Spindensities in Pseudo-classical kinetic theory

In this paper the classical limit of relativistic transport theories for spin 1/2 fermions is examined through a comparison with the classical kinetic theory derived from N=1 supersymmetric classical mechanics. The conclusion is that in the classical limit spindensities, i.e. the axial-vector contribution to the relativistic Wigner-function, vanishes and dipole-densities, i.e. the spin-tensor contributions to the relativistic Wigner function, may survive.Comment: Latex 22 pages, 63628 bytes. No figure

Tidal evolution of eccentric orbits in massive binary systems; a study of resonance locking

We study the tidal evolution of a binary system consisting of a 1.4 Msun compact object in elliptic orbit about a 10 Msun uniformly rotating main sequence star for various values of the initial orbital parameters. We apply our previously published results of 2D non-adiabatic calculations of the non-radial g- and r-mode oscillations of the uniformly rotating MS star, and include the effects of resonant excitation of these modes in the tidal evolution calculations. A high orbital eccentricity enhances the effectiveness of the tidal interaction because of the large number of harmonic components of the tidal potential and the reduced orbital separation near periastron. By including the evolution of the MS star, especially of its rotation rate, many resonance crossings occur with enhanced tidal interaction. We analyse the phenomenon of resonance locking whereby a particular tidal harmonic is kept resonant with a stellar oscillation mode. Resonance locking of prograde g-modes appears an effective mechanism for orbital circularization of eccentric orbits. We consider the orbital evolution of the binary pulsar PSR J0045-7319 and conclude that resonance locking could explain the observed short orbital decay time of this system if the B-star spins in the direction counter to the orbital motion.Comment: 21 pages, 11 figures; some at reduced resolution, accepted for publication in A&

Tidal interaction of a rotating 1 Msun star with a binary companion

We calculate the tidal torque on a uniformly rotating 1 Msun star at various stages of core hydrogen burning by an orbiting companion. We apply the `traditional approximation' and solve the radial part of the tidal perturbations by matrix inversion of the set of finite difference equations on a very fine grid. We have identified resonances with gravity- and quasi-toroidal modes with up to 1000 radial nodes in the more evolved stellar models. For low forcing frequencies we find significant tidal response due to viscous damping of inertial modes in the convective envelope of the solar-type star. We conclude that effects due to stellar rotation (including resonance locking) may considerably enhance the speed of tidal evolution in solar-type stars.Comment: accepted for publ. in A&A, 11 pages, 6 figure

Construction of a Lax Pair for the E6(1)E_6^{(1)} qq-Painlev\'e System

We construct a Lax pair for the $E^{(1)}_6$ $q$-Painlev\'e system from first principles by employing the general theory of semi-classical orthogonal polynomial systems characterised by divided-difference operators on discrete, quadratic lattices [arXiv:1204.2328]. Our study treats one special case of such lattices - the $q$-linear lattice - through a natural generalisation of the big $q$-Jacobi weight. As a by-product of our construction we derive the coupled first-order $q$-difference equations for the $E^{(1)}_6$ $q$-Painlev\'e system, thus verifying our identification. Finally we establish the correspondences of our result with the Lax pairs given earlier and separately by Sakai and Yamada, through explicit transformations

Estimating and explaining efficiency in a multilevel setting: A robust two-stage approach

Various applications require multilevel settings (e.g., for estimating fixed and random effects). However, due to the curse of dimensionality, the literature on non-parametric efficiency analysis did not yet explore the estimation of performance drivers in highly multilevel settings. As such, it lacks models which are particularly designed for multilevel estimations. This paper suggests a semi-parametric two-stage framework in which, in a first stage, non-parametric a effciency estimators are determined. As such, we do not require any a priori information on the production possibility set. In a second stage, a semiparametric Generalized Additive Mixed Model (GAMM) examines the sign and significance of both discrete and continuous background characteristics. The proper working of the procedure is illustrated by simulated data. Finally, the model is applied on real life data. In particular, using the proposed robust two-stage approach, we examine a claim by the Dutch Ministry of Education in that three out of the twelve Dutch provinces would provide lower quality education. When properly controlled for abilities, background variables, peer group and ability track effects, we do not observe differences among the provinces in educational attainments.Productivity estimation; Multilevel setting; Generalized Additive Mixed Model; Education; Social segregation

On estimating the effectiveness of resources. A local maximum likelihood frontier approach on care for students

To study education as a complex production process in a noisy and heterogeneous setting, this paper suggests to using a stochastic frontier model estimated by a local maximum likelihood approach (LMLSF). The LMLSF smoothly combines the virtues of the non-parametric Data Envelopment Analysis model and the semi-parametric Stochastic Frontier model. Additionally, by the LMLSF approach one can deduce the eectiveness of resources by examining the impact of inputs on the frontier. Indeed, while eciency estimations (i.e., doing the things right) received considerable attention in the literature, the analysis of effectiveness (i.e., doing the right things) is less explored. The approach is illustrated on a sample of Dutch primary education pupils. We examine the eectiveness of instruction time, experience of the teacher, and student care (both social worker and psychologist) on educational attainments of native and non-native students.Stochastic Frontier Analysis; Data Envelopment Analysis; Local Maximum Likelihood; Education; Student care