On the possibility of applying the quasi-isothermal St\"ackel's model to our Galaxy

An earlier derived quasi-isothermal St\"ackel's model of mass distribution in stellar systems and the corresponding formula for space density are applied to our Galaxy. The model rotation curve is fitted to HI kinematical data. The structural and scale parameters of the model are estimated and the corresponding density contours for our Galaxy are presented.Comment: 7 pages, 3 figures. Accepted for publication in Baltic Astronomy (BA

Higgsless Electroweak Model and Contraction of Gauge Group

A modified formulation of the Electroweak Model with 3-dimensional spherical geometry in the target space is suggested. The {\it free} Lagrangian in the spherical field space along with the standard gauge field Lagrangian form the full Higgsless Lagrangian of the model, whose second order terms reproduce the same experimentally verified fields with the same masses as the Standard Electroweak Model. The vector bosons masses are automatically generated, so there is no need in special mechanism of spontaneous symmetry breaking. The limiting case of the modified Higgsless Electroweak Model, which corresponds to the contracted gauge group $SU(2;j)\times U(1)$ is discussed. Within framework of the limit model Z-boson, electromagnetic and electron fields are interpreted as an external ones with respect to W-bosons and neutrino fields. The W-bosons and neutrino fields do not effect on these external fields. The masses of all particles remain the same, but the field interactions in contracted model are more simple as compared with the standard Electroweak Model due to nullification of some terms.Comment: Talk at the International Workshop "`Supersymmetries and Quantum Symmetries"' (SQS-09), Dubna, Russia, July 29 -- August 3, 2009, 11

The Quantum Symplectic Cayley-Klein Groups

The contraction method applied to the construction of the nonsemisimple quantum symplectic Cayley-Klein groups $Fun(Sp_q(n;j))$. This groups has been realised as Hopf algebra of the noncommutative functions over the algebra with nilpotent generators. The dual quantum algebras $sp_q(n;j)$ are constructed.Comment: 6 pages, LaTeX, submitted to Proceedings of ' II International Workshop on Classical and Quantum Integrible Systems' (Dubna, 8-12 July,1996), to be published in Int.J.Mod.Phy

Contractions of Integrable Equations

The contraction is applied to obtaining of integrable systems associated with nonsemisimple algebras. The effect of contraction is splitting off some components from initial system without loss of integrability.Comment: 6 pages, LaTeX, submitted to Proceedings of ' II International Workshop on Classical and Quantum Integrible Systems' (Dubna, 8-12 July,1996), to be published in Int.J.Mod.Phy