The symplectic structure of rational Lax pair systems

We consider dynamical systems associated to Lax pairs depending rationnally on a spectral parameter. We show that we can express the symplectic form in terms of algebro--geometric data provided that the symplectic structure on L is of Kirillov type. In particular, in this case the dynamical system is integrable.Comment: 8 pages, no figure, Late

Kowalevski's analysis of the swinging Atwood's machine

We study the Kowalevski expansions near singularities of the swinging Atwood's machine. We show that there is a infinite number of mass ratios $M/m$ where such expansions exist with the maximal number of arbitrary constants. These expansions are of the so--called weak Painlev\'e type. However, in view of these expansions, it is not possible to distinguish between integrable and non integrable cases.Comment: 30 page

A Cost-Benefit Analysis of Pilot Training Next

The United States Air Force (USAF) is currently facing a 2,400-pilot shortage in an increasingly constrained budgetary environment. Without pilots to engage the enemy, deliver weapons, and provide logistics support for operations, the USAF could lose the ability to fly, fight, and win global engagements and defend the homeland. This study focused on Undergraduate Pilot Training (UPT) as a means of producing the USAF’s pilots to offset the current shortage. Specifically, this study compared UPT to the recently initiated Pilot Training-Next (PTN) program through a cost-benefit analysis. Like any new technology integration, PTN’s virtual reality training will require further study for proofing and justification prior to full-scale implementation and further utilization of constrained USAF resources. This study’s use of extant financial and historical production data, coupled with interviews with PTN instructors, highlights the potential of PTN. Ultimately, this study’s cost-benefit analysis uniquely contributes to the growing body of virtual reality training research through a Formula for Change theoretical lens, while simultaneously providing USAF decision makers a comparison of program costs, projected production capacity, and quality of training

Persistent time intervals between features in solar flare hard X-ray emission

Several solar hard X-ray events (greater than 100 keV) were observed simultaneously with identical instruments on the Venera 11, 12, 13, 14, and Prognoz spacecraft. High time resolution (= 2 ms) data were stored in memory when a trigger occurred. The observations of modulation are presented with a period of 1.6 s for the event on December 3, 1978. Evidence is also presented for fast time fluctuations from an event on November 6, 1979, observed from Venera 12 and another on September 6, 1981, observed from the Solar Maximum Mission. Power spectrum analysis, epoch folding, and Monte Carlo simulation were used to evaluate the statistical significance of persistent time delays between features. The results are discussed in light of the MHD model proposed by Zaitsev and Stepanov

Separation of variables for the classical and quantum Neumann model

The method of separation of variables is shown to apply to both the classical and quantum Neumann model. In the classical case this nicely yields the linearization of the flow on the Jacobian of the spectral curve. In the quantum case the Schr\"odinger equation separates into one--dimensional equations belonging to the class of generalized Lam\'e differential equations.Comment: 16 page