Cluster algebras in algebraic Lie theory

We survey some recent constructions of cluster algebra structures on coordinate rings of unipotent subgroups and unipotent cells of Kac-Moody groups. We also review a quantized version of these results.Comment: Invited survey; to appear in Transformation Group

Fractional smoothness and applications in finance

This overview article concerns the notion of fractional smoothness of random variables of the form $g(X_T)$, where $X=(X_t)_{t\in [0,T]}$ is a certain diffusion process. We review the connection to the real interpolation theory, give examples and applications of this concept. The applications in stochastic finance mainly concern the analysis of discrete time hedging errors. We close the review by indicating some further developments.Comment: Chapter of AMAMEF book. 20 pages

Algorithm for Liapunov stability analysis

Development of algorithm provides automatic computation of quadratic estimate of domain of stability for stable equilibrium states of nonlinear systems of ordinary differential equations

Cascaded third harmonic generation in lithium niobate nanowaveguides

We predict highly efficient third harmonic generation through simultaneous phase-matching of second-harmonic generation and sum-frequency generation in lithium niobate nanowaveguides, enabled due to strong modal dispersion. We demonstrate that the waveguide size which corresponds to phase-matching is also optimal for highest mode confinement and therefore for strongly enhanced conversion efficiency.We acknowledge the support by the Australian Research Council, the Australian Academy of Science, Australian National Computational Infrastructure, and German Research Foundation, Grant No. NanoGuide, PE 1524/5-1

Isotopic Composition of Solar Wind Calcium: First in Situ Measurement by CELIAS/MTOF on Board SOHO

We present first results on the Ca isotopic abundances derived from the high resolution Mass Time-of-Flight (MTOF) spectrometer of the charge, element, and isotope analysis system (CELIAS) experiment on board the Solar and Heliospheric Observatory (SOHO). We obtain isotopic ratios 40Ca/42Ca = (128+-47) and 40Ca/44Ca = (50+-8), consistent with terrestrial values. This is the first in situ determination of the solar wind calcium isotopic composition and is important for studies of stellar modeling and solar system formation since the present-day solar Ca isotopic abundances are unchanged from their original isotopic composition in the solar nebula.Comment: 14 pages, 3 figure

Control of Risk Factors Among People With Diagnosed Diabetes, by Lower Extremity Disease Status

Introduction We examined the control of modifiable risk factors among a national sample of diabetic people with and without lower extremity disease (LED). Methods The sample from the 1999-2004 National Health and Nutrition Examination Survey consisted of 948 adults aged 40 years or older with diagnosed diabetes and who had been assessed for LED. LED was defined as peripheral arterial disease (ankle-brachial index <0.9), peripheral neuropathy (≥1 insensate area), or presence of foot ulcer. Good control of modifiable risk factors, based on American Diabetes Association recommendations, included being a nonsmoker and having the following measurements: hemoglobin A1c (HbA1c) less than 7%, systolic blood pressure less than or equal to 130 mm Hg, diastolic blood pressure less than or equal to 80 mm Hg, high-density lipoprotein (HDL) cholesterol greater than 50 mg/dL, and body mass index (BMI) between 18.5 kg/m2 and 24.9 kg/m2. Results Diabetic people with LED were less likely than were people without LED to have recommended levels of HbA1c (39.3% vs 53.5%) and HDL cholesterol (29.7% vs 41.1%), but there were no differences in systolic or diastolic blood pressure, BMI classification, or smoking status between people with and without LED. Control of some risk factors differed among population subgroups. Notably, among diabetic people with LED, non-Hispanic blacks were more likely to have improper control of HbA1c (adjusted odds ratio [AOR] = 2.0; 95% confidence interval [CI], 1.1-3.9), systolic blood pressure (AOR = 1.9; 95% CI, 1.1-3.2), and diastolic blood pressure (AOR = 2.6; 95% CI, 1.1-5.8), compared with non-Hispanic whites. Conclusion Control of 2 of 6 modifiable risk factors was worse in diabetic adults with LED compared with diabetic adults without LED. Among diabetic people with LED, non-Hispanic blacks had worse control of 3 of 6 risk factors compared with non-Hispanic whites