The dynamics of vortex laments has provided for almost a century one of the most interesting connections between diierential geometry and integrable equations, and an example in which knotted curves arise as solutions of diierential equations possessing remarkably rich geometrical structures. In this paper we present several aspects of the integrable evolution of a closed vor-tex lament in an E...

The time-optimal trajectory for an airplane from some starting point to some final point is studied by many authors. Here, we consider the extension of robot planer motion of Dubins model in three dimensional spaces. In this model, the system has independent bounded control over both the altitude velocity and the turning rate of airplane movement in a non-obstacle space. Here, in this paper a g...

patriotic pride, who called conical refraction “the radiant stranger” in a florid passage in his memoirs. The two physicists responsible for the theoretical prediction and experimental confirmation of conical refraction were William Rowan Hamilton (1805-1865) and Humphrey Lloyd (1800-1881), both professors of Trinity College Dublin (fig. 1). Ireland’s recent Year of Hamilton (2005) provided an ...

A network of nine marine protected areas was established on the west coast of the island of Hawai’i in 2000 in response to declines of reef fishes taken by aquarium collectors. In 1999, we established 23 study sites in MPA areas, areas open to fishing, and control areas (existing protected areas) to collect data both prior to and after the closure of the MPA network in 2000. To date we have con...

The Letter discusses the Berry phase influence on the weak localization phenomenon at the adiabatic backscattering of ultrarelativistic particles in a random medium. We demonstrate that bosons that pass along a certain closed path in opposite directions come back always in phase (an example: the backscattering enhancement of electromagnetic waves), whereas fermions come exactly in antiphase. Th...

In the present lecture some basic problems of state and solving of radiation heat transfer equation as applied to radiation modelling in shock-tubes and entry flow are discussed. The lecture contains five parts. In the first part the radiation heat transfer equation and the general definitions of the radiation heat transfer theory are presented. The definitions introduced in the first part are ...

Inherent and Operational Error Within a GIS: Evaluation From a User Perspective Stephen Walsh University of North Carolina Inherent and operational errors contribute to a reduction in the accuracy of data contained within a geographic information system, and, thereby, affect the quality of the analysis and the resulting products that are generated by such systems. Inherent error is the error pr...