The motion of a compressible viscous fluid around rotating body

We consider the motion of compressible viscous fluids around a rotating rigid obstacle when the velocity at infinity is non zero and parallel to the axis of rotation. We prove the existence of weak solution.     

Interior C 1, γ-Regularity for Weak Solutions of Nonlinear Second Order Parabolic Systems

The interior C ^{γ, γ/2}-regularity for the first gradient with respect to the space variables of a weak solution to a class of nonlinear second order parabolic systems is proven under the assumption that oscillations of coefficients are controlled by the ellipticity constant.     

On random permutations without cycles of some lenghts

We deal with random permutations of the symmetric group S_Nendowed with the Haar probability measure. The main purpose of the remark is to obtain uniform lower estimates for the probability of a permutation without cycles having lengths in some J ⊂ {1, . . . . N} . ThesetJcan itself depend on N. The only information used is a bound for the sum of reciprocals of elements in J.     

Magnetic Effects in Curved Quantum Waveguides

The interplay among the spectrum, geometry and magnetic field in tubular neighbourhoods of curves in Euclidean spaces is investigated in the limit when the cross section shrinks to a point. Proving a norm resolvent convergence, we derive effective, lower-dimensional models which depend on the intensity of the magnetic field and curvatures. The results are used to establish complete asymptotic expansions for eigenvalues. Spectral stability properties based on Hardy-type inequalities induced by magnetic fields are also analysed.     

A Law of the Iterated Logarithm for the Sojourn Time Process in Queues in Series

The object of this research in the sphere of queueing theory is the law of the iterated logarithm under the conditions of heavy traffic in queues in series. In this paper, the laws of the iterated logarithm are proved for the values of important probabilistic characteristics of the queueing system, like the sojourn time of a customer, and maximum of the sojourn time of a customer. Also, we prove that the sojourn time of a customer can be approximated by some recurrent functional. We also provide the results of statistical simulations for various system parameters and distributions.