Lax Operator for the Quantised Orthosymplectic Superalgebra U_q[osp(2|n)]

Each quantum superalgebra is a quasi-triangular Hopf superalgebra, so contains a \textit{universal $R$-matrix} in the tensor product algebra which satisfies the Yang-Baxter equation. Applying the vector representation $\pi$, which acts on the vector module $V$, to one side of a universal $R$-matrix gives a Lax operator. In this paper a Lax operator is constructed for the $C$-type quantum superalgebras $U_q[osp(2|n)]$. This can in turn be used to find a solution to the Yang-Baxter equation acting on $V \otimes V \otimes W$ where $W$ is an arbitrary $U_q[osp(2|n)]$ module. The case $W=V$ is included here as an example.Comment: 15 page

Microlens Parallax Measurements with a Warm Spitzer

Because Spitzer is an Earth-trailing orbit, losing about 0.1 AU/yr, it is excellently located to perform microlens parallax observations toward the Magellanic Clouds (LMC/SMC) and the Galactic bulge. These yield the so-called ``projected velocity'' of the lens, which can distinguish statistically among different populations. A few such measurements toward the LMC/SMC would reveal the nature of the lenses being detected in this direction (dark halo objects, or ordinary LMC/SMC stars). Cool Spitzer has already made one such measurement of a (rare) bright red-clump source, but warm (presumably less oversubscribed) Spitzer could devote the extra time required to obtain microlens parallaxes for the more common, but fainter, turnoff sources. Warm Spitzer could observe bulge microlenses for 38 days per year, which would permit up to 24 microlens parallaxes per year. This would yield interesting information on the disk mass function, particularly old brown dwarfs, which at present are inaccessible by other techniques. Target-of-Opportunity (TOO) observations should be divided into RTOO/DTOO, i.e., ``regular'' and ``disruptive'' TOOs, as pioneered by the Space Interferometry Mission (SIM). LMC/SMC parallax measurements would be DTOO, but bulge measurements would be RTOO, i.e., they could be scheduled in advance, without knowing exactly which star was to be observed.Comment: 6 pages + 1 Figure, To be presented at The Warm Spitzer Mission Workshop, 4-5 June 2007, Pasaden

Generalised Perk--Schultz models: solutions of the Yang-Baxter equation associated with quantised orthosymplectic superalgebras

The Perk--Schultz model may be expressed in terms of the solution of the Yang--Baxter equation associated with the fundamental representation of the untwisted affine extension of the general linear quantum superalgebra $U_q[sl(m|n)]$, with a multiparametric co-product action as given by Reshetikhin. Here we present analogous explicit expressions for solutions of the Yang-Baxter equation associated with the fundamental representations of the twisted and untwisted affine extensions of the orthosymplectic quantum superalgebras $U_q[osp(m|n)]$. In this manner we obtain generalisations of the Perk--Schultz model.Comment: 10 pages, 2 figure

A dc to dc converter

The object of the invention is to provide an improved converter for converting one direct current voltage to another. A plurality of phased square wave voltages are provided from a ring counter through amplifiers to a like plurality of output transformers. Each of these transformers has two windings, and S(1) winding and an S(2) winding. The S(1) windings are connected in series, then the S(2) windings are connected in series, and finally, the two sets of windings are connected in series. One of six SCRs is connected between each two series connected windings to a positive output terminal and one of diodes is connected between each set of two windings of a zero output terminal. By virtue of this configuration, a quite high average direct current voltage is obtained, which varies between full voltage and two-thirds full voltage rather than from full voltage to zero. Further, its variation, ripple frequency, is reduced to one-sixth of that present in a single phase system. Application to raising battery voltage for an ion propulsion system is mentioned

Systemic Risk: Simulating Local Shocks To A Global System

Using our updated model of the payment exchange system within the banking industry, we have introduced sudden local economic shocks and calculated their effect on the stability of the financial system. Our results suggest that the probability of a total banking failure, i.e., the systemic risk of the system, is insignificant unless the degree of the shock and the degree of integration between banks are very large. We find that the larger the shock, i.e., the greater the amount of loss amongst all banks, and the more isolated banks are within the payment system, the greater the likelihood of a localized or global banking system failure. However, given the current limits percentages of capitol banks can loan each other, only worldwide economic crises of cataclysmic significance would cause a collapse of the entire banking system. Hence we affirm the findings of our previous work which considered the effects of a bank failure generated by factors internal to the banking system (internal instead of internal shocks), which suggest there is minimal systemic risk in an integrated, minimally regulated, banking system.

Tempo and Mode of Evolution in the Tangled Nature Model

We study the Tangled Nature model of macro evolution and demonstrate that the co-evolutionary dynamics produces an increasingly correlated core of well occupied types. At the same time the entire configuration of types becomes increasing de-correlated. This finding is related to ecosystem evolution. The systems level dynamics of the model is subordinated to intermittent transitions between meta-stable states. We improve on previous studies of the statistics of the transition times and show that the fluctuations in the offspring probability decreases with number of transitions. The longtime adaptation, as seen by an increasing population size is demonstrated to be related to the convexity of the offspring probability. We explain how the models behaviour is a mathematical reflection of Darwin's concept of adaptation of profitable variations.Comment: 6 pages, 5 figure