The Dimensions of American Constitutional Equality

Liberty and equality are the hallmark characteristics of any legal order. Constitutional equality in the US is discussed. The rights of equality are not economic in nature, and they are not subject to strictly majority rule

Improvements in ERBS attitude determination without gyros

Previous papers have described the modification of the Earth Radiation Budget Satellite (ERBS) Attitude Determination System (ADS) to overcome the impact of on board gyro degradation and failure on attitude ground support of the mission. Two approaches were taken: implementing a Kalman filter in place of the batch-least-squares attitude estimator to account for the propagation error produced by high-noise gyro data, and modeling the ERBS attitude dynamics to restore rate information in the case of gyro failure. Both of these methods had shortcomings. In practice, the filter attitude diverged without complete sensor observability, and accurate dynamics modeling required knowledge of disturbance torque parameters that had to be determined manually. These difficulties have been overcome by improved tuning of the filter and by incorporating dynamics parameter estimation into the ERBS ADS

Why material slow light does not improve cavity-enhanced atom detection

We discuss the prospects for enhancing absorption and scattering of light from a weakly coupled atom in a high-finesse optical cavity by adding a medium with large, positive group index of refraction. The slow-light effect is known to narrow the cavity transmission spectrum and increase the photon lifetime, but the quality factor of the cavity may not be increased in a metrologically useful sense. Specifically, detection of the weakly coupled atom through either cavity ringdown measurements or the Purcell effect fails to improve with the addition of material slow light. A single-atom model of the dispersive medium helps elucidate why this is the case.Comment: 11 pages, 4 figures; QuTiP python file included. This version: changed title and added several references; results are unchanged. Accepted for open access publication in a special issue of Journal of Modern Optics in memory of Prof Danny Segal. Publisher's version available at http://dx.doi.org/10.1080/09500340.2017.138451