Many closed K-magnetic geodesics on S^2

2noIn this paper we adopt an alternative, analytical approach to Arnol’d problem about the existence of closed and embedded K-magnetic geodesics in the round 2-sphere ^2, where :^2→ℝ is a smooth scalar function. In particular, we use Lyapunov-Schmidt finite-dimensional reduction coupled with a local variational formulation in order to get some existence and multiplicity results bypassing the use of symplectic geometric tools such as the celebrated Viterbo’s theorem and Bottkoll results.openopenopenMusina, Roberta; Zuddas, FabioMusina, Roberta; Zuddas, Fabi

Bubbles with constant mean curvature, and almost constant mean curvature, in the hyperbolic space

Given a constant $k>1$, let $Z$ be the family of round spheres of radius $extrm{artanh}(k^{-1})$ in the hyperbolic space $mathbb{H}^3$, so that any sphere in $Z$ has mean curvature $k$. We prove a crucial nondegeneracy result involving the manifold $Z$. As an application, we provide sufficient conditions on a prescribed function $phi$ on $mathbb{H}^3$, which ensure the existence of a ${cal C}^1$-curve, parametrized by $arepsilonapprox 0$, of embedded spheres in $mathbb{H}^3$ having mean curvature $k +arepsilonphi$ at each point

Fractional operators as traces of operator-valued curves

We relate non integer powers ${\mathcal L}^{s}$, $s>0$ of a given (unbounded) positive self-adjoint operator $\mathcal L$ in a real separable Hilbert space $\mathcal H$ with a certain differential operator of order $2\lceil{s}\rceil$, acting on even curves $\mathbb R\to \mathcal H$. This extends the results by Caffarelli--Silvestre and Stinga--Torrea regarding the characterization of fractional powers of differential operators via an extension problem

Heterogeneity of filtration in the upper part of the geologic cross-section in Vostochno-Zakamsky oil region of the Republic of Tatarstan

In Tatarstan continuous oil mining has caused large scale pollution of underground water in upper part of the geological section. As a result, there is the increasing problem of quality drinking water supply in many settlements. In this connection, we examined the nature and major filtration heterogeneity Nizhnekazanskogo aquifer. This is the most productive part of the section on underground water for drinking water.Comprehensive review of a variety of data allowed us to establish five main factors: geological, structural, hypsometric, geomorphological and facial. Their combination forms an increased filtration background of rocks. First of all, results allow to choose optimal position of the new water wells and rational planning and exploration work for the underground drinking water

The role of english langauge at the Ural state medical university.

This study considers efficiency of the English language education in the Ural state medical university. The students survey showed the necessity of additional English classes to increase the level of vocational training and communication with colleagues

Weighted Sobolev spaces of radially symmetric functions

We prove dilation invariant inequalities involving radial functions, poliharmonic operators and weights that are powers of the distance from the origin. Then we discuss the existence of extremals and in some cases we compute the best constants.Comment: 38 page

Integration of a specialist into the international space: linguistic training and cross cultural interaction

The article considers the possibilities of international internships for medical students and doctors. The problems of insufficient linguistic training of health care manpower for representing Russian Federation at the international level are discussed. Ways to work out these issues are suggested