Two generalizations of the PRV conjecture

Let G be a complex connected reductive group. The PRV conjecture, which was proved independently by S. Kumar and O. Mathieu in 1989, gives explicit irreducible submodules of the tensor product of two irreducible G-modules. This paper has three aims. First, we simplify the proof of the PRV conjecture, then we generalize it to other branching problems. Finally, we find other irreducible components of the tensor product of two irreducible G-modules that appear for "the same reason" as the PRV ones

Cosmic acceleration in a model of scalar-tensor gravitation

In this paper we consider a model of scalar-tensor theory of gravitation in which the scalar field, $\phi$ determines the gravitational coupling G and has a Lagrangian of the form, $\mathcal{L}_{\phi} =-V(\phi)\sqrt{1 - \partial_{\mu}\phi\partial^{\mu}\phi}$. We study the cosmological consequence of this theory in the matter dominated era and show that this leads to a transition from an initial decelerated expansion to an accelerated expansion phase at the present epoch. Using observational constraints, we see that the effective equation of state today for the scalar field turns out to be $p_{\phi}=w_{\phi}{\rho}_{\phi}$, with $w_{\phi}=-0.88$ and that the transition to an accelerated phase happened at a redshift of about 0.3.Comment: 12 pages, 2 figures, matches published versio

Performance Enhancement Using Selective Reinforcement for Metallic Single- and Multi-Pin Loaded Holes

An analysis based investigation of aluminum with metal matrix composite selectively reinforced single- and multi-hole specimens was performed and their results compared with results from geometrically comparable non-reinforced specimens. All reinforced specimens exhibited a significant increase in performance. Performance increase of up to 170 percent was achieved. Specimen failure modes were consistent with results from reinforced polymeric matrix composite specimens. Localized reinforcement application (circular) proved as effective as a broader area (strip) reinforcement. Also, selective reinforcement is an excellent method of increasing the performance of multi-hole specimens

Superfluid-Insulator transition of ultracold atoms in an optical lattice in the presence of a synthetic magnetic field

We study the Mott insulator-superfluid transition of ultracold bosonic atoms in a two-dimensional square optical lattice in the presence of a synthetic magnetic field with p/q (p and q being co-prime integers) flux quanta passing through each lattice plaquette. We show that on approach to the transition from the Mott side, the momentum distribution of the bosons exhibits q precursor peaks within the first magnetic Brillouin zone. We also provide an effective theory for the transition and show that it involves q interacting boson fields. We construct, from a mean-field analysis of this effective theory, the superfluid ground states near the transition and compute, for q=2,3, both the gapped and the gapless collective modes of these states. We suggest experiments to test our theory.Comment: 4 pages, 4 figs; v

Tuning magnetic frustration on the diamond lattice of the A-site magnetic spinels CoAl2−x_{2-x}Gax_xO4_4: Lattice expansion and site disorder

The spinels CoB$_2$O$_4$ with magnetic Co$^{2+}$ ions on the diamond lattice A site can be frustrated because of competing near-neighbor ($J_1$) and next-near neighbor ($J_2$) interactions. Here we describe attempts to tune the relative strengths of these interactions by substitution on the non-magnetic B-site. The system we employ is CoAl$_{2-x}$Ga$_x$O$_4$, where Al is systematically replaced by the larger Ga, ostensibly on the B site. As expected, Ga substitution expands the lattice, resulting in Co atoms on the A-site being pushed further from one other and thereby weakening magnetic interactions. In addition, Ga distributes between the B and the A site in a concentration dependent manner displacing an increasing amount of Co from the A site with increasing $x$. This increased inversion, which is confirmed by neutron diffraction studies carried out at room temperature, affects magnetic ordering very significantly, and changes the nature of the ground state. Modeling of the magnetic coupling illustrates the complexity that arises from the cation site disorder.Comment: 9 pages, 10 figure

Hodge polynomials of some moduli spaces of Coherent Systems

When $k<n$, we study the coherent systems that come from a BGN extension in which the quotient bundle is strictly semistable. In this case we describe a stratification of the moduli space of coherent systems. We also describe the strata as complements of determinantal varieties and we prove that these are irreducible and smooth. These descriptions allow us to compute the Hodge polynomials of this moduli space in some cases. In particular, we give explicit computations for the cases in which $(n,d,k)=(3,d,1)$ and $d$ is even, obtaining from them the usual Poincar\'e polynomials.Comment: Formerly entitled: "A stratification of some moduli spaces of coherent systems on algebraic curves and their Hodge--Poincar\'e polynomials". The paper has been substantially shorten. Theorem 8.20 has been revised and corrected. Final version accepted for publication in International Journal of Mathematics. arXiv admin note: text overlap with arXiv:math/0407523 by other author