Ultracold polarized Fermi gas at intermediate temperatures

We consider non-zero temperature properties of the polarized two-component Fermi gas. We point out that stable polarized paired states which are more stable than their phase separated counterparts with unpolarized superfluid region can exist below the critical temperature. We also solve the system behavior in a trap using the local density approximation and find gradually increasing polarization in the center of the system as the temperature is increased. However, in the strongly interacting region the central polarization increases most rapidly close to the mean-field critical temperature, which is known to be substantially higher than the critical temperature for superfluidity. This indicates that most of the phase separation occurs in the fluctuation region prior to superfluidity and that the polarization in the actual superfluid is modest.Comment: Final published versio

Coupling internal atomic states in a two-component Bose-Einstein condensate via an optical lattice: Extended Mott-superfluid transitions

An ultracold gas of coupled two-component atoms in an optical field is studied. Due to the internal two-level structure of the atoms, three competing energy terms exist; atomic kinetic, atomic internal, and atom-atom interaction energies. A novel outcome of this interplay, not present in the regular Bose-Hubbard model, is that in the single band and tight binding approximations four different phases appear: two superfluid and two Mott phases. When passing through the critical point between the two superfluid or the two Mott phases, a swapping of the internal atomic populations takes place. By means of the strong coupling expansion, we find the full phase diagram for the four different phases.Comment: 9 pages, 7 figure

Space time neural networks for tether operations in space

A space shuttle flight scheduled for 1992 will attempt to prove the feasibility of operating tethered payloads in earth orbit. due to the interaction between the Earth's magnetic field and current pulsing through the tether, the tethered system may exhibit a circular transverse oscillation referred to as the 'skiprope' phenomenon. Effective damping of skiprope motion depends on rapid and accurate detection of skiprope magnitude and phase. Because of non-linear dynamic coupling, the satellite attitude behavior has characteristic oscillations during the skiprope motion. Since the satellite attitude motion has many other perturbations, the relationship between the skiprope parameters and attitude time history is very involved and non-linear. We propose a Space-Time Neural Network implementation for filtering satellite rate gyro data to rapidly detect and predict skiprope magnitude and phase. Training and testing of the skiprope detection system will be performed using a validated Orbital Operations Simulator and Space-Time Neural Network software developed in the Software Technology Branch at NASA's Lyndon B. Johnson Space Center

Learning characteristics of a space-time neural network as a tether skiprope observer

The Software Technology Laboratory at the Johnson Space Center is testing a Space Time Neural Network (STNN) for observing tether oscillations present during retrieval of a tethered satellite. Proper identification of tether oscillations, known as 'skiprope' motion, is vital to safe retrieval of the tethered satellite. Our studies indicate that STNN has certain learning characteristics that must be understood properly to utilize this type of neural network for the tethered satellite problem. We present our findings on the learning characteristics including a learning rate versus momentum performance table

A Longitudinal Assessment of the Quality of Insulin Prescribing with Different Prescribing Systems.

Accurate and complete prescriptions of insulin are crucial to prevent medication errors from occurring. Two core components for safe insulin prescriptions are the word 'units' being written in full for the dose, and clear documentation of the insulin device alongside the name. A retrospective review of annual audit data was conducted for insulin prescriptions to assess the impact of changes to the prescribing system within a secondary care setting, at five time points over a period of 7 years (2014 to 2020). The review points were based on when changes were made, from standardized paper charts with a dedicated section for insulin prescribing, to a standalone hospital wide electronic prescribing and medicines administration (ePMA) system, and finally an integrated electronic health record system (EHRS). The measured outcomes were compliance with recommended standards for documentation of 'units' in full, and inclusion of the insulin device as part of the prescription. Overall, an improvement was seen in both outcomes of interest. Device documentation improved incrementally with each system change-34% for paper charts, 23%-56% for standalone ePMA, and 100% for ePMA integrated within EHRS. Findings highlight that differences in ePMA systems may have varying impact on safe prescribing practices

Hankel operators on Fock spaces

We study Hankel operators on the weighted Fock spaces Fp. The boundedness and compactness of these operators are characterized in terms of BMO and VMO, respectively. Along the way, we also study Berezin transform and harmonic conjugates on the plane. Our results are analogous to Zhu's characterization of bounded and compact Hankel operators on Bergman spaces of the unit disk

Spectral theory of Toeplitz and Hankel operators on the Bergman space A1

The Fredholm properties of Toeplitz operators on the Bergman space A2 have been well-known for continuous symbols since the 1970s. We investigate the case p=1 with continuous symbols under a mild additional condition, namely that of the logarithmic vanishing mean oscillation in the Bergman metric. Most differences are related to boundedness properties of Toeplitz operators acting on Ap that arise when we no longer have 1<p<∞; in particular bounded Toeplitz operators on A1 were characterized completely very recently but only for bounded symbols. We also consider compactness of Hankel operators on A1

New results and open problems on Toeplitz operators in Bergman spaces

We discuss some of the recent progress in the field of Toeplitz operators acting on Bergman spaces of the unit disk, formulate some new results, and describe a list of open problems -- concerning boundedness, compactness and Fredholm properties -- which was presented at the conference "Recent Advances in Function Related Operator Theory'' in Puerto Rico in March 2010