Deligne-Lusztig varieties and period domains over finite fields

We prove that the Drinfeld halfspace is essentially the only Deligne-Lusztig variety which is at the same time a period domain over a finite field. This is done by comparing a cohomology vanishing theorem for DL-varieties, due to Digne, Michel, and Rouquier, with a non-vanishing theorem for PD, due to the first author. We also discuss an affineness criterion for DL-varieties.Comment: 16 pages, reference added to the paper of X. He (arXiv:0707.0259) in which the affineness conjecture for DL-varieties is prove

Development of the children's eating behaviour questionnaire

Individual differences in several aspects of eating style have been implicated in the development of weight problems in children and adults, but there are presently no reliable and valid scales that assess a range of dimensions of eating style. This paper describes the development and preliminary validation of a parent-rated instrument to assess eight dimensions of eating style in children; the Children's Eating Behaviour Questionnaire (CEBQ). Constructs for inclusion were derived both from the existing literature on eating behaviour in children and adults, and from interviews with parents. They included reponsiveness to food, enjoyment of food, satiety responsiveness, slowness in eating, fussiness, emotional overeating, emotional undereating, and desire for drinks. A. large pool of items covering each of these: constructs was developed. The number of items was then successively culled through analysis of responses from three samples of families of young children (N = 131; N = 187, N = 218), to produce a 35-item instrument with eight scales which were internally valid and had good test-retest reliability. Investigation of variations by gender and age revealed only minimal gender differences in any aspect of eating style. Satiety responsiveness and slowness in eating diminished from age 3 to 8. Enjoyment of food and food responsiveness increased over this age range. The CEBQ should provide a useful measure of eating style for research into the early precursors of obesity or eating disorders. This is especially important in relation to the growing evidence for the heritability of obesity, where good measurement of the associated behavioural phenotype will be crucial in investigating the contribution of inherited variations in eating behaviour to the process of weight gain

An instability criterion for a finite amplitude localized disturbance in a shear flow of electrically conducting fluids

The stability of shear flows of electrically conducting fluids, with respect to finite amplitude three-dimensional localized disturbances is considered. The time evolution of the fluid impulse integral, characterizing such disturbances, for the case of low magnetic Reynolds number is obtained by integrating analytically the vorticity equation. Analysis of the resulted equation reveals a new instability criterion.Comment: 10 pages in LaTex, no figures, accepted in Phys. Fluid