Integrability and exact spectrum of a pairing model for nucleons

A pairing model for nucleons, introduced by Richardson in 1966, which describes proton-neutron pairing as well as proton-proton and neutron-neutron pairing, is re-examined in the context of the quantum inverse scattering method. Specifically, this shows that the model is integrable by enabling the explicit construction of the conserved operators. We determine the eigenvalues of these operators in terms of the Bethe ansatz, which in turn leads to an expression for the energy eigenvalues of the Hamiltonian.

Play Preferences and Behavior of Preschool Children with Autistic Spectrum Disorder in the Clinical Environment

The play of children with autistic spectrum disorder (ASD) is a valuable medium for assessment and intervention, and its analysis has the potential to aid diagnosis. This study investigated spontaneous play behavior and play object preferences for 24 preschool children with ASD in a typical occupational therapy clinical environment. Play behavior was rated and choice of play object noted at 10-second intervals from a 15-minute video recording of unstructured play. Statistical analyses indicated that play behavior was consistent with descriptions in the literature. In addition, the children demonstrated clear preferences for play objects in the form of popular characters (e.g., Thomas the Tank Engine) and those with sensorimotor properties. We propose that the inclusion of preferred play objects in a clinical environment may increase intrinsic motivation to play, and thereby enhance assessment and intervention.

The spectrum of minimal defining sets of some Steiner systems

For a design D, define spec(D) = {\M\ \ M is a minimal defining set of D} to be the spectrum of minimal defining sets of D. In this note we give bounds on the size of an element in spec(D) when D is a Steiner system. We also show that the spectrum of minimal defining sets of the Steiner triple system given by the points and lines of PG(3,2) equals {16,17,18,19,20,21,22}, and point out some open questions concerning the Steiner triple systems associated with PG(n, 2) in general. (C) 2002 Elsevier Science B.V. All rights reserved.