Quasi-Chaplygin Systems and Nonholonimic Rigid Body Dynamics

We show that the Suslov nonholonomic rigid body problem can be regarded almost everywhere as a generalized Chaplygin system. Furthermore, this provides a new example of a multidimensional nonholonomic system which can be reduced to a Hamiltonian form by means of Chaplygin reducing multiplier. Since we deal with Chaplygin systems in the local sense, the invariant manifolds of the integrable examples are not necessary tori.Comment: minor changes, to appear in Letters in Mathematical Physic

An Extended Abel-Jacobi Map

We solve the problem of inversion of an extended Abel-Jacobi map $$\int_{P_{0}}^{P_{1}}\omega +...+\int_{P_{0}}^{P_{g+n-1}}\omega ={\bf z}, \qquad \int_{P_{0}}^{P_{1}}\Omega_{j1}+... +\int_{P_{0}}^{P_{g+n-1}}\Omega_{j1} =Z_{j},\quad j=2,...,n,$$ where $\Omega_{j1}$ are (normalised) abelian differentials of the third kind. In contrast to the extensions already studied, this one contains meromorphic differentials having a common pole $Q_1$. This inversion problem arises in algebraic geometric description of monopoles, as well as in the linearization of integrable systems on finite-dimensional unreduced coadjoint orbits on loop algebras.Comment: 11 page

EVALUATION OF HEALTH IN CHILDREN LIVING IN REGION WITH DEVELOPED CEMENT INDUSTRY

Evaluation of health state in children living in the city with developed cement industry showed presence of pre-nosological forms of ecologically conditioned diseases coming into being as a result of exposure with salts of heavy metals in cement dust. Key words: children, cement dust, bronchial asthma, pneumoconiosis, dermatosis, crystaluria, nephropathy, gestosis.(Voprosy sovremennoi pediatrii — Current Pediatrics. 2010;9(5):42-47

Measurements of the gamma-quanta angular distributions emitted from neutron inelastic scattering on 28Si

The characteristic gamma radiation from the interaction of 14.1 MeV neutrons with a natural silicon sample is investigated with Tagged Neutron Method (TNM). The anisotropy of gamma-ray emission of 1.779 MeV was measured at 11 azimuth angles with a step of ∠15°. The present results are in good agreement with some recent experimental data