Approximating parabolas as natural bounds of Heisenberg spectra: Reply on the comment of O. Waldmann

O. Waldmann has shown that some spin systems, which fulfill the condition of a weakly homogeneous coupling matrix, have a spectrum whose minimal or maximal energies are rather poorly approximated by a quadratic dependence on the total spin quantum number. We comment on this observation and provide the new argument that, under certain conditions, the approximating parabolas appear as natural bounds of the spectrum generated by spin coherent states.Comment: 2 pages, accepted for Europhysics Letter

Hourly Variability in Q0957+561

We have continued our effort to re-reduce archival Q0957+561 brightness monitoring data and present results for 1629 R-band images using the methods for galaxy subtraction and seeing correction reported previously. The new dataset comes from 4 observing runs, several nights apiece, with sampling of typically 5 minutes, which allows the first measurement of the structure function for variations in the R-band from timescales of hours to years. Comparison of our reductions to previous reductions of the same data, and to r-band photometry produced at Apache Point Observatory shows good overall agreement. Two of the data runs, separated by 417 days, permit a sharpened value for the time delay of 417.4 days, valid only if the time delay is close to the now-fashionable 417-day value; our data do not constrain a delay if it is more than three days from this 417-day estimate. Our present results show no unambiguous signature of the daily microlensing, though a suggestive feature is found in the data. Both time delay measurement and microlensing searches suffer from from the lack of sampling at half-day offsets, inevitable at a single observatory, hence the need for round-the-clock monitoring with participation by multiple observatories.Comment: AASTeX 4.0 preprint style, 21 pages, 8 EPS figure

How to measure spatial distances?

The use of time--like geodesics to measure temporal distances is better justified than the use of space--like geodesics for a measurement of spatial distances. We give examples where a ''spatial distance'' cannot be appropriately determined by the length of a space--like geodesic.Comment: 4 pages, latex, no figure

Internal electrostatic discharge hazard risk assessment to the Galileo orbiter

A worst case assessment was performed on the Command Data System (CDS) multilayer printed circuit board and an output power transformer module in the power subsystem. An estimate of the Jovian environment during the 35 hour orbit insertion was supplied by JPL and used as an input to calculate the electron transport into the Galileo components. A radiation shielding analysis computer code, CHARGE, calculated the electron transport deposition trapped in the anticipated sensitive areas of the multilayer board and transformer module. Based on these trapped charge calculations electric fields were calculated between the identified isolated areas and the spacecraft ground. The results of the assessment of electrostatic discharge (DSD) in the CDS multilayer printed circuit board indicate that the probability of ESD in the FR4 is low. The probability of ESD in the components attached to the multilayer board, however, is uncertain based on a lack of prior experimental data