Convergence of optimal controls in some optimization problems

We consider the behavior of bundles of optimal controls when the initial state of the system goes to some given vector. We investigate three types of optimization problems: problems with fixed process length and a free right endpoint; problems with fixed process length and a fixed right endpoint; time-optimal problems. The article is a review of recent results obtained by the author. __________ Translated from Nelineinaya Dinamika i Upravlenie, No. 4, pp. 301–314, 2004.     

Fano direct products as rationally connected fibrations

Combining the connectedness principle of Shokurov and Kollár, we develop a new technique of studying birational maps of natural Fano fiber spaces. We prove that the only structures of a rationally connected fibration on direct products of typical Fano varieties are projections onto the factors. In particular, the groups of biregular and birational self-maps of Fano direct products coincide. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 4, pp. 183–206, 2004.     

Calculation of the bond ionicity in complex oxides

A technique for calculating the bond ionicity of crystalline materials using electronegativities of elements and taking into account the structure of polyhedra of the complex-oxide structure is proposed.     

The effect of technological microdefects of structure on service life of polymer materials

Within the framework of the kinetic theory of strength, relations for estimation of durability of thermoplastic materials under stationary and non-stationary thermomechanical impacts are obtained It is shown that durability decreases linearly with increase in the natural (Napierian) logarithm of the mean size of microcracks formed during manufacturing of polymer products. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 3–6, July, 2007.