An algebraic procedure for obtaining oscillator realizations of quantum \((q\)-) oscillators is described for both bosonic and fermionic \(q\)-oscillators. The existence of canonical \(q\)-transformations is demonstrated and some interesting aspects of such transformations are discussed.
There are reported results on the following problems: (i) on the validity of the Penrose inequality; (ii) on the hoop conjecture; (iii) on the physical criteria for the formation of trapped surfaces; (iv) on estimates of a total scalar curvature. A special emphasis is put on the last two points.
The standard Higgs boson production in deep inelastic scattering is considered. The contribution from the quark and gluon structure of the photon is calculated. At HERA energies this production channel is below the weak boson fusion.
The effective Hamiltonian governing the decays \(K \to 2\pi \) depends on the Wilson coefficients \(z_1,\dots ,z_6,y_1,\dots ,y_6\). We express these coefficients as convergent series in the parameter \(x = 1/N\), where \(N\) is the number of colours. Analytic formulae for the (\(N\)-dependent) coefficients of these series are given. The first approximation reproduces the results of Bardeen, Burns and Gérard. Two more expansion terms are calculated and the corresponding approximations to \(z_1,\dots ,y_6\) are compared with the exact results.
The elastic scattering differential cross sections and polarization observables for 200 and 398 MeV protons on \(^{12}\)C and \(^{16}\)C nuclei are calculated on the basis of the multiple diffraction scattering theory and \(\alpha \)-cluster model with dispersion. We have shown that our calculations and those based on the Kerman, McManus and Thaler theory lead to the systematic differences in the observables for p-\(^{12}\)C and p-\(^{16}\)O scattering at the energies considered.
Following the idea of Lopez and Randrup (Nucl. Phys.A491, 477 (1989)) the influence of the Coulomb interaction on trajectories of particles emitted from a hot nuclear system is investigated. It is found that the Coulomb field of the two heaviest fragments focuses velocities of the other intermediate mass fragments when the hot system breaks up simultaneously, while in the case of the sequential binary decay these velocities exhibit a nearly isotropic distribution.
