Equilibria in reflexive Banach lattices with a continuum of agents.

We consider exchange economies with a measure space of agents and for which the commodity space is a separable and reflexive Banach lattice. Under assumptions imposing uniform bounds on marginal rates of substitution, positive results on core-Walras equivalence were established in Rustichini-Yannelis [27] and Podczeck [25]. In this paper we prove that under similar assumptions on marginal rates of substitution, the set of competitive equilibria (and thus the core) is non-empty.Competitive equilibria; Continuum of agents; Reflexive Banach lattice commodity spaces; Uniform properness;

Electron-positron annihilation into phi f_{0}(980) and clues for a new 1^{--} resonance

We study the e^{+}e^{-} to phi pi pi reaction for pions in an isoscalar s-wave which is dominated by loop mechanisms. For kaon loops we start from the conventional RCHPT, but use the unitarized amplitude for KbarK-pipi scattering and the full kaon form factor instead of the lowest order terms. We study also effects of vector mesons using RCHPT supplemented with the conventional anomalous term for VVP interactions and taking into account the effects of heavy vector mesons in the K*K transition form factor. We find a peak in the dipion invariant mass around the f_{0}(980) as in the experiment. Selecting the phi f_{0}(980) contribution as a function of the e^{+}e^{-} energy we also reproduce the experimental data except for a narrow peak, yielding support to the existence of a 1^{--} resonance above the phi f_{0}(980) threshold, coupling strongly to this state.Comment: 18 pages, 4 figure

II in generalized supergravity

We showed in previous work that for homogeneous Yang-Baxter (YB) deformations of AdS$_5\times$S$^5$, the open string metric and coupling, and as a result the closed string density $e^{-2 \Phi} \sqrt{g}$, remain undeformed. In this work, in addition to extending these results to the deformation associated with the modified CYBE, or $\eta$-deformation, we identify the Page forms as the open string counterpart for RR fields and demonstrate case by case that the non-zero Page forms remain invariant under YB deformations. We give a physical meaning to the Killing vector $I$ of generalized supergravity and show for all YB deformations: 1) $I$ appears as a current for center of mass motion on the worldvolume of a D-branes probing the background, 2) $I$ is equal to the divergence of the noncommutativity parameter, 3) $I$ exhibits "holographic" behavior, where the radial component of $I$ vanishes at the AdS boundary, and 4) in pure spinor formalism $I$ is related to a certain state in the BRST cohomology.Comment: 11 pages, 2 column; v2 references updated; v3 to appear in EPJ

Phonon self-energy corrections to non-zero wavevector phonon modes in single-layer graphene

Phonon self-energy corrections have mostly been studied theoretically and experimentally for phonon modes with zone-center (q = 0) wave-vectors. Here, gate-modulated Raman scattering is used to study phonons of a single layer of graphene (1LG) in the frequency range from 2350 to 2750 cm-1, which shows the G* and the G'-band features originating from a double-resonant Raman process with q \not= 0. The observed phonon renormalization effects are different from what is observed for the zone-center q = 0 case. To explain our experimental findings, we explored the phonon self-energy for the phonons with non-zero wave-vectors (q \not= 0) in 1LG in which the frequencies and decay widths are expected to behave oppositely to the behavior observed in the corresponding zone-center q = 0 processes. Within this framework, we resolve the identification of the phonon modes contributing to the G* Raman feature at 2450 cm-1 to include the iTO+LA combination modes with q \not= 0 and the 2iTO overtone modes with q = 0, showing both to be associated with wave-vectors near the high symmetry point K in the Brillouin zone