Perturbative Symmetry Approach

Perturbative Symmetry Approach is formulated in symbolic representation. Easily verifiable integrability conditions of a given equation are constructed in the frame of the approach. Generalisation for the case of non-local and non-evolution equations is disscused. Application of the theory to the Benjamin-Ono and Camassa-Holm type equations is considered.Comment: 16 page

Analysis of segregated boundary-domain integral equations for mixed variable-coefficient BVPs in exterior domains

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2011 Birkhäuser Boston.Some direct segregated systems of boundary–domain integral equations (LBDIEs) associated with the mixed boundary value problems for scalar PDEs with variable coefficients in exterior domains are formulated and analyzed in the paper. The LBDIE equivalence to the original boundary value problems and the invertibility of the corresponding boundary–domain integral operators are proved in weighted Sobolev spaces suitable for exterior domains. This extends the results obtained by the authors for interior domains in non-weighted Sobolev spaces.The work was supported by the grant EP/H020497/1 ”Mathematical analysis of localised boundary-domain integral equations for BVPs with variable coefficients” of the EPSRC, UK

Ground experiments for finding principles and working out methods for preventing adverse effects of weightlessness on the human organism

A comparative assessment of the effectiveness of different prophylactic procedures to prevent the adverse effects of weightlessness is presented. It is concluded that: physical training is most effective but no single method by itself produces the full effect, and an adjustment of regimes to one another enhances the effect. The approved complex of prophylactic procedures affected basic changes occurring in hypokinesia: deficit of muscular activity, no or reduced BP hydrostatic component, reduced volume of blood circulation, reduced hydration level, and the application of various prophylactic complexes during 49 day antiorthostatic hypodynamia eliminated or reduced the adverse effects of weightlessness in simulation

Algebraic entropy for semi-discrete equations

We extend the definition of algebraic entropy to semi-discrete (difference-differential) equations. Calculating the entropy for a number of integrable and non integrable systems, we show that its vanishing is a characteristic feature of integrability for this type of equations

Relativistic theory of the double photoionization of helium-like atoms

A fully relativistic calculation of the double photoionization of helium-like atoms is presented. The approach is based on the partial-wave representation of the Dirac continuum states and accounts for the retardation in the electron-electron interaction as well as the higher-order multipoles of the absorbed photon. The electron-electron interaction is taken into account to the leading order of perturbation theory. The relativistic effects are shown to become prominent already for the medium-Z ions, changing the shape and the asymptotic behaviour of the photon energy dependence of the ratio of the double-to-single photoionization cross section

Classical properties of low-dimensional conductors: Giant capacitance and non-Ohmic potential drop

Electrical field arising around an inhomogeneous conductor when an electrical current passes through it is not screened, as distinct from 3D conductors, in low-dimensional conductors. As a result, the electrical field depends on the global distribution of the conductivity sigma(x) rather than on the local value of it, inhomogeneities of sigma(x) produce giant capacitances C(omega) that show frequency dependence at relatively low omega, and electrical fields develop in vast regions around the inhomogeneities of sigma(x). A theory of these phenomena is presented for 2D conductors.Comment: 5 pages, two-column REVTeX, to be published in Physical Review Letter

Vector, Axial, Tensor and Pseudoscalar Vacuum Susceptibilities

Using a recently developed three-point formalism within the method of QCD Sum Rules we determine the vacuum susceptibilities needed in the two-point formalism for the coupling of axial, vector, tensor and pseudoscalar currents to hadrons. All susceptibilities are determined by the space-time scale of condensates, which is estimated from data for deep inelastic scattering on nucleons

Evolution of magnetic fields through cosmological perturbation theory

The origin of galactic and extra-galactic magnetic fields is an unsolved problem in modern cosmology. A possible scenario comes from the idea of these fields emerged from a small field, a seed, which was produced in the early universe (phase transitions, inflation, ...) and it evolves in time. Cosmological perturbation theory offers a natural way to study the evolution of primordial magnetic fields. The dynamics for this field in the cosmological context is described by a cosmic dynamo like equation, through the dynamo term. In this paper we get the perturbed Maxwell's equations and compute the energy momentum tensor to second order in perturbation theory in terms of gauge invariant quantities. Two possible scenarios are discussed, first we consider a FLRW background without magnetic field and we study the perturbation theory introducing the magnetic field as a perturbation. The second scenario, we consider a magnetized FLRW and build up the perturbation theory from this background. We compare the cosmological dynamo like equation in both scenarios