MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

Smoking and Second Hand Smoking in Adolescents with Chronic Kidney Disease: A Report from the Chronic Kidney Disease in Children (CKiD) Cohort Study

The goal of this study was to determine the prevalence of smoking and second hand smoking [SHS] in adolescents with CKD and their relationship to baseline parameters at enrollment in the CKiD, observational cohort study of 600 children (aged 1-16 yrs) with Schwartz estimated GFR of 30-90 ml/min/1.73m2. 239 adolescents had self-report survey data on smoking and SHS exposure: 21 [9%] subjects had “ever” smoked a cigarette. Among them, 4 were current and 17 were former smokers. Hypertension was more prevalent in those that had “ever” smoked a cigarette (42%) compared to non-smokers (9%), p\u3c0.01. Among 218 non-smokers, 130 (59%) were male, 142 (65%) were Caucasian; 60 (28%) reported SHS exposure compared to 158 (72%) with no exposure. Non-smoker adolescents with SHS exposure were compared to those without SHS exposure. There was no racial, age, or gender differences between both groups. Baseline creatinine, diastolic hypertension, C reactive protein, lipid profile, GFR and hemoglobin were not statistically different. Significantly higher protein to creatinine ratio (0.90 vs. 0.53, p\u3c0.01) was observed in those exposed to SHS compared to those not exposed. Exposed adolescents were heavier than non-exposed adolescents (85th percentile vs. 55th percentile for BMI, p\u3c 0.01). Uncontrolled casual systolic hypertension was twice as prevalent among those exposed to SHS (16%) compared to those not exposed to SHS (7%), though the difference was not statistically significant (p= 0.07). Adjusted multivariate regression analysis [OR (95% CI)] showed that increased protein to creatinine ratio [1.34 (1.03, 1.75)] and higher BMI [1.14 (1.02, 1.29)] were independently associated with exposure to SHS among non-smoker adolescents. These results reveal that among adolescents with CKD, cigarette use is low and SHS is highly prevalent. The association of smoking with hypertension and SHS with increased proteinuria suggests a possible role of these factors in CKD progression and cardiovascular outcomes