Constant directions of the Riccati equation

A constant direction of the Riccati equation associated with a class of singular discrete-time optimization problems is defined. The set of constant directions is completely characterized using a control viewpoint. Constant directions are used to reduce the computational complexity of the optimal system. Application to optimal filtering in colored noise is given

Formation of Short-Period Binary Pulsars in Globular Clusters

We present a new dynamical scenario for the formation of short-period binary millisecond pulsars in globular clusters. Our work is motivated by the recent observations of 20 radio pulsars in 47 Tuc. In a dense cluster such as 47 Tuc, most neutron stars acquire binary companions through exchange interactions with primordial binaries. The resulting systems have semimajor axes in the range \~0.1-1 AU and neutron star companion masses ~1-3 Msun. For many of these systems we find that, when the companion evolves off the main sequence and fills its Roche lobe, the subsequent mass transfer is dynamically unstable. This leads to a common envelope phase and the formation of short-period neutron star - white dwarf binaries. For a significant fraction of these binaries, the decay of the orbit due to gravitational radiation will be followed by a period of stable mass transfer driven by a combination of gravitational radiation and tidal heating of the companion. The properties of the resulting short-period binaries match well those of observed binary pulsars in 47 Tuc.Comment: To appear in ApJ Letters, slightly abbreviated version with only minor change

Women Mathematicians: A Bibliography

Although long ignored or unrecognized, there have been several notable women in the history of mathematics. That the list is not long is due to the barriers presented to women trying to study mathematics. Those who were able to learn the subject encountered many more difficulties in their attempts to apply their knowledge. Yet in spite of these difficulties there were women who, because of circumstances, force of will, and/or brilliance, were able to achieve some recognition

The U.S. as a Coastal Nation

U.S. economic activity is overwhelmingly concentrated at its ocean and Great Lakes coasts and at navigable rivers. Economic theory suggests four possible explanations: a present-day productivity effect, a present-day quality-of-life effect, delayed adjustment following a historical productivity or quality-of-life effect, and an agglomeration effect following a historical productivity or quality-of-life effect. Controlling for correlated natural attributes such as the weather and including proximity measures which a priori should absorb any quality-of-life effect, linear regressions suggest that the high coastal concentration of economic activity is primarily due to a productivity effect. Extensively controlling for historical economic density suggests that such a productivity effect continues to be operative today