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A Comparative Study of Coq and HOL
This paper illustrates the differences between the style of theory mechanisation of Coq and of HOL. This comparative study is based on the mechanisation of fragments of the theory of computation in these systems. Examples from these implementations are given to support some of the arguments discussed in this paper. The mechanisms for specifying definitions and for theorem proving are discussed separately, building in parallel two pictures of the different approaches of mechanisation given by these systems
Spectral Investigations of the nature of the Sco X-1 like sources
We present results of spectral investigations of the Sco X-1 like Z-track
sources Sco X-1, GX 349+2 and GX 17+2 based on Rossi-XTE observations using an
extended accretion disk corona model. The results are compared with previous
results for the Cyg X-2 like group: Cyg X-2, GX 340+0 and GX 5-1 and a general
model for the Z-track sources proposed. On the normal branch, the Sco-like and
Cyg-like sources are similar, the results indicating an increase of mass
accretion rate Mdot between soft and hard apex, not as in the standard view
that this increases around the Z. In the Cyg-like sources, increasing Mdot
causes the neutron star temperature kT to increase from ~1 to ~2 keV. At the
lower kT, the radiation pressure is small, but at the higher kT, the emitted
flux of the neutron star is several times super-Eddington and the high
radiation pressure disrupts the inner disk launching the relativistic jets
observed on the upper normal and horizontal branches. In the Sco-like sources,
the main physical difference is the high kT of more than 2 keV on all parts of
the Z-track suggesting that jets are always possible, even on the flaring
branch. The flaring branch in the Cyg-like sources is associated with release
of energy on the neutron star consistent with unstable nuclear burning. The
Sco-like sources are very different as flaring appears to be a combination of
unstable burning and an increase of Mdot which makes flaring much stronger.
Analysis of 15 years or RXTE ASM data on all 6 classic Z-track sources shows
the high rate and strength of flaring in the Sco-like sources suggesting that
continual release of energy heats the neutron star causing the high kT. A Sco
X-1 observation with unusually little flaring supports this. GX 17+2 appears to
be transitional between the Cyg and Sco-like types. Our results do not support
the suggestion that Cyg or Sco-like nature is determined by luminosity.Comment: Astronomy and Astrophysics in press; 21 pages, 13 figure
On the nature of the Cygnus X-2 like Z-track sources
Based on the results of applying the extended ADC emission model for low mass
X-ray binaries to three Z-track sources: GX340+0, GX5-1 and CygX-2, we propose
an explanation of the CygnusX-2 like Z-track sources. The Normal Branch is
dominated by the increasing radiation pressure of the neutron star caused by a
mass accretion rate that increases between the soft apex and the hard apex. The
radiation pressure continues to increase on the Horizontal Branch becoming
several times super-Eddington. We suggest that this disrupts the inner
accretion disk and that part of the accretion flow is diverted vertically
forming jets which are detected by their radio emission on this part of the
Z-track. We thus propose that high radiation pressure is the necessary
condition for the launching of jets. On the Flaring Branch there is a large
increase in the neutron star blackbody luminosity at constant mass accretion
rate indicating an additional energy source on the neutron star. We find that
there is good agreement between the mass accretion rate per unit emitting area
of the neutron star mdot at the onset of flaring and the theoretical critical
value at which burning becomes unstable. We thus propose that flaring in the
CygnusX-2 like sources consists of unstable nuclear burning. Correlation of
measurements of kilohertz QPO frequencies in all three sources with spectral
fitting results leads to the proposal that the upper kHz QPO is an oscillation
always taking place at the inner accretion disk edge, the radius of which
increases due to disruption of the disk by the high radiation pressure of the
neutron star.Comment: Astronomy and Astrophysics, in pres
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