Nash constructible functions

Nash constructible functions on a real algebraic set V are defined as linear combinations, with integer coefficients, of Euler characteristic of fibres of proper regular morphisms restricted to connected components of algebraic sets. We prove that if V is compact, these functions are sums of signs of semialgebraic arc-analytic functions (i.e. functions which become analytic when composed with any analytic arc). We also give a sharp upper bound to the number of semialgebraic arc-analytic functions which are necessary to define any given Nash constructible functions.     

Measurement of the transverse Doppler shift using a stored relativistic7Li+ ion beam

We have performed for the first time precision spectroscopy on a coasting fast⁷Li⁺ ion beam in a storage ring. The ion beam moving with 6.4% speed of light was first electron cooled and then merged with two counterpropagating laser beams acting on two different hyperfine transitions sharing a common upper level (λ-system). One laser was frequency locked to thea ₃ ¹²⁷J₂ hfs frequency component established as a secondary frequency standard at 514 nm. The second laser was tuned over theλ-resonance, which was recorded relative to¹²⁷J₂ hfs components. This experiment is sensitive to the time dilation in fast moving frames and will lead to new limits for the verification of special relatively. The present status of the experiment and perspectives in accuracy are discussed.     

Production of slow muonic hydrogen isotopes in vacuum

Muonic hydrogen isotopes (μ⁻ p, μ⁻ d, and μ⁻t) are simple quantum mechanical systems ideally suited for studies of numerous fundamental phenomena in electroweak and strong interactions as well as in applied areas such as muon chemistry or muon catalyzed fusion. Emission of muonic hydrogen isotopes into vacuum helps to overcome the limitations which are normally imposed on conventional investigations with gaseous and liquid targets. A proof of principle experiment for this new technique was performed at TRIUMF last year. Negative muons with 30 MeV/c momentum were stopped in a thin film of solid hydrogen and produced very low energy μ⁻d in vacuum. The distribution center of the normal velocity components of emitted μ⁻d atoms was measured to be ∼1 cm/μs. The yield of μ⁻d in vacuum is an increasing function of H₂ film thickness δ up to a value of δ≥1 mm.     

Statistical properties of aggregation with injection

We study a generalized aggregation process in which charged particles diffuse and coalesce randomly on a lattice. For one-dimensional and mean-field models, we show that there exists a statistically-invariant steady state when randomly charged particles are continuously injected. The steady-state charge distribution obeys a power law with the exponent depending both on the type of the injection and on the spatial dimension. The response of the system to a perturbation (i.e., relaxation) is characterized by either a power law decay (t ^– ,1) or a compressed exponential decay [exp(–t ),>1].     

Band-edge-induced Bragg diffraction in two-dimensional photonic crystals

Two-dimensional photonic crystals composed of two orthogonal volume diffraction gratings have been photogenerated in photopolymers. When the read beam is set at the Bragg angle, the diffraction efficiency of the transmission grating is strongly enhanced at the band edge of the reflection grating recorded in the material. Such a device provides Bragg operation and enhancement of the diffraction efficiency of the thin diffraction grating together with good wavelength selectivity. Such advantages could be interesting for optical signal processing.     

Sex differences in the relationship between white matter microstructure and impulsivity in adolescents

Rapid maturational brain changes occur during adolescence--a time associated with risk-taking behaviors and improvements in cognition. The present study examined the relationship between white matter (WM) microstructure, impulsive behavior and response inhibition in female and male adolescents. Twenty-one healthy adolescents underwent diffusion tensor imaging using a 3.0-T magnetic resonance imaging system. Impulse control was assessed using the Bar-On Emotional Quotient Inventory, Youth Version. Response inhibition was assessed using the Stroop Color-Word Interference Test. Fractional anisotropy (FA), a measure of WM coherence, and trace, a measure of overall diffusivity, were determined from voxels manually placed in the midline and in the left and right forward-projecting arms of the genu and the splenium of the corpus callosum. Sex-specific differences were observed for the relationship between FA and impulsive behavior in the right anterior callosum for males and in the splenium for females. Males, compared to females, displayed significantly higher FA in the left WM region. Although trace was not associated with impulse control, trace in the genu (for females) and splenium (males and females) was associated with Stroop performance. Regional differences in trace also were evident, with lower values in the splenium observed than in all other regions. Although the latter significantly improved with age, no sex differences in impulse control or in Stroop performance were detected. The present findings provide supporting evidence for sex-related differences in the development of WM microstructure during adolescence. These data further suggest a neurobiological mechanism underlying some of the emotional and cognitive changes commonly observed in males versus females during the adolescent period.     

Nuclear moments and the change in the mean square charge radius of neutron deficient thallium isotopes

The hyperfine structure, isotope and isomeric shifts in the atomic transition 6p ² P _3/2–7s ² S _1/2, =535 nm have been measured for theI=7 andI=2 states of^{190, 192, 194, 196}Tl; theI=1/2 andI=9/2 states of¹⁹¹Tl and the I=7 isomer of¹⁸⁸Tl. The thallium isotopes were prepared as fast atomic beams at the GSI on-line mass separator following fusion reactions and — in some cases — subsequent-decay. The nuclear dipole moments, electric quadrupole moments and the change in the nuclear mean square charge radius are evaluated. Theuu-isotopes show an isomeric shift which changes sign between¹⁹²Tl and¹⁹⁴Tl.Dedicated to P. Armbruster on the occasion of his 60th birthday