The Segal--Bargmann transform for odd-dimensional hyperbolic spaces

We develop isometry and inversion formulas for the Segal--Bargmann transform on odd-dimensional hyperbolic spaces that are as parallel as possible to the dual case of odd-dimensional spheres.Comment: To appear in Mathematic

Coherent states for a 2-sphere with a magnetic field

We consider a particle moving on a 2-sphere in the presence of a constant magnetic field. Building on earlier work in the nonmagnetic case, we construct coherent states for this system. The coherent states are labeled by points in the associated phase space, the (co)tangent bundle of S^2. They are constructed as eigenvectors for certain annihilation operators and expressed in terms of a certain heat kernel. These coherent states are not of Perelomov type, but rather are constructed according to the "complexifier" approach of T. Thiemann. We describe the Segal--Bargmann representation associated to the coherent states, which is equivalent to a resolution of the identity.Comment: 23 pages. To appear in Journal of Physics A, Special Issue on Coherent State

Serre Duality, Abel's Theorem, and Jacobi Inversion for Supercurves Over a Thick Superpoint

The principal aim of this paper is to extend Abel's theorem to the setting of complex supermanifolds of dimension 1|q over a finite-dimensional local supercommutative C-algebra. The theorem is proved by establishing a compatibility of Serre duality for the supercurve with Poincare duality on the reduced curve. We include an elementary algebraic proof of the requisite form of Serre duality, closely based on the account of the reduced case given by Serre in Algebraic Groups and Class Fields, combined with an invariance result for the topology on the dual of the space of repartitions. Our Abel map, taking Cartier divisors of degree zero to the dual of the space of sections of the Berezinian sheaf, modulo periods, is defined via Penkov's characterization of the Berezinian sheaf as the cohomology of the de Rham complex of the sheaf D of differential operators, as a right module over itself. We discuss the Jacobi inversion problem for the Abel map and give an example demonstrating that if n is an integer sufficiently large that the generic divisor of degree n is linearly equivalent to an effective divisor, this need not be the case for all divisors of degree n.Comment: 14 page

The Segal-Bargmann transform for noncompact symmetric spaces of the complex type

We consider the generalized Segal-Bargmann transform, defined in terms of the heat operator, for a noncompact symmetric space of the complex type. For radial functions, we show that the Segal-Bargmann transform is a unitary map onto a certain L^2 space of meromorphic functions. For general functions, we give an inversion formula for the Segal-Bargmann transform, involving integration against an "unwrapped" version of the heat kernel for the dual compact symmetric space. Both results involve delicate cancellations of singularities.Comment: 28 pages. Minor corrections made. To appear in J. Functional Analysi

FIRM EFFICIENCY AND INFORMATION TECHNOLOGY USE: EVIDENCE FROM U.S. CASH GRAIN FARMS

We implement stochastic frontier analysis techniques to show the effects of information technology use on firm efficiency. Results from a sample of 1,865 U.S. cash grain farms reveals that information technology use within the farm business moved farms significantly towards the efficiency frontier. Also moving farms towards the efficiency frontier were the use of written long-term plans, advanced input acquisition strategies, and increased farm labor hours relative to total labor hours. In contrast, an increase in the debt to asset ratio was associated with movements away from the efficiency frontier.Crop Production/Industries,

DISTRIBUTIONAL ANALYSIS OF U.S. FARM HOUSEHOLD INCOME

expenditures, farm safety net, household income, poverty, stochastic dominance, wealth, Consumer/Household Economics,

The Economic Impact of Nonprofit Organizations in New Mexico

Nonprofit organizations make a substantial contribution to the quality of life and economic well-being of New Mexicans. These organizations provide health care, social and educational services, advocate for social and environmental change, support businesses and communities, conduct research, support the arts and other cultural activities, and provide credit and basic utilities where the market does not. This report provides information on and analysis of the size, composition and geographic distribution of paid employment by the nonprofit sector in New Mexico for the year 2003

Clayton MainStreet Community Economic Assessment

An economic analysis of the Clayton, New Mexico market area. Sales data from the retail and service sectors are examined to determine pull factors and leakage. Tables and charts illustrating local demographics, housing, and economic conditions are included