Unary Primitive Recursive Functions

In this article, we study some new characterizations of primitive recursive functions based on restricted forms of primitive recursion, improving the pioneering work of R. M. Robinson and M. D. Gladstone in this area. We reduce certain recursion schemes (mixed/pure iteration without parameters) and we characterize one-argument primitive recursive functions as the closure under substitution and iteration of certain optimal sets

Lyman alpha line shapes from electron impact H2 dissociative processes in the Jovian auroral zone

Over the past two years several Lyman alpha line profile spectra of Jupiter were obtained using the International Ultraviolet Explorer (IUE) telescope. Several different regions of the planet were observed including the auroral zone, the low and mid latitudes, and the equatorial region which includes the Lyman alpha bulge region. These results have presented a very interesting picture of atomic hydrogen on Jupiter with explanations that range from ion outflow in the auroral zone to large thermospheric winds at low and mid latitudes. New data are needed to address the outstanding questions. Almost certainly, high resolution spectra from the Hubble Space Telescope will play a role in new observations. Better data also require better models, and better models require new laboratory data as inputs. The purpose of this program is two-fold: (1) to introduce a method by which new laboratory electron impact measurements of H2 dissociation can be used to calculate both the slow and fast H(S-2) and H(P-2) fragments in an H2 atmosphere; and (2) to determine the predicted Lyman alpha line shape that would result from electron impact production of these dissociative fragments in the Jovian auroral zone

Latest results on Jovian disk X-rays from XMM-Newton

We present the results of a spectral study of the soft X-ray emission (0.2-2.5 keV) from low-latitude (`disk') regions of Jupiter. The data were obtained during two observing campaigns with XMM-Newton in April and November 2003. While the level of the emission remained approximately the same between April and the first half of the November observation, the second part of the latter shows an enhancement by about 40% in the 0.2-2.5 keV flux. A very similar, and apparently correlated increase, in time and scale, was observed in the solar X-ray and EUV flux. The months of October and November 2003 saw a period of particularly intense solar activity, which appears reflected in the behaviour of the soft X-rays from Jupiter's disk. The X-ray spectra, from the XMM-Newton EPIC CCD cameras, are all well fitted by a coronal model with temperatures in the range 0.4-0.5 keV, with additional line emission from Mg XI (1.35 keV) and Si XIII (1.86 keV): these are characteristic lines of solar X-ray spectra at maximum activity and during flares. The XMM-Newton observations lend further support to the theory that Jupiter's disk X-ray emission is controlled by the Sun, and may be produced in large part by scattering, elastic and fluorescent, of solar X-rays in the upper atmosphere of the planet.Comment: 17 pages, 7 figures, accepted for publication in a special issue of Planetary and Space Scienc

An updated hydrocarbon photochemical model for the Jovian atmosphere from the troposphere through the homopause: A prelude to Galileo

A photochemical model for the atmosphere of Jupiter, including 1-D vertical eddy diffusive transport, was developed. It extends from the upper troposphere through the homopause. The hydrocarbon chemistry involves species containing up to four carbon atoms (and polyynes through C8H2). The calculations show that a large fraction of photochemical carbon may be contained in molecules with more than two carbon atoms. At the tropopause, C2H6 is the major photochemical species and C2H2, C3H8, and C4H10 are of comparable abundance and down from C2H6 by a factor of ten. These species may be detectable with the mass spectrometer of the Galileo Probe. The vertical distributions of the photochemical species are sensitive to the magnitude of eddy diffusive mixing in the troposphere and stratosphere and the details of the interface region