalization group flow into the branched polymer problem, combined with the dimensional reduction arguments of Parisi and Sourlas. The result is generalized to higher-order multicritical points, yielding exact values for all their critical exponents and exact forms for the associated scaling functions.

Experiments using a photomultiplier in the determination of the effective ionization coefficient of ambient room air stressed at very high voltages are described, and the results compared with data previously obtained by conventional current measurement techniques. Good agreement has been achieved, and the advantages of the photomultiplier method are discussed.