The Method of Alternating Relaxed Projections for two nonconvex sets

The Method of Alternating Projections (MAP), a classical algorithm for solving feasibility prob- lems, has recently been intensely studied for nonconvex sets. However, intrinsically available are only local convergence results: convergence occurs if the starting point is not too far away from solutions to avoid getting trapped in certain regions. Instead of taking full projection steps, it can be advantageous to underrelax, i.e., to move only part way towards the constraint set, in order to enlarge the regions of convergence. In this paper, we thus systematically study the Method of Alternating Relaxed Projections (MARP) for two (possibly nonconvex) sets. Complementing our recent work on MAP, we es- tablish local linear convergence results for the MARP. Several examples illustrate our analysis

Magnetocaloric effect in nano- and polycrystalline manganite La0.7Ca0.3MnO3La_{0.7}Ca_{0.3}MnO_3

$La_{0.7}Ca_{0.3}MnO_3$ samples were prepared in nano- and polycrystalline forms by sol-gel and solid state reaction methods, respectively, and structurally characterized by synchrotron X-ray diffraction. The magnetic properties determined by ac susceptibility and dc magnetization measurements are discussed. The magnetocaloric effect in this nanocrystalline manganite is spread over a broader temperature interval than in the polycrystalline case. The relative cooling power of the poly- and nanocrystalline manganites is used to evaluate a possible application for magnetic cooling below room temperature.Comment: 6 pages, 5 (double) figures, 1 table, 16 references; submitted to Appl. Phys.

Beam polarization effects on top-pair production at the ILC

Full one-loop electroweak-corrections for an $e^-e^+\rightarrow t \bar{t}$ process associated with sequential $t\rightarrow b \mu\nu_\mu$ decay are discussed. At the one-loop level, the spin-polarization effects of the initial electron and positron beams are included in the total and differential cross sections. A narrow-width approximation is used to treat the top-quark production and decay while including full spin correlations between them. We observed that the radiative corrections due to the weak interaction have a large polarization dependence on both the total and differential cross sections. Therefore, experimental observables that depend on angular distributions such as the forward-backward asymmetry of the top production angle must be treated carefully including radiative corrections. We also observed that the energy distribution of bottom quarks is majorly affected by the radiative corrections.Comment: 15 pages, 8 figure