Representation Theory Approach to the Polynomial Solutions of q - Difference Equations : U_q(sl(3)) and Beyond,

A new approach to the theory of polynomial solutions of q - difference equations is proposed. The approach is based on the representation theory of simple Lie algebras and their q - deformations and is presented here for U_q(sl(n)). First a q - difference realization of U_q(sl(n)) in terms of n(n-1)/2 commuting variables and depending on n-1 complex representation parameters r_i, is constructed. From this realization lowest weight modules (LWM) are obtained which are studied in detail for the case n=3 (the well known n=2 case is also recovered). All reducible LWM are found and the polynomial bases of their invariant irreducible subrepresentations are explicitly given. This also gives a classification of the quasi-exactly solvable operators in the present setting. The invariant subspaces are obtained as solutions of certain invariant q - difference equations, i.e., these are kernels of invariant q - difference operators, which are also explicitly given. Such operators were not used until now in the theory of polynomial solutions. Finally the states in all subrepresentations are depicted graphically via the so called Newton diagrams.Comment: uuencoded Z-compressed .tar file containing two ps files

Radiation sensitive area detection device and method

A radiation sensitive area detection device for use in conjunction with an X ray, ultraviolet or other radiation source is provided which comprises a phosphor containing film which releases a stored diffraction pattern image in response to incoming light or other electromagnetic wave. A light source such as a helium-neon laser, an optical fiber capable of directing light from the laser source onto the phosphor film and also capable of channelling the fluoresced light from the phosphor film to an integrating sphere which directs the light to a signal processing means including a light receiving means such as a photomultiplier tube. The signal processing means allows translation of the fluoresced light in order to detect the original pattern caused by the diffraction of the radiation by the original sample. The optical fiber is retained directly in front of the phosphor screen by a thin metal holder which moves up and down across the phosphor screen and which features a replaceable pinhole which allows easy adjustment of the resolution of the light projected onto the phosphor film. The device produces near real time images with high spatial resolution and without the distortion that accompanies prior art devices employing photomultiplier tubes. A method is also provided for carrying out radiation area detection using the device of the invention

Detailed analysis of quantum phase transitions within the u(2)u(2) algebra

We analyze in detail the quantum phase transitions that arise in models based on the $u(2)$ algebraic description for bosonic systems with two types of scalar bosons. First we discuss the quantum phase transition that occurs in hamiltonians that admix the two dynamical symmetry chains $u(2)\supset u(1)$ and $u(2)\supset so(2)$ by diagonalizing the problem exactly in the $u(1)$ basis. Then we apply the coherent state formalism to determine the energy functional. Finally we show that a quantum phase transition of a different nature, but displaying similar characteristics, may arise also within a single chain just by including higher order terms in the hamiltonian.Comment: 5 figure

Airglow observations of dynamical (wind shear-induced) instabilities over Adelaide, Australia, associated with atmospheric gravity waves

While several observations have been made in recent years of instability features in airglow images of atmospheric gravity waves (AGWs), such measurements are still rare. To date, these features are characterized by appearing to be aligned perpendicular to the AGW wave fronts. Multi-instrument observations confirm the theoretical prediction that such features are caused by convective instabilities where the AGW-induced temperature variation causes the total lapse rate to exceed the adiabatic lapse rate. In February 2000, airglow observations were obtained at Buckland Park, Australia, which showed instability features with a different characteristic. These images showed small-scale (less than 10 km horizontal wavelength) features aligned parallel to the larger scale AGW wave fronts. These features were only seen in OH images, not in O2A images, indicating that they originate below 90 km altitude. Simultaneous MF radar wind data reveal the presence of a mean wind shear which, during the period of the small-scale features, was aligned nearly in the direction of AGW propagation. In addition, the larger scale AGW approached a critical level near 90 km altitude. While the wind shear itself is not large enough to cause an instability, an analysis of the data suggests that the small-scale features are the result of a dynamic (wind shear-induced) instability in the 87–90 km altitude region. The instability was due to a combination of the background wind shear and the large shear induced by the passage of the larger scale AGW as it approached the critical level.J. H. Hecht, R. L. Walterscheid and R. A. Vincen

Barriers, control and identity in health information seeking among African American women

Qualitative research methods were used to examine the role of racial, cultural, and socio-economic group (i.e., communal) identities on perceptions of barriers and control related to traditional and internet resources for seeking health information. Eighteen lower income, African American women participated in training workshops on using the internet for health, followed by two focus groups. Transcripts were analyzed using standardized coding methods. Results demonstrated that participants perceived the internet as a tool for seeking health information, which they believed would empower them within formal healthcare settings. Participants invoked racial, cultural, and socio-economic identities when discussing barriers to seeking health information within healthcare systems and the internet. The findings indicate that the internet may be a valuable tool for accessing health information among lower income African American women if barriers are reduced. Recommendations are made that may assist health providers in improving health information seeking outcomes of African American women