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

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

Surface-wave attenuation and crustal anelasticity in Central North America

The southeastern Missouri earthquake of October 21, 1965 generated fundamental- and higher-mode Love and Rayleigh waves which were recorded at numerous North American stations. Love-wave amplitude radiation patterns were determined and found to be consistent with theoretical patterns predicted by a fault-plane solution previously inferred from Rayleigh-wave data. The radiation patterns were used to estimate the source spectrum and values for Love-wave attenuation coefficients for the mid-continent of North America by a least-squares iterative process. The source spectrum derived from Love-wave amplitudes exhibits a peak at periods between 5 and 9 sec and decreases to a lower DC level at longer periods, in agreement with the source spectrum determined previously for Rayleigh waves. The Love-wave attenuation coefficients decrease rapidly from about 0.0018 km^(−1) at a period of 4 sec to about 0.0001 km^(−1) at a period of 20 sec. At periods between 20 and 40 sec the values seem to remain nearly constant. The crust in the mid-continent of North America is characterized by relatively low Q_β values, 75 to 300, in its upper portion. At depths between 15 and 20 km, Q_β increases sharply and decreases again at greater depths. The decrease can be explained as being due to increasing temperature in a homogeneous material, but the sharp increase requires a change in the chemical constitution of the material at mid-crustal depths

Credit Access: Implications for Sole-Proprietor Household Production

The objective of this study is to explain the determinants of farm and non-farm sole proprietorship households access to credit as well as the extent their credit constraints impact their value of production. A propensity, kernel-based matching estimator was employed to provide unbiased estimates of the production impacts of being denied credit. Prior research efforts have used inferior methods, including the two-stage Heckman estimator deal with estimation issues (selection bias and endogeneity) inherent in determining impacts of credit access and use. Results suggest that credit constrained sole-proprietorships, farm and non-farm, have a significantly lower value of production, but this drop in production, when aggregated to a national level, is small.farm credit, credit constraint, debt, Agricultural Finance,

Rotation of Coulomb crystals in a magnetized inductively coupled complex plasma

Under suitable conditions, micron-sized dust particles introduced into inductively coupled argon plasma form a stable microscopic crystal lattice, known as a Coulomb (or plasma) crystal. In the experiment described, an external axial magnetic field was applied to various configurations of Coulomb crystal, including small crystal lattices consisting of one to several particles, and large crystal lattices with many hundreds of particles. The crystals were observed to rotate collectively under the influence of the magnetic field. This paper describes the experimental procedures and the preliminary results of this investigation

Spinal Progenitor-Laden Bridges Support Earlier Axon Regeneration Following Spinal Cord Injury.

Impact statementSpinal cord injury (SCI) results in loss of tissue innervation below the injury. Spinal progenitors have a greater ability to repair the damage and can be injected into the injury, but their regenerative potential is hampered by their poor survival after transplantation. Biomaterials can create a cell delivery platform and generate a more hospitable microenvironment for the progenitors within the injury. In this work, polymeric bridges are used to deliver embryonic spinal progenitors to the injury, resulting in increased progenitor survival and subsequent regeneration and functional recovery, thus demonstrating the importance of combined therapeutic approaches for SCI