On Maximally Inflected Hyperbolic Curves

In this note we study the distribution of real inflection points among the ovals of a real non-singular hyperbolic curve of even degree. Using Hilbert’s method we show that for any integers \(d\) and \(r\) such that \(4\le r \le 2d^2-2d\) , there is a non-singular hyperbolic curve of degree \(2d\) in \({\mathbb R}^2\) with exactly \(r\) line segments in the boundary of its convex hull. We also give a complete classification of possible distributions of inflection points among the ovals of a maximally inflected non-singular hyperbolic curve of degree \(6\) .     

Fundamental symmetries studies with cold trapped francium atoms at ISAC

Francium combines a heavy nucleus (Z = 87) with the simple atomic structure of alkalis and is a very promising candidate for precision tests of fundamental symmetries such as atomic parity non-conservation measurements. Fr has no stable isotopes, and the ISAC radioactive beam facility at TRIUMF, equipped with an actinide target, promises to provide record quantities of Fr atoms, up to 10¹⁰/s for some isotopes. We discuss our plans for a Fr on-line laser trapping facility at ISAC and experiments with samples of cold Fr atoms. We outline our plans for a measurement of the nuclear anapole moment – a parity non-conserving, time-reversal conserving moment that arises from weak interactions between nucleons – in a chain of Fr isotopes. Its measurement is a unique probe for neutral weak interactions inside the nucleus.      

Erratum to: Thermal conductivity as a probe of unconventional superconducting gap

We have carried out a comparative study of the thermal conductivity of two rectangular single crystals: a niobium sample and a detwinned YBCO. Thermal conductivity was measured as a function of the relative orientation of the crystaline axes and a magnetic field applied parallel to the sample plane. Different angular variations, two-fold for Nb and four-fold for YBCO, were observed in the two case. We discuss the microscopic effects related to the gap structure which are at the origin of this qualitative difference in the behavior of thermal conductivity in these two superconductors.     

A viability approach to the inverse set-valued map theorem

The purpose of this paper is to characterize by means of viability tools the pseudo-lipschitzianity property of a set-valued map F in a neighborhood of a point of its graph in terms of derivatives of this set-valued map F in a neighborhood of a point of its graph, instead of using the transposes of the derivatives. On the way, we relate these properties to the calmness index of a set-valued map, an extensions of Clarke’s calmness of a function, as well as Doyen’s Lipschitz kernel of a set-valued map, which is the largest Lipschitz submap.     

Electrical properties of vapour grown ZrSe3 single crystals

Resistivity, Hall coefficient and thermoelectric power measurements of ZrSe₃ single crystals along the chain axis were carried out in the temperature range from 200 to 400 K. Experimental results are explained by the model of compensated semiconductors with two-dimensional characteristics. The activation energy of the donor level is determined to be 0.25 eV and the effective mass of the conduction band parallel to the layer is estimated to be 0.3m₀.     

Boundary-value problems for systems of first-order partial differential inclusions

((Without abstract.))     

Compensation strategies for a lip-tube perturbation of French [u]: an acoustic and perceptual study of 4-year-old children

The relations between production and perception in 4-year-old children were examined in a study of compensation strategies for a lip-tube perturbation. Acoustic and perceptual analyses of the rounded vowel [u] produced by twelve 4-year-old French speakers were conducted under two conditions: normal and with a 15-mm-diam tube inserted between the lips. Recordings of isolated vowels were made in the normal condition before any perturbation (N1), immediately upon insertion of the tube and for the next 19 trials in this perturbed condition, with (P2) or without articulatory instructions (P1), and in the normal condition after the perturbed trials (N2). The results of the acoustic analyses reveal speaker-dependent alterations of F1, F2, and/or F0 in the perturbed conditions and after the removal of the tube. For some subjects, the presence of the tube resulted in very little change; for others, an increase in F2 was observed in P1, which was generally reduced in some of the 20 repetitions, but not systematically and not continuously. The use of articulatory instructions provided in the P2 condition was detrimental to the achievement of a good acoustic target. Perceptual data are used to determine optimal combinations of F0, F1, and F2 (in bark) related to these patterns. The data are compared to a previous study conducted with adults [Savariaux et al., J. Acoust. Soc. Am. 106, 381-393 (1999)].     

Nuclear magnetic moment of 210Fr: a combined theoretical and experimental approach

We measure the hyperfine splitting of the 9S_{1/2} level of 210Fr, and find a magnetic dipole hyperfine constant A=622.25(36) MHz. The theoretical value, obtained using the relativistic all-order method from the electronic wave function at the nucleus, allows us to extract a nuclear magnetic moment of 4.38(5)micro_{N} for this isotope, which represents a factor of 2 improvement in precision over previous measurements. The same method can be applied to other rare isotopes and elements.