The Canonical Form of the Rabi Hamiltonian

The Rabi Hamiltonian, describing the coupling of a two-level system to a single quantized boson mode, is studied in the Bargmann-Fock representation. The corresponding system of differential equations is transformed into a canonical form in which all regular singularities between zero and infinity have been removed. The canonical or Birkhoff-transformed equations give rise to a two-dimensional eigenvalue problem, involving the energy and a transformational parameter which affects the coupling strength. The known isolated exact solutions of the Rabi Hamiltonian are found to correspond to the uncoupled form of the canonical system.Comment: 17 pages, LaTeX, no figures, to appear in J.Math.Phy

Rock and roll bands, (in)complete contracts and creativity

Members of a rock and roll band are endowed with different creativity. They match and eventually obtain credit for song writing as well as a share of the returns from sales. More creative members increase the probability of success but may also claim a larger share of the pie. In our theoretical model, the nature of matching (postive or negative assortative) as well as the covariation between the probability of having a “hit” and the dispersion of credits given to individual members are a function of the completeness of contracting. When members adopt a “gentleman’s agreement” to share credits equally, the covariation between the probability of a hit and the dispersion of credits is negative, which is the consequence of positive assortative matching in creativity. The data show that the relation between dispersion and success is significantly negative, and that rock bands are thus likely to sign incomplete contracts.overlapping generations, resource management, common pool resource, spatial interdependence, strategic behaviour, cooperative behaviour

Ecophisiological aspects in horticultural research

Peer Reviewe

Preschool predictors of mathematics in first grade children with autism spectrum disorder

AbstractUp till now, research evidence on the mathematical abilities of children with autism spectrum disorder (ASD) has been scarce and provided mixed results. The current study examined the predictive value of five early numerical competencies for four domains of mathematics in first grade. Thirty-three high-functioning children with ASD were followed up from preschool to first grade and compared with 54 typically developing children, as well as with normed samples in first grade. Five early numerical competencies were tested in preschool (5–6 years): verbal subitizing, counting, magnitude comparison, estimation, and arithmetic operations. Four domains of mathematics were used as outcome variables in first grade (6–7 years): procedural calculation, number fact retrieval, word/language problems, and time-related competences. Children with ASD showed similar early numerical competencies at preschool age as typically developing children. Moreover, they scored average on number fact retrieval and time-related competences and higher on procedural calculation and word/language problems compared to the normed population in first grade. When predicting first grade mathematics performance in children with ASD, both verbal subitizing and counting seemed to be important to evaluate at preschool age. Verbal subitizing had a higher predictive value in children with ASD than in typically developing children. Whereas verbal subitizing was predictive for procedural calculation, number fact retrieval, and word/language problems, counting was predictive for procedural calculation and, to a lesser extent, number fact retrieval. Implications and directions for future research are discussed