On the absence of the new meromorphic first integral in the planar three–body problem

We consider the planar three‐body problem and prove that, besides some exceptional cases, in a neighborhood of the Lagrangian particular solution for this problem, there is no an additional meromorphic first integral.     

The necessary conditions for the existence of an additional integral in the problem of the motion of a heavy ellipsoid on a smooth horizontal plane

The equations of motion of an ellipsoid on a smooth horizontal plane are similar to the equations of motion of a heavy rigid body with a fixed point. In general, one integral is also lacking in order to integrate them. For a triaxial ellipsoid, the centre of mass of which coincides with the geometrical centre, it is proved that an additional integral is lacking (in the generic case).     

The number of additional singular points in the Riemann-Hilbert problem on a Riemann surface

We present an upper bound for the number of additional singular points that are sufficient to construct a system of linear equations with given regular singular points and a given monodromy on a Riemann surface.     

Value-sharing of meromorphic functions on a Riemann surface

We present some results on two meromorphic functions from S to sharing a number of values where S is a Riemann surface of one of the following types: compact, compact minus finitely many points, the unit disk, a torus, the complex plane.     

Linear problem of tracking a given motion under an integral constraint on control

We consider the problem of optimally tracking a given vector function by means of a generalized projection of the trajectory of a linear controlled object with an integral constraint on the control. The deviation from a given motion is measured in the metric of the space C ^m [0, T] of continuous vector functions of appropriate dimension m. We describe a constructive method for solving this optimization problem with a given accuracy.     

Non-existence of an invariant measure for a homogeneous ellipsoid rolling on the plane

It is known that the reduced equations for an axially symmetric homogeneous ellipsoid that rolls without slipping on the plane possess a smooth invariant measure. We show that such an invariant measure does not exist in the case when all of the semi-axes of the ellipsoid have different length.     

On an integral equation of first kind

We study an integral equation of first kind that arises in the study of inverse problems for nonlinear differential equations. The peculiarity of the equation is that the argument of the unknown function is a given function of two variables. We obtain conditions for this integral equation to have a unique solution. Translated fromMetody Matematicheskogo Modelirovaniya, 1998, pp. 54–58.     

Nonexistence of liouvillian solutions in the problem of motion of a rotationally symmetric ellipsoid on a perfectly rough plane

Using the Kovacic algorithm, the nonexistence of liouvillian solutions in the problem of motion of a rotationally symmetric ellipsoid on a perfectly rough horizontal plane for almost all values of parameters of the problem is proven.     

On the Wiener integral with respect to a sub-fractional Brownian motion on an interval

The domain of the Wiener integral with respect to a sub-fractional Brownian motion , , k≠0, is characterized. The set is a Hilbert space which contains the class of elementary functions as a dense subset. If , any element of is a function and if , the domain is a space of distributions.     

Cluster sets in the large of meromorphic functions on Riemann surfaces

In this note we obtain the relationships in the large between cluster sets, asymptotic values, exceptional values of meromorphic functions on hyperbolic Riemann surfaces. Some of these are generalizations of the boundary theorems given by E. F. Collingwood and M. L. Cartwright.