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2012 June 10th. Beginning of the project. August 7th. An article was accepted for publication. Authors: A.V. Arutyunov, N.G. Pavlova, S.E. Zhukovskiy Title: Equilibrium Price as a Coincidence Point of Two Mappings Abstract: The existence of an equilibrium price vector in a nonlinear market model is analyzed. In the model, the demand and supply functions are obtained by maximizing the producer utility and profit, respectively. Sufficient conditions for the existence of an equilibrium price vector and its stability with respect to small perturbations in the model are given. The results are consequences of theorems on the existence and stability of coincidence points in the theory of covering mappings. Journal: Computational Mathematics and Mathematical Physics Expected publication date: March 2013. October 29th. Participation in the conference "Tikhonov readings" MSU, Moscow, October 29-31. Speaker: S.E. Zhukovskiy Title: Correctness of the differential equations unsolved for the derivative of unknown function (in Russian) Abstract: Covering mappings theory is widely used for investigation of extremum and optimal control problems. Recently this theory has reinforced the arsenal of tools for investigation of differential and integral equations. The corresponding results are based on the theorems on Lipschitz perturbations of covering mappings which can be used instead of "classical" fixed point principles. In particular, covering mappings theory can be used to investigate correctness of differential equations unsolved for the derivative of unknown function. 2013 February 8th. Participation in the conference EPCO-2013, Portuguese Meetings in Optimal Control 2013, February 7-8, 2013, Faculdade de Engenharia da Universidade do Porto, Porto, Portugal. Speaker: S.E. Zhukovskiy Title: Covering Mappings. Theory and Applications Abstract: In the first part of the talk there will be introduced definitions of covering and locally covering mappings. A short review of the modern results in this area (such as coincidence points theorems and perturbation theorems) will be presented. The second part of the talk is devoted to applications of the mentioned results to differential equations. There will be presented sufficient conditions for local solvability of ordinary differential equations unsolved for the derivative of unknown function. Webpage of the conference: http://paginas.fe.up.pt/~mrpinho/EPCO/ February 10th. An article A.V. Arutyunov, N.G. Pavlova, S.E. Zhukovskiy, Equilibrium Price as a Coincidence Point of two mappings, Computational Mathematics and Mathematical Physics, 2013, Vol. 53, No 2, pp. 158--169 was published. May 8th. Participation in the conference Voronezh Spring Mathematical School "Contemporary Methods in Boundary Value Problems Theory", Voronezh, Russia, May 6-11, 2013, Speaker: S.E. Zhukovskiy Title: Covering Mappings in Metric Spaces (in Russian) Abstract: A brief discussion on modern results related to covering mappings will be presented. There will be introduced some properties of covering mappings acting in metric spaces and paerially ordered sets. May 15th. A thesis "Solvability of Constrained Dynamic Systems", by A.V. Arutyunov, F.L. Pereira, S. E. Zhukovskiy was submitted to the 52nd IEEE Conference on Decision and Control to be held in Florence, Italy, December 10-13, 2013. June 15th. A talk at the Dynamical Systems Seminar at the University of Porto Center of Mathematics Speaker: S.E. Zhukovskiy Title: Covering Mappings. Theory and Applications Abstract: In the first part of the talk there will be introduced definitions of covering and locally covering mappings. A short review of the modern results in this area (such as coincidence points theorems and perturbation theorems) will be presented. The second part of the talk is devoted to applications of the mentioned results to differential equations. There will be presented sufficient conditions for local solvability of ordinary differential equations unsolved for the derivative of unknown function. June 20th. A thesis "On an Application of Covering Mappings to an Initial Value Problem for Differential Inclusion" by S.E. Zhukovskiy, F.L. Pereira was accepted in the conference Kolmogorov Readings-VI, General Control Problems and Their Applications, Tambov, Russia, October 7-11, 2013. |