Groups of diffeomorphisms and the solution of the classical Euler equations for a perfect fluid.

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On the motion of incompressible fluids

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Motion of slightly compressible fluids in a bounded domain. II

We study the problem of inviscid slightly compressible fluids in a bounded domain. We find a unique solution to the initial-boundary value problem and show that it is near the analogous solution for an incompressible fluid provided the initial conditions for the two problems are close. In particular, the divergence of the initial velocity of the compressible flow at time zero is assumed to be small. Furthermore we find that solutions to the compressible motion problem in Lagrangian coordinates depend differentiably on their initial data, an unexpected result for this type of non-linear equations.Comment: to appear in Communications in Contemporary Mathematic

Quantum gravitational measure for three-geometries

The gravitational measure on an arbitrary topological three-manifold is constructed. The nontrivial dependence of the measure on the conformal factor is discussed. We show that only in the case of a compact manifold with boundary the measure acquires a nontrivial dependence on the conformal factor which is given by the Liouville action. A nontrivial Jacobian (the divergent part of it) generates the Einstein-Hilbert action. The Hartle-Hawking wave function of Universe is given in terms of the Liouville action. In the gaussian approximation to the Wheeler-DeWitt equation this result was earlier derived by Banks et al. Possible connection with the Chern-Simons gravity is also discussed.Comment: 16 pages, TeX. This is the original, preprint version of the paper that with some modifications was published i

Sintering and properties of ZrO[2](Mg)-MgO composites

These studies shows which structures and properties have composites based on ZrO[2](Mg)-MgO sintered in a wide temperature range from 1400to 1650{о}С. X-ray diffraction showed an increasing of crystalline size with increasing of magnesia concentration. Decreasing of sintering temperature accompanied with an increasing of porosity and reduction of the compressive strength. Scanning electron microscopy showed the morphology of the composite structure. It is discovered that the pore size in the zirconia matrix in an order of magnitude higher than in magnesia inclusions

Deformations of 2k-Einstein structures

It is shown that the space of infinitesimal deformations of 2k-Einstein structures is finite dimensional at compact non-flat space forms. Moreover, spherical space forms are shown to be rigid in the sense that they are isolated in the corresponding moduli space.Comment: 12 pages. Manuscript accepted for publication on Journal of Geometry and Physic