Theoretical characterization of intermolecular vibrational states through the multi-configuration time dependent Hartree approach: the He2,3ICl clusters

Benchmark, full-dimensional calculations on the ground and excited vibrational states for the tetra-, and penta-atomic weakly bound He(2,3)ICl complexes are reported. The representation of the potential energy surfaces includes three-body HeICl potentials parameterized to coupled-cluster singles, doubles, and perturbative triples ab initio data. These terms are important in accurately describing the interactions of such highly floppy systems. The corresponding 6D/9D computations are performed with the multi-configuration time dependent Hartree method, using natural potential fits, and a mode combination scheme to optimize the computational effort in the improved relaxation calculations. For these complexes several low-lying vibrational states are computed, and their binding energies and radial/angular probability density distributions are obtained. We found various isomers which are assigned to different structural models related with combinations of the triatomic isomers, like linear, T-shaped, and antilinear ones. Comparison of these results with recent experimental data is presented, and the quantitative deviations found with respect to the experiment are discussed.     

Application of the stabilization method to interacting resonances

The stabilization method is applied to the case of interacting resonances in the photo-dissociation of van der Waals clusters composed by a rare gas atom bound to a dihalogen molecule. The study of an illustrative two-dimensional model consisting in a T-shaped NeI₂ molecule shows the adequacy of the method whenever the projection of the stabilization wave functions on the assumed prepared initial state is accounted for. The agreement of the fragmentation cross-sections with some previous results using the effective resolvent method and accurate close-coupling calculations is excellent. The method reveals its utility as a complementary tool since allows, through the analysis of the stabilization wave function in terms of zero-order levels, a precise characterization of the resonant states involved. Received 5 April 2002 / Received in final form 24 May 2002 Published online 19 July 2002     

Novel nitration of estrone by metal nitrates

Nitration of estrone has been investigated with different types of metal salts in the presence of solid surfaces under various conditions.     

On the equations of the edge cone of a graph¶and some applications

Let G be a graph such that none of its components is bipartite. We describe the facets of the cone generated by the columns of the incidence matrix of G. Let k[G] be the subring generated by the monomials of degree two defining the edges of G, where k is a field. Some estimates for the a-invariant of k[G] are shown when G is the cone of a normal connected non bipartite graph or G is the join of two normal connected non bipartite graphs. Received: 24 July 1997 / Revised version: 3 March 1998     

Effect of diluents on poly(vinyl acetate) dynamics

The effect of diluents and temperature on segmental motion in poly(vinyl acetate) was investigated by both NMR and ESR spectroscopy. Three classes of diluents were studied: chloroform, a thermodynamically good solvent; water, a poor solvent which slightly swells the polymer and lowers its glass transition temperature; and decane, a nonsolvent so poor it does not appear to swell the polymer nor lower the calorimetric glass transition temperature. At all temperatures investigated each type of diluent increased the segmental motion of the polymer over that of the bulk sample. Under the conditions studied, ¹³C and ²H NMR and nitroxide spin-label ESR data gave similar views of segmental motion of the polymer, indicating that in this amorphous polymer the segmental motion of the polymer may be safely inferred from spin-label data.     

Collectives of humans-with-media in mathematics education: notebooks, blackboards, calculators, computers and … notebooks throughout 100 years of ICMI

The main aim of this study was to present evidence of the ways in which different media have conditioned and dramatically reorganized education, in general, and mathematics education, in particular. After an introduction of the theme, we discuss the epistemological perspective that provides the foundation for our analysis: the notion of humans-with-media. Then, we briefly illustrate how the medium is related to the scientific production of mathematical knowledge. We take a detour into the world of art to examine how devices and instruments have historically been associated with the production of mathematical knowledge. Then, we review studies on the history of education to show how traditional media were introduced into schools and have influenced education. In particular, we examine how devices such as blackboards and notebooks, which were novelties a 100 years ago, came to be accepted in schools and the mathematical activities that were promoted with their use. Finally, we discuss how information technology has changed education and how the Internet may have an impact on mathematics education comparable to that of the notebook over a century ago.