83,266 research outputs found
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
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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
Late com plications with gallbladder conduit biliary reconstruction after liver transplantation
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
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