Magnetic moments of the 12+ isomeric states in 194, 196, 198Pb

The g-factor of the 12⁺ isomeric state in lead isotopes with A = 194, 196, 198 was measured using the time-differential perturbed angular distribution method (TDPAD). The values obtained are respectively g(194) = ?0.158(6); g(196) = ?0.157(7); g(198) = ?0.144(11). A more precise determination of the 12⁺ level half-life is also made. The g-factprs of these nuclear states, which are described with v(i_{$\text{13}\text{2}$})^?2 as the main configuration, are surprisingly constant over a large mass range (between A = 206 and 194). A core polarization analysis explains this trend: the polarization induced on neutrons in i_{$\text{13}\text{2}$} orbit decreases with the mass number A (blocking effect), but a compensation is provided by the other spin-orbit partners f_{$\text{7}\text{2}$}-f_{$\text{5}\text{2}$} and P_{$\text{3}\text{2}$}-P_{$\text{1}\text{2}$}.     

Scanning tunneling spectroscopy on the novel superconductor CaC6

We present scanning tunneling microscopy and spectroscopy of the newly discovered superconductor CaC6. The tunneling conductance spectra, measured between 3 and 15 K, show a clear superconducting gap in the quasiparticle density of states. The gap function extracted from the spectra is in good agreement with the conventional BCS theory with Delta0=1.6+/-0.2 meV. The possibility of gap anisotropy and two-gap superconductivity is also discussed. In a magnetic field, direct imaging of the vortices allows us to deduce a coherence length in the ab plane xiab approximately 33 nm.     

Velocity locking of incoherent nonlinear wave packets

We show both theoretically and experimentally in an optical fiber system that a set of incoherent nonlinear waves irreversibly evolves to a specific equilibrium state, in which the individual wave packets propagate with identical group velocities. This intriguing process of velocity locking can be explained in detail by simple thermodynamic arguments based on the kinetic wave theory. Accordingly, the selection of the velocity-locked state is shown to result from the natural tendency of the isolated wave system to approach the state that maximizes the nonequilibrium entropy.     

Compression-induced stiffness in the buckling of a one fiber composite

We study the buckling of a one fiber composite whose matrix stiffness is slightly dependent on the compressive force. We show that the equilibrium curves of the system exhibit a limit load when the induced stiffness parameter gets bigger than a threshold. This limit load increases when the stiffness parameter is increasing and it is related to a possible localized path in the post-buckling domain. Such a change in the maximum load may be very desirable from a structural stand point.     

Curriculum, Classroom Practices, and Tool Design in the Learning of Functions Through Technology-Aided Experimental Approaches

The paper starts from classroom situations about the study of a functional relationship with help of technological tools as a ‘transposition’ of experimental approaches from research mathematical practices. It considers the limitation of this transposition in existing curricula and practices based on the use of non-symbolic software like dynamic geometry and spreadsheets. The paper focuses then on the potentialities of classroom use of computer algebra packages that could help to go beyond this shortcoming. It looks at a contradiction: while symbolic calculation is a basic tool for mathematicians, curricula and teachers are very cautious regarding their use by students. The rest of the paper considers the design and experiment of a computer environment Casyopée as means to contribute to an evolution of curricula and classroom practices to achieve the transposition in the domain of algebraic activities linked to functions.     

Preparation and characterization of manganese and cobalt based semiconducting ceramics

The spinel phases Mn_3-x Co _x O₄ are prepared directly and at low temperature (600-700°C) by means of thermal decomposition of mixed oxalate salt precursors in air or controlled atmosphere. The powders so obtained when sintered at 1200°C behave as semiconducting or insulating ceramics, depending on their cobalt content. The electrical properties of these ceramics have been found to be related to the distribution and valencies of the cations in the spinel structure. The study of their crystalline structure and stability, complemented by electrical measurements have permitted us to distinguish two types of compounds. The first type includes those given by Mn_3-x Co _x O₄ with 0 < x < 1. These are stable at high temperature, have a tetragonal structure and are insulators. The cation distributions for them can be deduced from that of hausmannite as given by Mn²⁺ [Mn³⁺ ₂]O₄, by substituting Mn²⁺ ions with Co²⁺ ions. The second type of compounds correspond to the cubic phases and occur for 1 < x < 3. These are unstable at high temperature and show a lower resistivity (e.g. 360 ° cm) which is of particular interest for their application in the design of negative temperature coefficient (N.T.C.) thermistor components.     

Low-energy transitions in the 197Pb and 198Pb isotopes

The ¹⁹⁸Pb and ¹⁹⁷Pb isotopes are produced through the ¹⁸⁶W(¹⁶O, 4n, 5n) reactions. Conversion-electron, γ- and X-ray spectra are measured using the compound-nucleus recoil method. Conversion coefficients and multipolarities are deduced for a large number of transitions. Together with angular distribution measurements and the results of γγt multidimensional coincidences they lead to decay schemes for the two isotopes. Microscopic calculations, performed in the two- or three-quasiparticle approximation with a surface delta interaction, fail to reproduce completely the observed properties, showing similar defects for the odd and even isotope.     

Pupils learning algebra with DERIVE

This article deals with the use of computer algebra systems in mathematics secondary education. First, we present the global framework of a research project carried out in France with pupils of grades 9 to 12, from 1993 through 1995. Then we focus on a specific part of this project concerning two grade 9 classes of different mathematical ability taught by the same teacher. We briefly present the aims and organisation of DERIVE's use in the two classes, before embarking with more details on a specific topic: systems of linear equations. Finally, we present the data provided by the pupils' answers to a questionnaire taken at the end of the academic year; we use them for investigating pupils' assumptions about DERIVE's potential for mathematics learning, and compare these representations with those emerging from the entire population.     

Complex calculators in the classroom: theoretical and practical reflections on teaching pre-calculus

University and older school students following scientific courses now use complex calculators with graphical, numerical and symbolic capabilities. In this context, the design of lessons for 11th grade pre-calculus students was a stimulating challenge.In the design of lessons, emphasising the role of mediation of calculators and the development of schemes of use in an 'instrumental genesis' was productive. Techniques, often discarded in teaching with technology, were viewed as a means to connect task to theories. Teaching techniques of use of a complex calculator in relation with 'traditional' techniques was considered to help students to develop instrumental and paper/pencil schemes, rich in mathematical meanings and to give sense to symbolic calculations as well as graphical and numerical approaches.The paper looks at tasks and techniques to help students to develop an appropriate instrumental genesis for algebra and functions, and to prepare for calculus. It then focuses on the potential of the calculator for connecting enactive representations and theoretical calculus. Finally, it looks at strategies to help students to experiment with symbolic concepts in calculus.This revised version was published online in September 2005 with corrections to the Cover Date.