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 $W$

Epidemiology of hypertension and associated cardiovascular risk factors in a country in transition: a population based survey in Tirana City, Albania.

STUDY OBJECTIVE: To describe the prevalence of hypertension and other cardiovascular risk factors on the adult population of Tirana City (Albania). DESIGN: Cross sectional survey. SETTING: Tirana City in mid-2001. PARTICIPANTS: 1120 adults aged 25 years and over (response rate=72.7%). MAIN RESULTS: Overall, hypertension prevalence (blood pressure =140 and/or 90 mm Hg, or known hypertensive receiving anti-hypertensive treatment) was 31.8% (36.6% and 27.4% in men and women respectively). Age standardised prevalence of hypertension (adjusted to the adult population of Tirana) was 30.2% (99% confidence intervals 29.8% to 30.6%) in men and 22.7% (22.3% to 23.1%) in women. Men were significantly more likely to be hypertensive than women (p value=0.001). Of those who had been diagnosed with hypertension, 87% were receiving anti-hypertensive therapy and more than half of them (52%) were adequately controlled. The prevalence of hypertension increased with increasing age and was more common in the obese in both sexes. While the prevalence of hypertension matched that in other industrialised and transition countries, the combination of hypertension with other cardiovascular risk factors was rather less common. CONCLUSION: These findings provide important new evidence on the prevalence of hypertension and its association with other cardiovascular risk factors in Albania. Albania is in a state of rapid transition, with evidence that risk factors for non-communicable diseases have already increased considerably over the past two decades. These finding provide a unique baseline against which future change can be compared

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

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