A random version of Simons' inequality

The purpose of this paper is to provide a random version of Simons' inequality

Symmetry characterization of the collective modes of the phase diagram of the ν=0\nu=0 quantum Hall state in graphene: Mean-field and spontaneously broken symmetries

We devote this work to the study of the mean-field phase diagram of the $\nu=0$ quantum Hall state in bilayer graphene and the computation of the corresponding neutral collective modes, extending the results of recent works in the literature. Specifically, we provide a detailed classification of the complete orbital-valley-spin structure of the collective modes and show that phase transitions are characterized by singlet modes in orbital pseudospin, which are independent of the Coulomb strength and suffer strong many-body corrections from short-range interactions at low momentum. We describe the symmetry breaking mechanism for phase transitions in terms of the valley-spin structure of the Goldstone modes. For the remaining phase boundaries, we prove that the associated exact $SO(5)$ symmetry existing at zero Zeeman energy and interlayer voltage survives as a weaker mean-field symmetry of the Hartree-Fock equations. We extend the previous results for bilayer graphene to the monolayer scenario. Finally, we show that taking into account Landau level mixing through screening does not modify the physical picture explained above.Comment: 44 pages, 10 figure

String amplitudes in the Hpp-wave limit of AdS3xS3

We compute string amplitudes on pp-waves supported by NS-NS 3-form fluxes and arising in the Penrose limit of AdS3xS3xM. We clarify the role of the non-chiral accidental SU(2) symmetry of the background. We comment on the extension of our results to the superstring and propose a holographic formula in the BMN limit of the AdS3/CFT2 correspondence valid for any correlator.Comment: Latex,no figures, 47 p

THRESHOLD MODELS IN THEORY AND PRACTICE

Threshold models have gained much recent attention in applied economics for modeling nonlinear behavior. The appeal for these models is due in part to the observable pattern that many economic variables follow, such as asymmetric adjustment towards equilibrium. This paper reviews the literature and provides links to software programs.Research Methods/ Statistical Methods,

Analysis of Nd3+:glass, solar-pumped, high-powr laser systems

The operating characteristics of Nd(3+):glass lasers energized by a solar concentrator were analyzed for the hosts YAG, silicate glass, and phosphate glass. The modeling is based on the slab zigzag laser geometry and assumes that chemical hardening methods for glass are successful in increasing glass hardness by a factor of 4. On this basis, it was found that a realistic 1-MW solar-pumped laser might be constructed from phosphate glass 4 sq m in area and 2 mm thick. If YAG were the host medium, a 1-MW solar-pumped laser need only be 0.5 sq m in area and 0.5 cm thick, which is already possible. In addition, Nd(3+) doped glass fibers were found to be excellent solar-pumped laser candidates. The small diameter of fibers eliminates thermal stress problems, and if their diameter is kept small (10 microns), they propagate a Gaussian single mode which can be expanded and transmitted long distances in space. Fiber lasers could then be used for communications in space or could be bundled and the individual beams summed or phase-matched for high-power operation