I offer a simple and useful formula for the resolvent of a small rank perturbation of
large matrices. I discuss applications of this formula, in particular, to analytical and
numerical solving of difference boundary value problems. I present examples connected
with such problems for the difference...
An averaging method for getting uniformly valid asymptotic approximations of the
solution of hyperbolic systems of equations is presented. The averaged system of equtions disintegrates into independent equations for non-resonance systems. We consider
the resonance conditions for some classes of solutions....
We show that the concept of complete symmetry group introduced by Krause (J. Math.
Phys. 35 (1994), 57345748) in the context of the Newtonian Kepler problem has
wider applicability, extending to the relativistic context of the Einstein equations dscribing spherically symmetric bodies with certain...
We propose a new approach to the mathematical description of light propagation in
a single-mode fiber light-guide (SMFLG) with random inhomogeneities. We investgate statistics of complex amplitudes of the electric field of light wave by methods of
the random group theory. We have analyzed the behavior...
The definition of "classical anomaly" is introduced. It describes the situation in which
a purely classical dynamical system which presents both a lagrangian and a hamitonian formulation admits symmetries of the action for which the Noether conserved
charges, endorsed with the Poisson bracket structure,...
A heavy top with a fixed point and a rigid body in an ideal fluid are important
examples of Hamiltonian systems on a dual to the semidirect product Lie algebra
e(n) = so(n) Rn
. We give a Lagrangian derivation of the corresponding equations of
motion, and introduce discrete time analogs of two integrable...
We demonstrate, using the symbolic method together with p-adic and resultant
methods, the existence of systems with exactly one or two generalized symmetries.
Since the existence of one or two symmetries is often taken as a sure sign (or as the
definition) of integrability, that is, the existence...