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Анотация: Summary: This article deals with the problem of the mean value theorem for harmonic functions, defined on some given domain. Analysis of recent studies has been conducted. That allowed us to replace the classical metric sphere by so-called probabilistic sphere and the harmonic functions were the limits of the discrete functions, which describe the Brownian motion on the graph. The advantage of the described theory is that it can be devoted to the graph of arbitrary structure, and further it will be developed to the arbitrary stratified set. Several numerical ex- periments were made to demonstrate feasibility of our method.
Ключевые слова: Keywords: the mean value theorem, harmonic function, geometric graph, random walk, probabilistic sphere.
Данные для цитирования: Abdulkhayeva Z.T. Master’s Degree student Kazakh National Research Technical University after K.I. Satbayev Penkin O.M. Doctor of Math and Physics Sciences, professor Kazakh National Research Technical University after K.I. Satbayev . THE MEAN VALUE THEOREM FOR LAPLACIAN ON THE GRAPH. Физико-математические науки. ; ():-.