Cyclisation du dipropényl-2,2′ diphényle et du dipropényl-1,8 naphtalene

2,2′-Dipropenyldiphenyl with a suspension of sodium in isopropylamine leads to a mixture of Z and E isomers of 6-methyl-5-éthylidène-1,2,3,4-dibenzocycloheptane. In the same conditions, 1,8 dipropénylnaphthalene gives a mixture of Z and E isomers of 9-éthylidène-8-methylperinaphtane. In this last case, in order to explain the cyclisation, second order terms of the perturbation theory must be used. We reach then the limit of use of HOMO.     

A covalent model for the bonding of adsorbed hydrocarbon fragments on the (111) face of platinum

A systematic molecular orbital study of the location of CH_n and C-CH_n (n = 1, 2, 3) species on a Pt(111) single-crystal surface has been performed by using both a cluster model and a band structure calculation within the framework of the Extended Hückel Theory (EHT). These species may be involved in the hydrogenation/dehydrogenation processes of hydrocarbons. The observed dependence of the adsorption site on the number of hydrogens in the CH_n fragments suggests that any C-H bond breaking in CH_n species must involve a change of adsorbate bonding site. The carbon is found to be located on the surface in such a way as to complete its tetravalancy. Thus, CH occupies a three-fold coordinated hollow site, CH₂ a two-fold coordinated bridge site and CH₃ a one-fold coordinated top site. C-CH₃ is found to be perpendicular to the surface in a three-fold hollow site in agreement with experimental observations. It is also found that a displacement of C-CH₂-R to a top site makes a β C-R cleavage easier.     

The Kruskal-Katona method made explicit

Let K_c(e) = min |ΓX|, where the minimum is taken over all e-member families X of c-element subsets of a finite set S where ΓX is the family of (c?1)-element subsets of S contained in at least one member of X and where |ΓX| is the number of members in ΓX. J. B. Kruskal [5] and G. O. H. Katona [4] discovered independently an implicit method for calculating K_c(e). In this note a more explicit method is presented.     

Highly conducting transmembrane pores formed by aromatic oligoamide macrocycles

Oligoamide macrocycles 1d and 1e, which carry membrane-compatible side chains and contain a hydrophilic, noncollapsible cavity, were found to mediate high ion flux across a lipid bilayer, as demonstrated by results from (23)Na NMR and planar bilayer conductance measurements. The measured transmembrane single channel currents are very high, rivaling those typically associated with pore-forming protein toxins. The obtained results have demonstrated the promise of developing large, highly conducting channels based on nanopores formed by oligoamide macrocycles.     

Structural, vibrational and ab initio studies of L-histidine oxalate

Single crystals of L-histidine oxalate were obtained by slow evaporation of an aqueous solution at room temperature. The grown crystals have been subjected to X-ray diffraction (XRD), Infrared, and Raman spectroscopy. The title compound crystallises in the non-centrosymmetric space group P2(1)2(1)2(1,) the crystal cohesion is achieved by relatively strong hydrogen bonds, so that the NH3 groups show significant distortion with respect to the tetrahedral symmetry. Raman and infrared spectra of the title compound were recorded in the frequency range 300-3200 and 400-4000 cm-1, respectively. To obtain a reliable assignment of the observed spectral lines, we have calculated the geometry and the frequencies of the vibrational modes of histidine cation and the oxalate anion using the semi empirical PM3 method.     

The fluorite-pyrochlore transformation of Ho2−yNdyZr2O7

Twelve members of the Ho_2−yNd_yZr₂O₇ series, prepared using conventional solid state methods, have been characterised by neutron powder diffraction. Ho₂Zr₂O₇ has a defect fluorite structure whereas Nd₂Zr₂O₇ is found to adopt the ordered pyrochlore structure with the composition induced fluorite-pyrochlore transformation occurring near y=1. Rietveld analysis on the neutron data for all the compositions reveals an increase in lattice parameter as a function of y across the entire series, with a small discontinuity associated with the transformation. The neutron profile results suggest that domains of pyrochlore-type initially begin to form before crystallising into a separate phase, and therefore that anion and cation ordering processes are distinct. There is a strong correlation between the extent of disorder in the anion sublattice and the x-parameter of 48f oxygen. These results point the way to a better understanding of the stability observed in pyrochlore structures.     

Teaching Length Measurement: Research Challenges

Many publications and curriculum materials promote a specific instructional sequence for introducing length measure: gross comparisons of length, measurement with nonstandard units such as paper clips, measurement with manipulative standard units, and finally measurement with standard instruments such as rulers. Several recent studies, however, imply that aspects of this traditional approach may not match children's developmental progression. This article describes several studies that challenge conventional wisdom regarding the teaching and learning of nonstandard and standard units, rulers, and measurement sense and draws educational implications from their results.     

Quantum automaton in a 1-D box

A simple cellular automaton is conjectured based on the Dirac wave equation and a diffusion confinement which attempts to emulate quantum behaviour of a particle in a 1-D box. Some features of quantum behavior such as the collapse of the wave function upon measurement, the wave-like nature of particles, and the role of virtual and non-local interactions become evident after completing a series of computations and analyzing the results. A pronounced correspondence between an automaton and a quantum particle in a 1-D box is explicated and shows promise for explaining some of the cloudy conceptual difficulties enmeshed in present quantum space-time pictures of reality.     

Transient displacement and stress in non-homogeneous elastic shells

Summary Transient displacement and stress in thick inhomogeneous cylindrical and spherical shells is investigated for situations when the surfaces are subjected to dynamic loads consistent with the production of radial vibrations. In the first instance, transformation of the governing equations is sought to a form amenable to solution via a finite Hankel transform technique. Such reduction is available for a broad class of radial variations in the material density and elastic parameters. However, the solutions generated by this method are rather involved and two other approaches are indicated. Thus, reduction of the system to the conventional wave equation is obtained under certain restrictions on the nature of the inhomogeneities and a simple correspondence principle is presented for the imposed boundary stress boundary value problem. Finally an asymptotic wave front analysis is presented which has a wide generality of application.

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Zusammenfassung Es werden die zeitlich vorübergehenden Verrückungen und Spannungsänderungen in dicken inhomgenen zylinder-und kugelförmigen Schalen für den Fall untersucht, dass die Oberfläche dynamischen Belastungen ausgesetzt ist, die strahlenförmige Schwingungen produzieren. Zunächst werden Tranformationen der auftretended Gleichungen gesucht, die eine Lösung mit Hilfe von endlichen Hankeltransformations-Techniken zulassen. Eine solche Reduzierung ist für eine grosse Klasse von abstandsabhängigen Veränderungen der Dichte-und Elastizitätsparameter \:moglich.Die so erhaltenen Lösungen sind jedoch recht kompliziert, und zwei weitere Lösungsmöglichkeiten werden angedeutet. Einmal erhält man unter gewissen Beschränkungen bezüglich der Art der Inhomogenitäten eine Reduzierung des Gleichungssystems auf die gewögnliche Wellengleichung, zum anderen wird ein einfaches Korrespondensprinzip für das betrachtete Randwertproblem aufgestellt. Schliesslich wird eine asymptotische Wellenfrontanalyse entwickelt, die vielseitig verwendbar ist.