Weyl calculus and dual pairs

We consider a dual pair $(G,G')$, in the sense of Howe, with $G$ compact acting on $L^2(\mathbb R^n)$ for an appropriate $n$ via the Weil Representation. Let $\widetilde{G}$ be the preimage of $G$ in the metaplectic group. Given a genuine irreducible unitary representation $\Pi$ of $\widetilde{G}$ we compute the Weyl symbol of orthogonal projection onto $L^2(\mathbb R^n)_\Pi$, the $\Pi$-isotypic component. We apply the result to obtain an explicit formula for the character of the corresponding irreducible unitary representation $\Pi'$ of $\widetilde{G'}$ and to compute of the wave front set of $\Pi'$ by elementary means

Semisimple orbital integrals on the symplectic space for a real reductive dual pair

We prove a Weyl Harish-Chandra integration formula for the action of a reductive dual pair on the corresponding symplectic space $W$. As an intermediate step, we introduce a notion of a Cartan subspace and a notion of an almost semisimple element in the symplectic space $W$. We prove that the almost semisimple elements are dense in $W$. Finally, we provide estimates for the orbital integrals associated with the different Cartan subspaces in $W$

The GPRIME approach to finite element modeling

GPRIME, an interactive modeling system, runs on the CDC 6000 computers and the DEC VAX 11/780 minicomputer. This system includes three components: (1) GPRIME, a user friendly geometric language and a processor to translate that language into geometric entities, (2) GGEN, an interactive data generator for 2-D models; and (3) SOLIDGEN, a 3-D solid modeling program. Each component has a computer user interface of an extensive command set. All of these programs make use of a comprehensive B-spline mathematics subroutine library, which can be used for a wide variety of interpolation problems and other geometric calculations. Many other user aids, such as automatic saving of the geometric and finite element data bases and hidden line removal, are available. This interactive finite element modeling capability can produce a complete finite element model, producing an output file of grid and element data

Theoretical results of one class of multiderivative methods through order stars

Order stars are applied to Brown (K,L) methods. They are displayed pictorially for a selection of methods and are used to provide succinct proofs of existing results. Asymptotic results concerning their stability are also presented

Type 2 diabetes in Tirana City, Albania: a rapid increase in a country in transition.

AIMS: To determine how the prevalence of Type 2 diabetes mellitus has changed in Tirana, the capital of Albania, over 20 years. METHODS: Cluster sampling was used to select 700 households including 1540 adults 25 years of age and over in Tirana City, Albania in 2001. RESULTS: Of 1540 potential subjects, 1120 participated (response rate 72.7%). Using the 1985 WHO criteria to provide comparability with earlier data, the overall prevalence of Type 2 diabetes mellitus in the age group 25+ was 6.3% (95% confidence interval 4.8-7.7); 6.9% (4.8-9.1%) male; 5.6% (3.8-7.5%) female. The age-adjusted prevalence in those aged 25+ was 5.4%. Of respondents, 3.4% were known to have diabetes, and 2.9% were newly identified through the survey. The prevalence of diabetes increased with age, although among men there was a slight decline after age 65. Impaired glucose tolerance was found in a further 2.9% of respondents, again increasing with age. The prevalence of diabetes has increased significantly since 1980, doubling in the age group 50+. Use of the 1999 WHO diagnostic criteria produces a higher unadjusted prevalence, at 9.7% (8-11.4%). In a logistic regression model, obesity and family history were independent determinants of the probability of having diabetes. Among those known to have diabetes, control was poor. CONCLUSIONS: The prevalence of diabetes in Albania has increased rapidly, consistent with what has been seen in other countries undergoing rapid modernization. It is likely to increase further in the future, with important implications for health policy

Post-surgical pain, physical activity and satisfaction with the decision to undergo hernia surgery : a prospective qualitative investigation

Peer reviewedPublisher PD

Saccadic latency in amblyopia.

We measured saccadic latencies in a large sample (total n = 459) of individuals with amblyopia or risk factors for amblyopia, e.g., strabismus or anisometropia, and normal control subjects. We presented an easily visible target randomly to the left or right, 3.5° from fixation. The interocular difference in saccadic latency is highly correlated with the interocular difference in LogMAR (Snellen) acuity-as the acuity difference increases, so does the latency difference. Strabismic and strabismic-anisometropic amblyopes have, on average, a larger difference between their eyes in LogMAR acuity than anisometropic amblyopes and thus their interocular latency difference is, on average, significantly larger than anisometropic amblyopes. Despite its relation to LogMAR acuity, the longer latency in strabismic amblyopes cannot be attributed either to poor resolution or to reduced contrast sensitivity, because their interocular differences in grating acuity and in contrast sensitivity are roughly the same as for anisometropic amblyopes. The correlation between LogMAR acuity and saccadic latency arises because of the confluence of two separable effects in the strabismic amblyopic eye-poor letter recognition impairs LogMAR acuity while an intrinsic sluggishness delays reaction time. We speculate that the frequent microsaccades and the accompanying attentional shifts, made while strabismic amblyopes struggle to maintain fixation with their amblyopic eyes, result in all types of reactions being irreducibly delayed