Kovalevski exponents and integrability properties in class A homogeneous cosmological models

Qualitative approach to homogeneous anisotropic Bianchi class A models in terms of dynamical systems reveals a hierarchy of invariant manifolds. By calculating the Kovalevski Exponents according to Adler - van Moerbecke method we discuss how algebraic integrability property is distributed in this class of models. In particular we find that algebraic nonintegrability of vacuum Bianchi VII_0 model is inherited by more general Bianchi VIII and Bianchi IX vacuum types. Matter terms (cosmological constant, dust and radiation) in the Einstein equations typically generate irrational or complex Kovalevski exponents in class A homogeneous models thus introducing an element of nonintegrability even though the respective vacuum models are integrable.Comment: arxiv version is already officia

From Clock Synchronization to Dark Matter as a Relativistic Inertial Effect

Lecture at BOSS2011 on relativistic metrology, on clock synchronization, relativistic dynamics and non-inertial frames in Minkowski spacetime, on relativistic atomic physics, on ADM canonical tetrad gravity in asymptotically Minkowskian spacetimes, on the York canonical basis identifying the inertial (gauge) and tidal degrees of freedom of the gravitational field, on the Post-Minkowskian linearization in 3-orthogonal gauges, on the Post-Newtonian limit of matter Hamilton equations, on the possibility to interpret dark matter as a relativistic inertial effect connected with relativistic metrology (i.e. clock synchronization) in Einstein GR.Comment: 90 pages. Lecture at BOSS201

Solution of the problem of identification of metal heating process model at heat exchange by radiation

The results of parametric identification of the mathematical model of fine elements heating by radiation in pusher furnaces of modern construction are given