CONTROL PROBLEM FOR A PARABOLIC SYSTEM WITH UNCERTAINTIES AND A NON-CONVEX GOAL

We consider the control problem for a parabolic system that describes the heating of a given number of rods. Control is carried out through heat sources that are located at the ends of the rods (only at one end or at both). The density functions of the internal heat sources and exact values of the temperature at the right ends of some rods are unknown, and only the segments of their change are given. The goal of choosing control is to ensure that at a fixed time moment the weighted sum of the average temperatures of the rods belongs to a non-convex terminal set for any admissible unknown functions. After a change of variables, this problem reduces to a one-dimensional differential game. Necessary and sufficient conditions for the game termination are found

Thioterpenoids as Potential Antithrombotic Drugs: Molecular Docking, Antiaggregant, Anticoagulant and Antioxidant Activities

Natural monoterpenes and their derivatives are widely considered as effective ingredients for the design and production of new biologically active compounds with high antioxidant, antimicrobial and anti-protozoa properties. In this study, we synthesized two series of thiotherpenoids “sulfide-sulfoxide-sulfone”, with different bicyclic monoterpene skeleton (bornane and pinane) structures. The effect of the obtained compounds on platelet aggregation was investigated by using the molecular docking technique. The obtained data revealed that all the synthesized compounds may act as potential inhibitors of platelet aggregation. Moreover, the studied sulfides have shown high antioxidant activity as revealed by lipid peroxidation (LPO) process inhibition in a non-cellular substrate containing animal lipids. The sulfides were able to inhibit erythrocyte oxidative hemolysis, to reduce the accumulation of secondary LPO products in cells and to prevent the oxidation of native oxyhemoglobin. Additionally, the corresponding sulfones and sulfoxides exhibited insignificant antioxidant activity. However, the sulfides were found to exhibit significant antiaggregant and anticoagulant effects. These findings suggest as well that the sulfides could serve as a leader compound for future research and possible practical applications