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We consider inverse problems for differential systems in the presence of random perturbations. By the method of additional variables, we establish sufficient conditions for the representation of stochastic differential equations of the second order in the form of stochastic Lagrange equations, as well as for the representation of stochastic differential equations of the first order in the form of stochastic canonical equations. The obtained results are illustrated by specific examples., Author(s): M. I. Tleubergenov [sup.1], D. T. Azhymbaev [sup.2] Author Affiliations: (1) grid.473156.2, Institute of Mathematics and Mathematical Modelling, , Pushkin Str., 125, 050010, Almaty, Kazakhstan (2) grid.443407.0, Zhubanov Aktyubinsk [...]

Given second-order Ito stochastic equations, we construct almost surely equivalent stochastic equations of the Lagrangian structure. We establish the conditions for the direct and indirect analytical representations of the Lagrangian in the presence of random perturbations. The results obtained are illustrated by examples. [ABSTRACT FROM AUTHOR]

Objective: The analysis of the tumor resection degree using 5-ALA fluorescence in patients with a high level of malignancy. Materials and methods: The study included 18 patients with glial tumors of high malignancy degree. Out of those 18 patients, 8 patients were male, 10 patients were female. The average age was 44 years. The age categories of patients were from 26 to 66 years. Out of 18 patients, glioblastoma was diagnosed in 10 patients, glioma G = III was in 6 patients, and G = II was in 2 patients. Results: Total removal of tumors using 5-ALA was achieved in 13 patients, which was 72%. Subtotal removal was in 3 patients (17%) and partial removal was achieved in 2 patients, i.e in 11% of patients. Conclusion: The use of 5-ALA fluorescence makes it possible to remove totally the volume of brain tumors without causing a gross neurological deficit and increases the survival rate without progression. For optimal resection with glioblastomas, the use of 5-ALA is currently included in the standard scheme of operative treatment in Europe, the USA, Japan and Australia, and now it has found its application in the Republic of Kazakhstan. [ABSTRACT FROM AUTHOR]