Mathematical modeling of polymer film casting under biaxial stretching taking into account heat transfer

Polymer film casting is studied using a modified Vinogradov-Pokrovskii rheologicalmodel with heat transfer taken into account. Dependences of the film temperature, velocity, and width on the distance to the extruder exit was obtained and the effect of model parameters on these dependences was examined.     

Investigating semiconductor layered systems of photonics

The structure of a heterostructures-based semiconductor laser is experimentally investigated by complex means involving systems of scanning electron microscopy, scanning probe microscopy, and Raman spectroscopy. The possibilities of high-resolution microscopy for diagnostics of layered microelectronic systems are demonstrated.     

On the complete damping of oscillations of an inhomogeneous rod by means of a boundary control at one end

The process of damping oscillations of a rod consisting of two dissimilar segments and fixed at one end is considered. The damping is carried out by means of a boundary control at the other end of the rod.     

Weakened notions of equilibria and optimality in conflict problems

For arbitrary conflict and game problems stated in the most general setting, we introduce new notions of weak equilibrium and optimality, which are rather peculiar combinations of the notions of Pareto or Slater optimality and conflict stability. For an arbitrary conflict, these new notions simplify finding a unique fair solution suiting all participants.     

Construction of a Fuchs equation with four singular points and with given reducible 2 × 2 monodromy matrices on the complex projective line

On the complex projective line, we construct a Fuchs equation with four singular points and with given reducible 2 × 2 monodromy matrices such that the fundamental solution matrix of this equation realizes a given homomorphism.