Lyapunov vs. Geometrical Stability Analysis of the Kepler and the Restricted Three Body Problem

In this letter we show that although the application of standard Lyapunov analysis predicts that completely integrable Kepler motion is unstable, the geometrical analysis of Horwitz et al [1] predicts the observed stability. This seems to us to provide evidence for both the incompleteness of the standard Lyapunov analysis and the strength of the geometrical analysis. Moreover, we apply this approach to the three body problem in which the third body is restricted to move on a circle of large radius which induces an adiabatic time dependent potential on the second body. This causes the second body to move in a very interesting and intricate but periodic trajectory; however, the standard Lyapunov analysis, as well as methods based on the parametric variation of curvature associated with the Jacobi metric, incorrectly predict chaotic behavior. The geometric approach predicts the correct stable motion in this case as well.Comment: 9 pages, 14 figure

Recovery of a quarkonium system from experimental data

For confining potentials of the form q(r)=r+p(r), where p(r) decays rapidly and is smooth for r>0, it is proved that q(r) can be uniquely recovered from the data {E_j,s_j}, where E_j are the bound states energies and s_j are the values of u'_j(0), and u_j(r) are the normalized eigenfunctions of the problem -u_j" +q(r)u_j=E_ju_j, r>0, u_j(0)=0, ||u_j||=1, where the norm is L^2(0, \infty) norm. An algorithm is given for recovery of p(r) from few experimental data

OBEs-Are They Dreams?

A great deal of controversy has accompanied the presentation of the theory, as in Stephen LaBerge’s bookLucid Dreaming(LaBerge, 1985), that so-called out-of-body experiences (OBEs) are simply dreams or possibly even pre-lucid dreams. That this is true is not surprising, since, as many who have had such experiences have noted, these experiences often surpass all others in vividness and emotional intensity. They leave one with an extraordinary sense of conviction that what one has just experiences is real, perhaps even more so than ordinary reality. However, this same conviction is often experienced by people in ordinary dreams not involving the OBE feeling. I have often heard recounted, and personally experienced the thought, “This cannot be a dream; it is too vivid, too real.” Upon awakening, however, the dreamer realized that the situation he or she was just experiencing was entirely fictitious--a dream after all

SUSY transformation of the Green function and a trace formula

An integral relation is established between the Green functions corresponding to two Hamiltonians which are supersymmetric (SUSY) partners and in general may possess both discrete and continuous spectra. It is shown that when the continuous spectrum is present the trace of the difference of the Green functions for SUSY partners is a finite quantity which may or may not be equal to zero despite the divergence of the traces of each Green function. Our findings are illustrated by using the free particle example considered both on the whole real line and on a half line

A Second Chance: Training for Jobs

Levitan and Gallo make use of their considerable experience and prior research to provide a critical assessment of the Job Training Partnership Act (JTPA). The authors evaluate state governments\u27 role in guiding and monitoring the program, and suggest that the success rates are actually lower than the reported official figures. Anyone interested in the JTPA or other job training program will benefit from the assessments provided by the authors in this book.https://research.upjohn.org/up_press/1109/thumbnail.jp

A Continued Federal Commitment

Levitan and Gallo make use of their considerable experience and prior research to provide a critical assessment of the Job Training Partnership Act (JTPA). The authors evaluate state governments\u27 role in guiding and monitoring the program, and suggest that the success rates are actually lower than the reported official figures. Anyone interested in the JTPA or other job training program will benefit from the assessments provided by the authors in this book.https://research.upjohn.org/up_press/1109/thumbnail.jp