On the number of generators of modules over Laurent rings

Partially supported by DGICYT PB88-0224     

Lithium trienolate of sorbic acid as a d6 synthon. Synthesis of 7-hydroxy 2,4-dienoic acids.

The trienolate $\text{2}$ of sorbic acid is an easily available d⁶ synthon. Preparation of 7 hydroxy dienoic acids $\text{5}$ from ketones is here described.     

Symplectic approach to the theory of quantized fields. I

Our aim in this paper the first one of a series concerned with the problem of field quantization starting from the symplectic structure underlying the classical theory, is to build up the variational theory necessary to all further constructions. The basic notions are the vertical bundle and thestructure 1-form used to define thegeneralized infinitesimal contact transformation which allows us to state and solve the variational problem related to field physics.Giving a system of modulevalued differential forms of different degree on the vertical bundle which solutions are the stationary cross sections is the main result in the paper. In this scheme the Euler-Lagrange classical equations are the expressions induced by such a system of differential forms on any cross section of the vertical bundle. This gives us a complete linearization of the Euler-Lagrange equations and, starting from it, a natural globalization of these equations. Finally, the notion of variational problem invariant by a Lie group is defined in this scheme, Noether's theorem related to such invariant problem is formulated and an intrinsic version of the so-called Noether invariants of classical variational calculus is obtained.This work has been realized in the Seminar of Mathematical Physics, directed by ProfessorJ. Sancho, in the Faculty of Science at the University of Barcelona (Spain).     

Level structure of 82Rb,studied through the 81Br(α, 3n) reaction

Nuclear states of ⁸²Rb were studied through the ⁸¹Br(α, 3n) reaction at various bombarding energies between 30 and 55 MeV. Excitation functions, γ-ray angular distributions, γ-γ coincidences and γ-time distributions with respect to the beam bursts were determined. Levels at 123.2, 187.7, 233.6, 796.3, 1214.1 keV and tentatively at 1835.5 keV were observed. It was not possible to establish whether the lowest state of the proposed level scheme corresponds to the ground state or to the $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 6.2}\text{h}$ isomeric state. The 45.9 and 64.5 keV γ-rays do not exhibit any measurable lifetime and a limit $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{≦ 5}\text{ns}$ has been determined. The situation is similar for the 123.2 keV γ-ray, although in this case the presence of a long-lived component cannot be ruled out.     

Poincaré cycles and ergodic behavior of a linear diatomic chain

The ergodic behavior of a linear diatomic chain is shown to be analogous to that of a linear monatomic chain. Starting with the expressions for the time-relaxed correlation functions between any two particles in the chain, we show that the existence of Poincaré cycles is not inconsistent with the development of an equilibrium state. Also, we show that those dynamical variables that are ergodic for the linear monoatomic chain remain ergodic in the diatomic chain. It is shown that the autocorrelation functions for particles with equal or different masses decay in time ast ^–1/2 .This work was completed when the author was associated with the Institute for Fluid Dynamics and Applied Mathematics, University of Maryland and supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under contract No. AF18(600)1315.     

On the Enskog-Thorne theory for a binary mixture of dissimilar rigid spheres

Thorne's method for obtaining transport coefficients in a binary rigid-sphere mixture is reexamined. First, a close look is taken at the way in which the point where the Enskog functionsx _ij are evaluated is introduced. Second, the calculation of the fluxes in the system and the transport coefficients is given. Thorne's results are found to be correct and independent of the choice of the point where the transfer plane is located. This does not hold true for the diffusion flux. It is shown that a different diffusion force is obtained for each selection and that only those diffusional effects which are of first order in the density are consistent with irreversible thermodynamics.     

Nitroso group transfer in s-nitrosocysteine: evidence of a new decomposition pathway for nitrosothiols

The rate of S-nitrosocysteine decomposition in a pH range between 0.7 < pH < 13 exhibits first- and second-order dependence on total cysteine concentration. The second-order term is only observed for pH values between 6.9 < pH < 12. Both first- and second-order terms show a complex dependence on the acidity of the medium. They increase with increasing pH, reaching a maximum value around pH = 8 and then decrease with further increase in pH. An analysis of the reaction products reveals the absence of nitrite ion and ammonia. No evidence of catalysis by copper ions is observed. These results suggest the existence of a new decomposition pathway for S-nitrosocysteine, which proceeds via an intramolecular nitroso group transfer producing a primary N-nitrosamine that decomposes rapidly to give the corresponding diazonium salt. The nitroso group transfer reaction occurs intermolecularly for the decomposition pathway exhibiting a quadratic dependence on cysteine concentration. Both nitroso group transfer pathways are subject to acid catalysis by cysteine. Kinetic results indicate that the extent of S...NO bond cleavage in the transition state is ahead of protonation of the AH...S sulfur atom. The results obtained show the existence of a new decomposition pathway for the S-nitrosocysteine where NO is not released, and hence, it has a significant biological impact due to the potential use of nitrosothiols as NO donors.     

Shape-complementarity in the recognition of tricarboxylic acids by a [3+3] polyazacyclophane receptor

[structure: see text] The interaction of a macrocycle containing three trans-(1R,2R)-diaminocyclohexane units connected by p-xylene spacers with the isomers 1,3,5-benzenetricarboxylic (1,3,5-BTC), 1,2,4-benzenetricarboxylic (1,2,4-BTC), and 1,2,3-benzenetricarboxylic (1,2,3-BTC) acids and their relevant anions is studied by means of potentiometric and NMR analysis. The interaction is highest for the isomer 1,3,5-BTC, which perfectly fits within the macrocyclic cavity of the host species. The studies have been extended to the triacid 1,3,5-benzenetriacetic observing in this case the effect of a size mismatch between host and guest species.