Hypercyclic tuples of operators on $C^n$ and $R^n$

A tuple $(T_1,\dots,T_n)$ of continuous linear operators on a topological vector space $X$ is called hypercyclic if there is $x\in X$ such that the the orbit of $x$ under the action of the semigroup generated by $T_1,\dots,T_n$ is dense in $X$. This concept was introduced by N.~Feldman, who have raised 7 questions on hypercyclic tuples. We answer those 4 of them, which can be dealt with on the level of operators on finite dimensional spaces. Inr/>particular, we prove that the minimal cardinality of a hypercyclic tuple of operators on $\C^n$ (respectively, on $\R^n$) is $n+1$ (respectively, $\frac n2+\frac{5+(-1)^n}{4}$), that there are non-diagonalizable tuples of operators on $\R^2$ which possess an orbit being neither dense nor nowhere dense and construct a hypercyclic 6-tuple of operators on $\C^3$ such that every operator commuting with each member of the tuple is non-cyclic.

Atomic harmonic generation in time-dependent R-matrix theory

We have developed the capability to determine accurate harmonic spectra for multielectron atoms within time-dependent R-matrix (TDRM) theory. Harmonic spectra can be calculated using the expectation value of the dipole length, velocity, or acceleration operator. We assess the calculation of the harmonic spectrum from He irradiated by 390-nm laser light with intensities up to 4 x 10(14) W cm(-2) using each form, including the influence of the multielectron basis used in the TDRM code. The spectra are consistent between the different forms, although the dipole acceleration calculation breaks down at lower harmonics. The results obtained from TDRM theory are compared with results from the HELIUM code, finding good quantitative agreement between the methods. We find that bases which include pseudostates give the best comparison with the HELIUM code, but models comprising only physical orbitals also produce accurate results.

Hyperglycemia and adverse pregnancy outcome (HAPO) study:Associations with neonatal anthropometrics

OBJECTIVE-To examine associations of neonatal adiposity with maternal glucose levels and cord serum C-peptide in a multicenter multinational study, the Hyperglycemia and Adverse Pregnancy Outcome (HAPO) Study, thereby assessing the Pederson hypothesis linking maternal glycemia and fetal hyperinsulinemia to neonatal adiposity. RESEARCH DESIGN AND METHODS-Eligible pregnant women underwent a standard 75-g oral glucose tolerance test between 24 and 32 weeks gestation (as close to 28 weeks as possible). Neonatal anthropometrics and cord serum C-peptide were measured. Associations of maternal glucose and cord serum C-peptide with neonatal adiposity (sum of skin folds >90th percentile or percent body fat >90th percentile) were assessed using multiple logistic regression analyses, with adjustment for potential confounders, including maternal age, parity, BMI, mean arterial pressure, height, gestational age at delivery, and the baby's sex. RESULTS-Among 23,316 HAPO Study participants with glucose levels blinded to caregivers, cord serum C-peptide results were available for 19,885 babies and skin fold measurements for 19,389. For measures of neonatal adiposity, there were strong statistically significant gradients across increasing levels of maternal glucose and cord serum C-peptide, which persisted after adjustment for potential confounders. In fully adjusted continuous variable models, odds ratios ranged from 1.35 to 1.44 for the two measures of adiposity for fasting, 1-h, and 2-h plasma glucose higher by 1 SD. CONCLUSIONS-These findings confirm the link between maternal glucose and neonatal adiposity and suggest that the relationship is mediated by fetal insulin production and that the Pedersen hypothesis describes a basic biological relationship influencing fetal growth. © 2009 by the American Diabetes Association.

Mechanical characterization of the varian Exact-arm and R-arm support systems for eight aS500 electronic portal imaging devices

The aim of this study is to compare the positioning accuracy at different gantry angles of two electronic portal imaging devices (EPIDs) support arm systems by using EPID difference images as a measure for displacement. This work presents a comparison of the mechanical performance of eight Varian aS500 (Varian Medical Systems, Palo Alto, CA) EPIDs, mounted using either the Varian Exact-arm or R-arm.