Condensed vortex ground states of rotating Bose-Einstein condensate in harmonic atomic trap

We study a system of $N$ Bose atoms trapped by a symmetric harmonic potential, interacting via weak central forces. Considering the ground state of the rotating system as a function of the two conserved quantities, the total angular momentum and its collective component, we develop an algebraic approach to derive exact wave functions and energies of these ground states. We describe a broad class of the interactions for which these results are valid. This universality class is defined by simple integral condition on the potential. Most of the potentials of practical interest which have pronounced repulsive component belong to this universality class.Comment: 34 pages, 10 ps figures, minor revisions, to be publ. in Ann. Phy

Mortality following a brain tumour diagnosis in patients with multiple sclerosis

Objectives: As brain tumours and their treatment may theoretically have a poorer prognosis in inflammatory central nervous system diseases such as multiple sclerosis (MS), all-cause mortality following a brain tumour diagnosis was compared between patients with and without MS. The potential role of age at tumour diagnosis was also examined. Setting: Hospital inpatients in Sweden with assessment of mortality in hospital or following discharge. Participants: Swedish national registers identified 20 543 patients with an MS diagnosis (1969-2005) and they were matched individually to produce a comparison cohort of 204 163 members of the general population without MS. Everyone with a primary brain tumour diagnosis was selected for this study: 111 with MS and 907 without MS. Primary and secondary outcome measures: 5-year mortality risk following brain tumour diagnosis and age at brain tumour diagnosis. Results: A non-statistically significant lower mortality risk among patients with MS (lower for those with tumours of high-grade and uncertain-grade malignancy and no notable difference for low-grade tumours) produced an unadjusted HR (and 95% CI) of 0.75 (0.56 to 1.02). After adjustment for age at diagnosis, grade of malignancy, sex, region of residence and socioeconomic index, the HR is 0.91 (0.67-1.24). The change in estimate was largely due to adjustment for age at brain tumour diagnosis, as patients with MS were on average 4.7 years younger at brain tumour diagnosis than those in the comparison cohort (p<0.001). Conclusions: Younger age at tumour diagnosis may contribute to mortality reduction in those with highgrade and uncertain-grade brain tumours. Survival following a brain tumour is not worse in patients with MS; even after age at brain tumour diagnosis and grade of malignancy are taken into account