Parameterization of the set of positive- definite matrices and an algorithm for its generation

Numerical analysis on set elements for positive definite symmetric matrices by parameterizatio

Algorithm for Liapunov stability analysis

Development of algorithm provides automatic computation of quadratic estimate of domain of stability for stable equilibrium states of nonlinear systems of ordinary differential equations

Deformation of generic submanifolds in a complex manifold

This paper shows that an arbitrary generic submanifold in a complex manifold can be deformed into a 1-parameter family of generic submanifolds satisfying strong nondegeneracy conditions. The proofs use a careful analysis of the jet spaces of embeddings satisfying certain nondegeneracy properties, and also make use of the Thom transversality theorem, as well as the stratification of real-algebraic sets. Optimal results on the order of nondegeneracy are given.Comment: 24 page

Magnetic Field Limits on SGRs

We measure the period and spin-down rate for SGR 1900+14 during the quiescient period two years before the recent interval of renewed burst activity. We find that the spin-down rate doubled during the burst activity which is inconsistent with both mangetic dipole driven spin down and a magnetic field energy source for the bursts. We also show that SGRs 1900+14 and 1806-20 have braking indices of $\sim$1 which indicate that the spin-down is due to wind torques and not magnetic dipole radiation. We further show that a combination of dipole radiation, and wind luminosity, coupled with estimated ages and present spin parameters, imply that the magnetic fields of SGRs 1900+14 and 1806-20 are less than the critical field of 4$\times10^{13}$ G and that the efficiency for conversion of wind luminosity to x-ray luminosity is <2%.Comment: 5 pages, 2 figures submitted to 5th Huntsville GRB Symposium proceeding

Lockean Beliefs, Dutch Books, and Scoring Systems

On the Lockean thesis one ought to believe a proposition if and only if one assigns it a credence at or above a threshold (Foley in Am Philos Q 29(2):111–124, 1992). The Lockean thesis, thus, provides a way of characterizing sets of all-or-nothing beliefs. Here we give two independent characterizations of the sets of beliefs satisfying the Lockean thesis. One is in terms of betting dispositions associated with full beliefs and one is in terms of an accuracy scoring system for full beliefs. These characterizations are parallel to, but not merely derivative from, the more familiar Dutch Book (de Finetti in Theory of probability, vol 1, Wiley, London, 1974) and accuracy (Joyce in Philos Sci 65(4):575–603, 1998) arguments for probabilism

Renewable Energy Resources Impact on Clean Electrical Power by developing the North-West England Hydro Resource Model.

This paper describes the development of a sequential decision support system to promote hydroelectric power in North-West England. The system, composed of integrated models, addresses barriers to the installation of hydroelectric power schemes. Information is linked through an economic assessment which identifies different turbine options, assesses their suitability for location and demand; and combines the different types of information in a way that supports decision making. The system is structured into five components: the hydrological resource is modelled using Low Flows 2000, the turbine options are identified from hydrological, environmental and demand requirements; and the consequences of different solutions will be fed into other components so that the environmental impacts and public acceptability can be assessed and valued. A preliminary case study is presented on an old gunpowder works to illustrate how the resource model may be employed. Historical architectural structures, power uptake and educational instruction of hydro power technology are considered

Is SGR 1900+14 a Magnetar?

We present RXTE observations of the soft gamma--ray repeater SGR 1900+14 taken September 4-18, 1996, nearly 2 years before the 1998 active period of the source. The pulsar period (P) of 5.1558199 +/- 0.0000029 s and period derivative (Pdot) of (6.0 +/- 1.0) X 10^-11 s/s measured during the 2-week observation are consistent with the mean Pdot of (6.126 +/- 0.006) X 10^-11 s/s over the time up to the commencement of the active period. This Pdot is less than half that of (12.77 +/- 0.01) X 10^-11 s/s observed during and after the active period. If magnetic dipole radiation were the primary cause of the pulsar spindown, the implied pulsar magnetic field would exceed the critical field of 4.4 X 10^13 G by more than an order of magnitude, and such field estimates for this and other SGRs have been offered as evidence that the SGRs are magnetars, in which the neutron star magnetic energy exceeds the rotational energy. The observed doubling of Pdot, however, would suggest that the pulsar magnetic field energy increased by more than 100% as the source entered an active phase, which seems very hard to reconcile with models in which the SGR bursts are powered by the release of magnetic energy. Because of this, we suggest that the spindown of SGR pulsars is not driven by magnetic dipole radiation, but by some other process, most likely a relativistic wind. The Pdot, therefore, does not provide a measure of the pulsar magnetic field strength, nor evidence for a magnetar.Comment: 14 pages, aasms4 latex, figures 1 & 2 changed, accepted by ApJ letter

Thermonuclear burst physics with RXTE

Recently we have made measurements of thermonuclear burst energetics and recurrence times which are unprecedented in their precision, largely thanks to the sensitivity of the Rossi X-ray Timing Explorer. In the "Clocked Burster", GS 1826-24, hydrogen burns during the burst via the rapid-proton (rp) process, which has received particular attention in recent years through theoretical and modelling studies. The burst energies and the measured variation of alpha (the ratio of persistent to burst flux) with accretion rate strongly suggests solar metallicity in the neutron star atmosphere, although this is not consistent with the corresponding variation of the recurrence time. Possible explanations include extra heating between the bursts, or a change in the fraction of the neutron star over which accretion takes place. I also present results from 4U 1746-37, which exhibits regular burst trains which are interrupted by "out of phase" bursts.Comment: 4 pages, 2 figures, AIP conference proceedings format. To appear in the proceedings of the "X-ray Timing 2003: Rossi and Beyond" meeting held in Cambridge, MA, November, 200