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

WFIRST Ultra-Precise Astrometry II: Asteroseismology

WFIRST microlensing observations will return high-precision parallaxes, sigma(pi) < 0.3 microarcsec, for the roughly 1 million stars with H<14 in its 2.8 deg^2 field toward the Galactic bulge. Combined with its 40,000 epochs of high precision photometry (~0.7 mmag at H_vega=14 and ~0.1 mmag at H=8), this will yield a wealth of asteroseismic data of giant stars, primarily in the Galactic bulge but including a substantial fraction of disk stars at all Galactocentric radii interior to the Sun. For brighter stars, the astrometric data will yield an external check on the radii derived from the two asteroseismic parameters, and nu_max, while for the fainter ones, it will enable a mass measurement from the single measurable asteroseismic parameter nu_max. Simulations based on Kepler data indicate that WFIRST will be capable of detecting oscillations in stars from slightly less luminous than the red clump to the tip of the red giant branch, yielding roughly 1 million detections.Comment: 13 pages, 6 figures, submitted to JKA

Individual recognition between mother and infant bats (Myotis)

The recognition process and the basis for that recognition, in brown bats, between mother and infant are analyzed. Two parameters, ultrasonic communication and olfactory stimuli, are investigated. The test animals were not allowed any visual contact. It was concluded that individual recognition between mother and infant occurred. However, it could not be determined if the recognition was based on ultrasonic signals or olfactory stimuli

A class of quadratic deformations of Lie superalgebras

We study certain Z_2-graded, finite-dimensional polynomial algebras of degree 2 which are a special class of deformations of Lie superalgebras, which we call quadratic Lie superalgebras. Starting from the formal definition, we discuss the generalised Jacobi relations in the context of the Koszul property, and give a proof of the PBW basis theorem. We give several concrete examples of quadratic Lie superalgebras for low dimensional cases, and discuss aspects of their structure constants for the `type I' class. We derive the equivalent of the Kac module construction for typical and atypical modules, and a related direct construction of irreducible modules due to Gould. We investigate in detail one specific case, the quadratic generalisation gl_2(n/1) of the Lie superalgebra sl(n/1). We formulate the general atypicality conditions at level 1, and present an analysis of zero-and one-step atypical modules for a certain family of Kac modules.Comment: 26pp, LaTeX. Original title: "Finite dimensional quadratic Lie superalgebras"; abstract re-worded; text clarified; 3 references added; rearrangement of minor appendices into text; new subsection 4.

Counterparty Credit Limits: An Effective Tool for Mitigating Counterparty Risk?

A counterparty credit limit (CCL) is a limit imposed by a financial institution to cap its maximum possible exposure to a specified counterparty. Although CCLs are designed to help institutions mitigate counterparty risk by selective diversification of their exposures, their implementation restricts the liquidity that institutions can access in an otherwise centralized pool. We address the question of how this mechanism impacts trade prices and volatility, both empirically and via a new model of trading with CCLs. We find empirically that CCLs cause little impact on trade. However, our model highlights that in extreme situations, CCLs could serve to destabilize prices and thereby influence systemic risk

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

Novel battery model of an all-electric personal rapid transit vehicle to determine state-of-health through subspace parameter estimation and a Kalman Estimator

Abstract--The paper describes a real-time adaptive battery model for use in an all-electric Personal Rapid Transit vehicle. Whilst traditionally, circuit-based models for lead-acid batteries centre on the well-known Randles’ model, here the Randles’ model is mapped to an equivalent circuit, demonstrating improved modelling capabilities and more accurate estimates of circuit parameters when used in Subspace parameter estimation techniques. Combined with Kalman Estimator algorithms, these techniques are demonstrated to correctly identify and converge on voltages associated with the battery State-of-Charge, overcoming problems such as SoC drift (incurred by coulomb-counting methods due to over-charging or ambient temperature fluctuations). Online monitoring of the degradation of these estimated parameters allows battery ageing (State-of-Health) to be assessed and, in safety-critical systems, cell failure may be predicted in time to avoid inconvenience to passenger networks. Due to the adaptive nature of the proposed methodology, this system can be implemented over a wide range of operating environments, applications and battery topologies

Battery health determination by subspace parameter estimation and sliding mode control for an all-electric Personal Rapid Transit vehicle — the ULTra

The paper describes a real-time adaptive battery modelling methodology for use in an all electric personal rapid transit (PRT) vehicle. Through use of a sliding-mode observer and online subspace parameter estimation, the voltages associated with monitoring the state of charge (SoC) of the battery system are shown to be accurately estimated, even with erroneous initial conditions in both the model and parameters. In this way, problems such as self- discharge during storage of the cells and SoC drift (as usually incurred by coulomb-counting methods due to overcharging or ambient temperature fluctuations) are overcome. Moreover, through online monitoring of the degradation of the estimated parameters, battery ageing (State of Health) can be monitored and, in the case of safety- critical systems, cell failure may be predicted in time to avoid inconvenience to passenger networks. Due to the adaptive nature of the proposed methodology, this system can be implemented over a wide range of operating environments, applications and battery topologies, by adjustment of the underlying state-space model