Remarks on flat and differential K-theory

In this note we prove some results in flat and differential $K$-theory. The first one is a proof of the compatibility of the differential topological index and the flat topological index by a direct computation. The second one is the explicit isomorphisms between Bunke-Schick differential $K$-theory and Freed-Lott differential $K$-theory.Comment: 9 pages. Comments are welcome. Final version. To appear in Annales Mathematiques Blaise Pasca

Prepotential approach to quasinormal modes

In this paper we demonstrate how the recently reported exactly and quasi-exactly solvable models admitting quasinormal modes can be constructed and classified very simply and directly by the newly proposed prepotential approach. These new models were previously obtained within the Lie-algebraic approach. Unlike the Lie-algebraic approach, the prepotential approach does not require any knowledge of the underlying symmetry of the system. It treats both quasi-exact and exact solvabilities on the same footing, and gives the potential as well as the eigenfunctions and eigenvalues simultaneously. We also present three new models with quasinormal modes: a new exactly solvable Morse-like model, and two new quasi-exactly solvable models of the Scarf II and generalized P\"oschl-Teller types.Comment: 12 pages, no figure. Typos correcte

Simple unified derivation and solution of Coulomb, Eckart and Rosen-Morse potentials in prepotential approach

The four exactly-solvable models related to non-sinusoidal coordinates, namely, the Coulomb, Eckart, Rosen-Morse type I and II models are normally being treated separately, despite the similarity of the functional forms of the potentials, their eigenvalues and eigenfunctions. Based on an extension of the prepotential approach to exactly and quasi-exactly solvable models proposed previously, we show how these models can be derived and solved in a simple and unified way.Comment: 15 pages, no figure

Twisted Bundle On Quantum Torus and BPS States in Matrix Theory

Following the recent work of Connes, Douglas and Schwarz, we study the M(atrix) model compactified on a torus with a background of the three-form field. This model is given by a super Yang-Mills theory on a quantum torus. To consider twisted gauge field configurations, we construct twisted U(n) bundles on the quantum torus as a deformation of its classical counterpart. By properly taking into account membranes winding around the light-cone direction, we derive from the M(atrix) model the BPS spectrum which respects the full SL(2,Z)*SL(2,Z) U-duality in M theory.Comment: 14 pages, no figure. minor modification mad

On the Disappearance of the Broad-Line Region in Low-Luminosity Agns

The disk-wind scenario for the broad-line region (BLR) and toroidal obscuration in active galactic nuclei predicts the disappearance of the BLR at low luminosities. In accordance with the model predictions, data from a nearly complete sample of nearby AGNs show that the BLR disappears at luminosities lower than 5\times\E{39} (M/10^7\Mo)^{2/3} erg s^{-1), where $M$ is the black hole mass. The radiative efficiency of accretion onto the black hole is \la \E{-3} for these sources, indicating that their accretion is advection-dominated.Comment: ApJ Letters, to be publishe