Ternary analogues of Lie and Malcev algebras

We consider two analogues of associativity for ternary algebras: total and partial associativity. Using the corresponding ternary associators, we define ternary analogues of alternative and assosymmetric algebras. On any ternary algebra the alternating sum [a, b, c] = abc − acb − bac + bca + cab − cba (the ternary analogue of the Lie bracket) defines a structure of an anticommutative ternary algebra. We determine the polynomial identities of degree ?7 satisfied by this operation in totally and partially associative, alternative, and assosymmetric ternary algebras. These identities define varieties of ternary algebras which can be regarded as ternary analogues of Lie and Malcev algebras. Our methods involve computational linear algebra based on the representation theory of the symmetric group.     

Microdetermination of copper using dithiooxamide crayons and the ring-oven technique

A method for the microdetermination of copper in air pollution investigations, using a dithiooxamide crayon and the ring-oven technique is presented. The limit of detection for the method is 0.04 μg, and the quantitative determination is applicable in the range of 0.05 to 0.5 μg of copper. The method is free from interferences that might be of significance in the study of air samples.     

Weak convergence in Hilbert space and weak uncertainty relations in quantum theory

A suitable weak topology is considered on the Hilbert phase space of a quantum-mechanical system. It is then shown that if two bounded observables of the system have no common eigenvector, the sum of their variances in any state is always greater than some positive constant. Consequences of this result on some observables of simple physical systems are examined. First of all, the case of the position and momentum of the elementary particle in one dimension is studied and a comparation with Heisenberg's indeterminacy principle is carried out. Then, the case of angular variables is also examined, with special emphasis on spin 1/2. An experiment with neutrons is finally suggested and analysed with the help of the theory developed.     

A study of amino-protecting groups using the polarizable continuum model (PCM)

In order to better understand the performance of 1,2-dimethyl-5-acetyl barbituric acid (DMB) as an amino protecting group relative to 5,5-dimethylcyclohexane-1,3-dione (DMD), ab initio calculations were performed. pK_a calculations using the PCM model indicated that both molecules are more acidic in the enol form. Therefore, the protecting reaction of these molecules should involve the anions formed from the loss of a proton from the enol compounds. Contrary to what would be expected, the larger efficiency exhibited by the DMB molecule cannot be attributed to an extension of the electronic conjugation effect. In the absence of any other noticeable effect that could be responsible for the greater efficiency of the DMB molecule, we are inclined to believe that the difference could be accounted for by the presence of two independent centers of conjugation.This paper is dedicated to Jacopo Tomasi in recognition of his outstanding contribution to the field of computational chemistry in solution. The authors are honored to contribute to this volume; especially so for two of them (COS and MACN) who have the privilege of his friendship.Acknowledgements The authors would like to thank the Brazilian research agencies CNPq, CAPES and FAPERJ for the financial support. C. O. da Silva thanks the Dipartimento di Chimica e Chimica Industriale, University of Pisa, where the MCSCF calculations were performed.     

Algèbres de Boole monadiques libres

Sans résumé Presented by A. Horn.     

13C NMR spectroscopic data for glutinol and derivatives

The ¹³C NMR chemical shifts of the triterpenes glutinol, glutinone and acetylglutinol were measured and analysed.     

MS-Xα study of the KCl: Cu− spectrum

We have interpreted the KCl:Cu^? spectrum in the context of the MS-X_α method. The results, considering only allowed electric-dipole transitions, are in good agreement with the experimental data. Four new absorption bands, peaking at 573, 390, ～324 and ～310nm, at room temperature, are reported.     

Radiative neutron capture near threshold

The surprisingly large “pair” term corrections to threshold radiative neutron capture, previously calculated by Riska and Brown, and Gari and Huffman, are calculated in a new way in which they appear as relativistic corrections to the impulse approximation arising from the small negative energy components of the wave functions of the two nucleon system. Looking at these corrections from this point of view suggests not only that these small negative energy components are observable in non-relativistic processes, but also that the size of these corrections may ultimately depend on, or give information about, a consistent relativistic treatment of the nuclear force problem.