Tensor operators and Wigner-Eckart theorem for the quantum superalgebra U_{q}[osp(1\mid 2)]

Tensor operators in graded representations of Z_{2}-graded Hopf algebras are defined and their elementary properties are derived. Wigner-Eckart theorem for irreducible tensor operators for U_{q}[osp(1\mid 2)] is proven. Examples of tensor operators in the irreducible representation space of Hopf algebra U_{q}[osp(1\mid 2)] are considered. The reduced matrix elements for the irreducible tensor operators are calculated. A construction of some elements of the center of U_{q}[osp(1\mid 2)] is given.Comment: 16 pages, Late

Basic Hypergeometric Functions and Covariant Spaces for Even Dimensional Representations of U_q[osp(1/2)]

Representations of the quantum superalgebra U_q[osp(1/2)] and their relations to the basic hypergeometric functions are investigated. We first establish Clebsch-Gordan decomposition for the superalgebra U_q[osp(1/2)] in which the representations having no classical counterparts are incorporated. Formulae for these Clebsch-Gordan coefficients are derived, and it is observed that they may be expressed in terms of the $Q$-Hahn polynomials. We next investigate representations of the quantum supergroup OSp_q(1/2) which are not well-defined in the classical limit. Employing the universal T-matrix, the representation matrices are obtained explicitly, and found to be related to the little Q-Jacobi polynomials. Characteristically, the relation Q = -q is satisfied in all cases. Using the Clebsch-Gordan coefficients derived here, we construct new noncommutative spaces that are covariant under the coaction of the even dimensional representations of the quantum supergroup OSp_q(1/2).Comment: 16 pages, no figure

Backgrounds of language delays of young children in East Groningen

Oost-Groningen is een gebied met traditioneel veel leerlingen met taalachterstanden. Recent reviewonderzoek heeft dat nog eens bevestigd. Inmiddels is veel bekend over de achtergronden van taalachterstanden. Desondanks stagneert de achterstandsbestrijding in deze regio. In deze bijdrage wordt getracht na te gaan op welke manier achtergrondkenmerken van ouders uit Oost-Groningen, hun verwachtingen van hun kinderen, hun opvattingen ten aanzien van onderwijs en aspecten van informele educatie een verklaring vormen voor de taalontwikkeling van 4-jarige kinderen in groep 1. Uit toetsing van het gepresenteerde theoretische model met LISREL blijkt dat opvattingen en verwachtingen van ouders in Oost-Groningen substantieel mediëren tussen achtergrondkenmerken van ouders en de taalontwikkeling, ook als gecontroleerd wordt intelligentie en verbaal geheugen van de kinderen. Ook mediëren opvattingen en verwachtingen tussen de achtergrondkenmerken en aspecten van informele educatie. Informele educatie medieert echter niet tussen de achtergrondkenmerken en taalontwikkeling. Het belang van informatieve geletterdheid van ouders en van opvattingen en verwachtingen wordt besproken. Het feit dat opvattingen en verwachtingen als leefstijlkenmerk doorwerken in de proximale processen, maar tevens verankerd zijn in de culturele leefstijl van ouders weerspiegelt de complexiteit van het vraagstuk

Experimental demonstration of singular-optical colouring of regularly scattered white light

Experimental interference modelling of the effects of colouring of a beam traversing a light-scattering medium is presented. It is shown that the result of colouring of the beam at the output of the medium depends on the magnitudes of the phase delays of the singly forward scattered partial signals. The colouring mechanism has for the first time experimentally been illustrated for a forward propagating beam through a light-scattering medium. This is showed in video-fragments of the interferograms recorded within the zero interference fringe with a gradual change of the path difference of the interfering polychromatic wave trains. Spectral investigation of the effects of colouring has been carried out using a solution of liquid crystal in a polymer matrix. The amplitude ratio of the non-scattered and the singly forward scattered interfering components significantly affects the colour intensity. It has further been established that the spectral content of the illuminating beam strongly influences the colour of the resulting radiation