On the Theory of Killing Orbits in Space-Time

This paper gives a theoretical discussion of the orbits and isotropies which arise in a space-time which admits a Lie algebra of Killing vector fields. The submanifold structure of the orbits is explored together with their induced Killing vector structure. A general decomposition of a space-time in terms of the nature and dimension of its orbits is given and the concept of stability and instability for orbits introduced. A general relation is shown linking the dimensions of the Killing algebra, the orbits and the isotropies. The well-behaved nature of "stable" orbits and the possible miss-behaviour of the "unstable" ones is pointed out and, in particular, the fact that independent Killing vector fields in space-time may not induce independent such vector fields on unstable orbits. Several examples are presented to exhibit these features. Finally, an appendix is given which revisits and attempts to clarify the well-known theorem of Fubini on the dimension of Killing orbits.Comment: Latex, 19 pages, no figur

Coulomb plus power-law potentials in quantum mechanics

We study the discrete spectrum of the Hamiltonian H = -Delta + V(r) for the Coulomb plus power-law potential V(r)=-1/r+ beta sgn(q)r^q, where beta > 0, q > -2 and q \ne 0. We show by envelope theory that the discrete eigenvalues E_{n\ell} of H may be approximated by the semiclassical expression E_{n\ell}(q) \approx min_{r>0}\{1/r^2-1/(mu r)+ sgn(q) beta(nu r)^q}. Values of mu and nu are prescribed which yield upper and lower bounds. Accurate upper bounds are also obtained by use of a trial function of the form, psi(r)= r^{\ell+1}e^{-(xr)^{q}}. We give detailed results for V(r) = -1/r + beta r^q, q = 0.5, 1, 2 for n=1, \ell=0,1,2, along with comparison eigenvalues found by direct numerical methods.Comment: 11 pages, 3 figure

Semiclassical energy formulas for power-law and log potentials in quantum mechanics

We study a single particle which obeys non-relativistic quantum mechanics in R^N and has Hamiltonian H = -Delta + V(r), where V(r) = sgn(q)r^q. If N \geq 2, then q > -2, and if N = 1, then q > -1. The discrete eigenvalues E_{n\ell} may be represented exactly by the semiclassical expression E_{n\ell}(q) = min_{r>0}\{P_{n\ell}(q)^2/r^2+ V(r)}. The case q = 0 corresponds to V(r) = ln(r). By writing one power as a smooth transformation of another, and using envelope theory, it has earlier been proved that the P_{n\ell}(q) functions are monotone increasing. Recent refinements to the comparison theorem of QM in which comparison potentials can cross over, allow us to prove for n = 1 that Q(q)=Z(q)P(q) is monotone increasing, even though the factor Z(q)=(1+q/N)^{1/q} is monotone decreasing. Thus P(q) cannot increase too slowly. This result yields some sharper estimates for power-potential eigenvlaues at the bottom of each angular-momentum subspace.Comment: 20 pages, 5 figure

The Human Brain: A Multimedia Tutorial For The Independent Learner

The Human Brain is a multimedia, interactive, computer-based tutorial on the structure and function of the human nervous system. In creating it, we aim to solve a number of problems, both subject specific and general. As a subject, the structure and function of the nervous system is difficult to teach using traditional methods and there is a lack of integration in the teaching of structure and function. More generally, we are concerned with the difficulties of both assessing student understanding of a particular subject and remedying any deficiencies when the student is learning independently. Finally, we hope to resolve the conflict between linear and explorative modes of presentation of material in a teaching system

Photometric support for future astonomical research

The I.A.P.P.P. is described and how that organization can provide photometric support for future astronomical research projects such as the 1982-1984 eclipse of epsilon Aurigae discussed at this workshop. I.A.P.P.P., International Amateur-Professional Photoelectric Photometry, is an organization founded in Fairborn, Ohio by the authors in 1980. Its purpose is to encourage contact between amateur and professional astronomers interested in photoelectric photometry, for their mutual benefit and for the benefit of astronomical research. Aspects dealt with include instrumentation, electronics, computer hardware and software, observing techniques, data reduction, and observing programs. Starting with the June 1980 issue, I.A.P.P.P. has published the quarterly I.A.P.P.P. Communications. The Communications contain articles dealing with all the above aspects of photoelectric photometry, although it does not publish observational results as such. Photoelectric photometry obtained by amateurs is published in the same journals which publish photometry obtained by professionals

2MASS 1315-2649: A High Proper Motion L Dwarf with Strong H-alpha Emission

In Hall (2002) I reported that 2MASSI J1315309-264951 is an L dwarf with strong H-alpha emission. Two spectroscopic epochs appeared to show that the H-alpha was variable, decreasing from 121 Angstroms to 25 Angstroms EW, which I interpreted as a flare during the first observation. Gizis (2002) independently discovered this object, and his intermediate spectroscopic epoch shows H-alpha with 97 Angstroms EW. A new fourth epoch of spectroscopy again shows a very large H-alpha EW (124 Angstroms), confirming this object to be a persistent, strong H-alpha emitter. Whether the H-alpha is steady (like 2MASS 1237+6526) or from continuous strong flaring (like PC0025+0447) remains unclear. Imaging confirms that 2MASS 1315-2649 has a high proper motion (0.71"/year), corresponding to a transverse velocity of ~76 km/s at its distance of ~23 pc. Thus 2MASS 1315-2649 is consistent with being >~2 Gyr old and therefore relatively massive. If that is so, the correlation of H-alph activity with mass found by Gizis et al. (2000) would seem to support the continuous strong flaring scenario, though it does not rule out a brown dwarf binary accretion scenario.Comment: 2 pages, ApJL accepte

Liver transplantation in patients with situs inversus

Two patients with situs inversus and biliary atresia were treated with hepatic transplantation, one with an auxiliary liver and the other with an orthotopic graft which was placed using a piggy-back technique. Both transplants functioned well initially. The auxiliary liver was rejected after 1 1/2 months, and the patient died after an attempt at retransplantation many months later. The recipient of the orthotopic liver has perfect liver function 10 months postoperatively