From Coulomb excitation cross sections to non-resonant astrophysical rates in three-body systems: 17^{17}Ne case

Coulomb and nuclear dissociation of $^{17}$Ne on light and heavy targets are studied theoretically. The dipole E1 strength function is determined in a broad energy range including energies of astrophysical interest. Dependence of the strength function on different parameters of the $^{17}$Ne ground state structure and continuum dynamics is analyzed in a three-body model. The discovered dependence plays an important role for studies of the strength functions for the three-body E1 dissociation and radiative capture. The constraints on the $[s^2]/[d^2]$ configuration mixing in $^{17}$Ne and on $p$-wave interaction in the $^{15}$O+$p$ channel are imposed based on experimental data for $^{17}$Ne Coulomb dissociation on heavy target.Comment: 12 pages, 13 figure

Обязанности судей судов общей юрисдикции

У сучасних умовах розвитку України як незалежної, демократичної і правової держави особливої актуальності набуває проблема конституційно-правового статусу судів суддів загальної юрисдикції. З судово-правовою реформою особливої уваги заслуговують обов’язки судів суддів загальної юрисдикції.In the modern terms of development of Ukraine as the independent, democratic and legal state of the special actuality is acquired by a problem constitutionally legal to status of courts of judges of general jurisdiction.В нынешних условиях развития Украины как независимого, демократичного и правового государства особенной актуальности заслуживает проблема конституционно-правового статуса судей судов общей юрисдикции. С судебно-правовой реформы особенного внимания заслуживают обязанности судей судов общей юрисдикции

Некоторый сравнительный опит формирования судейского корпуса Украины и зарубежных стран

У сучасних умовах розвитку України як незалежної, демократичної і правової держави особливої актуальності набуває проблема формування суддівського корпусу України і зарубіжних країн. З судово-правовою реформою особливої уваги заслуговує формування суддівського корпусу.In the modern terms of development of Ukraine as the independent, democratic and legal state of the special actuality is acquired by the problem of forming of judge corps of Ukraine and foreign countries. Forming of judge corps deserves with sudovo-pravovoy reform of the special attention.В нынешних условиях развития Украины как независимого, демократичного и правового государства особенной актуальности заслуживает проблема формирования судейского корпуса в Украине и в зарубежных странах. С судебно-правовой реформы особенного внимания заслуживает формирование судейского корпуса

Scattering Theory for Jacobi Operators with Steplike Quasi-Periodic Background

We develop direct and inverse scattering theory for Jacobi operators with steplike quasi-periodic finite-gap background in the same isospectral class. We derive the corresponding Gel'fand-Levitan-Marchenko equation and find minimal scattering data which determine the perturbed operator uniquely. In addition, we show how the transmission coefficients can be reconstructed from the eigenvalues and one of the reflection coefficients.Comment: 14 page

Long-Time Asymptotics of Perturbed Finite-Gap Korteweg-de Vries Solutions

We apply the method of nonlinear steepest descent to compute the long-time asymptotics of solutions of the Korteweg--de Vries equation which are decaying perturbations of a quasi-periodic finite-gap background solution. We compute a nonlinear dispersion relation and show that the $x/t$ plane splits into $g+1$ soliton regions which are interlaced by $g+1$ oscillatory regions, where $g+1$ is the number of spectral gaps. In the soliton regions the solution is asymptotically given by a number of solitons travelling on top of finite-gap solutions which are in the same isospectral class as the background solution. In the oscillatory region the solution can be described by a modulated finite-gap solution plus a decaying dispersive tail. The modulation is given by phase transition on the isospectral torus and is, together with the dispersive tail, explicitly characterized in terms of Abelian integrals on the underlying hyperelliptic curve.Comment: 45 pages. arXiv admin note: substantial text overlap with arXiv:0705.034

Spectrum of cosmic rays, produced in supernova remnants

Nonlinear kinetic theory of cosmic ray (CR) acceleration in supernova remnants is employed to calculate CR spectra. The magnetic field in SNRs is assumed to be significantly amplified by the efficiently accelerating nuclear CR component. It is shown that the calculated CR spectra agree in a satisfactory way with the existing measurements up to the energy $10^{17}$ eV. The power law spectrum of protons extends up to the energy $3\times 10^{15}$ eV with a subsequent exponential cutoff. It gives a natural explanation for the observed knee in the Galactic CR spectrum. The maximum energy of the accelerated nuclei is proportional to their charge number $Z$. Therefore the break in the Galactic CR spectrum is the result of the contribution of progressively heavier species in the overall CR spectrum so that at $10^{17}$ eV the CR spectrum is dominated by iron group nuclei. It is shown that this component plus a suitably chosen extragalactic CR component can give a consistent description for the entire Galactic CR spectrum.Comment: 4 pages with emulateapj, 3 figures, accepted for publication in the Astrophysical Journal Letter