An index theorem for super derivations

We show that the Chern character given by a super-KMS functional on a quantum algebra can be interpreted in terms of the index of a super derivation on a projection of the algebra.Dedicated to Roland DobrushinSupported in part by the National Science Foundation under Grant DMS/PHY 8816214     

Quantum Riemann surfaces: II. The discrete series

We continue our study of noncommutative deformations of two-dimensional hyperbolic manifolds which we initiated in Part I. We construct a sequence of ^*-algebras which are quantizations of a compact Riemann surface of genus g corresponding to special values of the Planck constant. These algebras are direct integrals of finite-dimensional ^*-algebras.Supported by DOE under Grant DE-FG02-88ER25065.     

Super Toeplitz operators and non-perturbative deformation quantization of supermanifolds

The purpose of this paper is to construct non-perturbative deformation quantizations of the algebras of smooth functions on Poisson supermanifolds. For the examplesU ^1¦1 andC ^m¦n , algebras of super Toeplitz operators are defined with respect to certain Hilbert spaces of superholomorphic functions. Generators and relations for these algebras are given. The algebras can be thought of as algebras of quantized functions, and deformation conditions are proven which demonstrate the recovery of the super Poisson structures in a semi-classical limit.Supported in part by the Department of Energy under grant DE-FG02-88ER25065Supported in part by the Italian National Institute for Nuclear Physics (INFN)     

In Vivo EPR For Dosimetry

As a result of terrorism, accident, or war, populations potentially can be exposed to doses of ionizing radiation that could cause direct clinical effects within days or weeks. There is a critical need to determine the magnitude of the exposure to individuals so that those with significant risk have appropriate procedures initiated immediately, while those without a significant probability of acute effects can be reassured and removed from the need for further consideration in the medical/emergency system. In many of the plausible scenarios there is an urgent need to make the determination very soon after the event and while the subject is still present. In vivo EPR measurements of radiation-induced changes in the enamel of teeth is a method, perhaps the only such method, which can differentiate among doses sufficiently for classifying individuals into categories for treatment with sufficient accuracy to facilitate decisions on medical treatment. In its current state, the in vivo EPR dosimeter can provide estimates of absorbed dose with an error approximately +/- 50 cGy over the range of interest for acute biological effects of radiation, assuming repeated measurements of the tooth in the mouth of the subject. The time required for acquisition, the lower limit, and the precision are expected to improve, with improvements in the resonator and the algorithm for acquiring and calculating the dose. The magnet system that is currently used, while potentially deployable, is somewhat large and heavy, requiring that it be mounted on a small truck or trailer. Several smaller magnets, including an intraoral magnet are under development, which would extend the ease of use of this technique.