Some alternating sums of Lucas numbers

We consider alternating sums of squares of odd and even terms of the Lucas sequence and alternating sums of their products. These alternating sums have nice representations as products of appropriate Fibonacci and Lucas numbers.     

Aluminum(III) complexes containing O,O chelating ligand

The stoichiometric reactions of trimethylaluminum with 2,6‐(MeOCH₂)₂C₆H₃OH (LH) revealed compounds L₃Al ( 1 ) and L₂AlMe ( 2 ). On the other hand reaction of 1 equiv. of LH with trimethylaluminum did not lead to the formation of complex LAlMe₂ ( 3 ), rather 2 together with Me₃Al were observed as a result of a disproportionation of 3 . Compounds 1 and 2 were characterized by elemental analysis, ¹H and ¹³C NMR spectroscopy and in the case of 1 by X‐ray diffraction. Derivative 2 underwent transmetalation with Ph₃SnOH, giving LSnPh₃ ( 4 ) as the result of a migration of ligand L from the aluminum to the tin atom. The identity of 4 was established by elemental analysis, ¹H, ¹³C and ¹¹⁹Sn NMR spectroscopy and ¹H, ¹¹⁹Sn HMBC experiments. The system 2 and B(C₆F₅)₃ in a 1:1 molar ratio was shown to be active in the polymerization of propylene oxide and ε‐caprolactone. Copyright © 2007 John Wiley & Sons, Ltd.     

On FMR modes in bubble domain lattices

Two solutions of the problem of non-uniform ferromagnetic resonance in a hexagonal bubble domain lattice are presented under the simplifying assumption of lattice period much smaller than the film thickness. Fine divisions of the lattice cell into supposedly uniform subdomains render sets of linear equations for the local amplitudes which are solved numerically. Analytical solution of the time-dependent magnetostatic (Walker-mode) problem is obtained by expansion in simple elliptic functions similar to that suggested by Sigal. The results support, respectively, the interpretation of FMR experiments derived by Klem and Kaczér from a crude (minimal) subdivision of the elementary cell, and the three-mode dipolar-field model recently proposed by the author on a largely intuitive basis.     

Infrared laser ablation study of pressed soil pellets with inductively coupled plasma atomic emission spectrometry

Potential of infrared laser ablation (LA) coupled with ICP-AES as a technique suitable for the determination of trace elements (Zn, Cu, Ni, Cr, and V) in agricultural soils was studied. Operating parameters such as laser beam energy, laser beam focusing with respect to the sample surface, and velocity of the sample translation in the plane perpendicular to the laser beam were optimized. Soil samples were mixed with powdered Ag as a binder, and an internal standard (GeO(2)), and pressed into pellets. Calibration samples were prepared by adding known amounts of oxides of elements of interest into soils of known elemental composition and then processed in the same way as the analyzed samples. Calibration curves were found to be linear at least up to several hundreds of mg kg(-1) for the elements of interest. The elemental contents obtained by using LA-ICP-AES were compared with those obtained by analysis using wet chemistry followed by ICP-AES with pneumatic nebulization (PN). The results were in good agreement. Accuracy was also tested using certified reference soils with a bias not exceeding 10% relative.     

Aproximate pairing properties of SCF solutions in highly symmetric heteroatomic systems

Approximate pairing properties are proved for the Hartree-Fock solutions for highly symmetric heteroatomic molecules. These molecules have an alternant topology and are built from two kinds of atoms in such a way that by an operation the atoms of one kind go over into the atoms of the second kind and vice versa.

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Zusammenfassung Es werden genäherte alternierende Eigenschaften für Hartree-Fock-Lösungen hochsymmetrischer heterocyclischer Moleküle abgeleitet. Diese Moleküle haben eine alternierende Topologie, sie sind aus zwei Sorten von Atomen in solcher Weise aufgebaut, daß die Atome der ersten Sorte in die Atome der zweiten Sorte — und umgekehrt — transformiert werden können.

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Résumé Des propriétés d'accouplement orbital approché sont prouvées pour les solutions de type Hartree-Fock des molécules hétéroatomiques hautement symétriques. Ces molécules ont une topologie alternante et sont formées de deux classes d'atomes de telle sorte qu'il existe une opération interchangeant les atomes des deux classes.

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Supported in part by a grant to The Johns Hopkins University from the Petroleum Research Fund of the American Chemical Society.     

Solubility product relations in the rare earth hydrous hydroxides

The solubility products for some rare earth hydroxides and their temperature dependence have been shown. Greater solubility is shown for larger atomic radii and for lower temperature.     

A viscometric study of dilute aqueous solutions of poly(vinylalcohol)-polyacrylamide mixtures

The viscosity interaction coefficient, k_AB, for the system poly(vinylalcohol)-polyacrylamide-water was determined at 25° by two methods: (a) estimation of the Huggins slope coefficients for mixtures of polymers in different proportions; (b) determination of the intrinsic viscosity of polymer (A) in aqueous solutions of polymer (B). The result, k_AB = 0.3, indicates a low degree of overlapping of unlike polymer molecules.     

Molecular orbital study of gas phase basicities of carbofunctional derivatives of group IVB elements; stereochemical control

The gas phase basicities of a series of carbofunctional derivatives H₃M(CH₂)_nX (M = C, Si, Ge; X = NH₂, OH, F; n = 1–3) were investigated by the semiempirical CNDO/2 method. The calculations indicate that the electronic effects of silyl- and germyl-substituents differ greatly from the effect of simple alkyls. Moreover, in contrast to simple carbon derivatives, the overall nature of the electronic effects of siliyl- and germyl-substituents is crucially influenced by the molecular conformation.     

Volumetric determination of Pt(IV) in the presence of Ir,Pd, and Rh with ferrous ammonium sulfate in alkaline mannitol medium

A potentiometric reductimetric method for the determination of platinum (Pt(IV)Pt(II)) with a standard Fe(II) solution in an alkaline medium of mannitol is described. The method, the error of which does not exceed 2%, can be used in the presence of palladium, iridium, and rhodium.