Exponentially fitted fifth-order two-step peer explicit methods

The so called peer methods for the numerical solution of Initial Value Problems (IVP) in ordinary differential systems were introduced by R. Weiner et al [6, 7, 11, 12, 13] for solving different types of problems either in sequential or parallel computers. In this work, we study exponentially fitted three-stage peer schemes that are able to fit functional spaces with dimension six. Finally, some numerical experiments are presented to show the behaviour of the new peer schemes for some periodic problems

Long-range correlations in finite nuclei: comparison of two self-consistent treatments

Long-range correlations, which are partially responsible for the observed fragmentation and depletion of low-lying single-particle strength, are studied in the Green's function formalism. The self-energy is expanded up to second order in the residual interaction. We compare two methods of implementing self-consistency in the solution of the Dyson equation beyond Hartree-Fock, for the case of the 16O nucleus. It is found that the energy-bin method and the BAGEL method lead to globally equivalent results. In both methods the final single-particle strength functions are characterized by exponential tails at energies far from the Fermi level

Heisenberg double as braided commutative Yetter-Drinfel'd module algebra over Drinfel'd double in multiplier Hopf algebra case

Based on a pairing of two regular multiplier Hopf algebras $A$ and $B$, Heisenberg double $\mathscr{H}$ is the smash product $A \# B$ with respect to the left regular action of $B$ on $A$. Let $\mathscr{D}=A\bowtie B$ be the Drinfel'd double, then Heisenberg double $\mathscr{H}$ is a Yetter-Drinfel'd $\mathscr{D}$-module algebra, and it is also braided commutative by the braiding of Yetter-Drinfel'd module, which generalizes the results in [10] to some infinite dimensional cases.Comment: 18 pages. arXiv admin note: text overlap with arXiv:math/0404029 by other author

Compton scattering on the proton and light nuclei in the Delta-resonance region

Microscopic calculations of Compton scattering on the free proton and light nuclei are presented. For the description of Compton scattering on the proton the conventional K-matrix approach and the "Dressed K-Matrix" model are introduced. The latter approach can be used to calculate polarizabilities as well as Compton scattering for photon energies upto 1 GeV since it obeys the symmetry properties which are appropriate in the different energy regions. In particular, crossing symmetry, gauge invariance and unitarity are satisfied. The extent of violation of analyticity (causality) is used as an expansion parameter. Coherent Compton scattering on light nuclei at 200-300 MeV is studied in the impulse approximation and is shown to be a sensitive probe of the in-medium properties of the Delta-resonance. Modifications of the properties of the Delta-resonance due to the nuclear medium are accounted for through the self-energy operator of the Delta. The dominant medium effects such as the Pauli blocking effects in the decay width, effective nucleon mass and particle-hole excitations in the pion propagator axe consistently included in nuclear matter.</p