Left, right, and inner socles of associative systems

We investigate the basic properties of the different socles that can be considered in not necessarily semiprime associative systems. Among other things, we show that the socle defined as the sum of minimal (or minimal and trivial) inner ideals is always an ideal. When trivial inner ideals are included, this inner socle contains the socles defined in terms of minimal left or right ideals. This revised version was published online in June 2006 with corrections to the Cover Date.     

Crystal and molecular structures of 1-[3-(3,4-dimethoxyphenyl)-2-propenoyl]pyrrolidine.

The crystal structure of 1-[3-(3,4-dimethoxyphenyl)-2-propenoyl]pyrrolidine (C15H19NO3) (I) has been determined by X-ray analysis. It crystallizes orthorhombic space group Pbca with a = 24.295(3), b = 15.086(3), c = 7.552(3)A, V = 2768(1)A3, Z = 8, Dcalc = 1.254 g/cm3, mu = (Mo K(alpha)) = 0.87 cm(-1). The title compound has analgesic activity of cycloaliphatic amine part. The molecule is deviated from planar configuration.     

Interpretation of the polyelectrolyte and antipolyelectrolyte effects of poly(N‐vinylimidazole‐co‐sodium styrenesulfonate) hydrogels

Hydrogels of N‐vinylimidazole (VI) and sodium styrenesulfonate (SSS) were synthesized in aqueous solution by radical crosslinking copolymerization with N,N′‐methylene‐bis(acrylamide) as crosslinker. Swelling in several saline solutions was measured for hydrogel samples synthesized with different comonomer concentrations (C_T = 10, 25, or 40%) and with SSS mole fractions covering a broad range (f_SSS = 0–0.7), while the crosslinker ratio was 2 wt % in all cases. The degree of swelling in aqueous solution with a specific ionic strength (μ), plotted versus the SSS composition of the feed, shows a minimum for any set of samples synthesized with a fixed C_T. The dependence of swelling on μ shows both polyelectrolyte (f_SSS beyond the minimum) and antipolyelectrolyte behaviors (in the low f_SSS limit). It was found that the nonGaussian factor of the crosslinking density and the polymer‐solvent interaction parameter increase with f_SSS for any C_T. Moreover, in the low f_SSS limit, the osmotic swelling pressure is governed not only by the ionic contribution, but also by the polymer‐solvent mixing and, the concentration of mobile counterions inside the gel is not proportional to the net fixed charge but to the addition of cationic and anionic side groups, what discards the formation of ionic pairs. The antipolyelectrolyte effect is interpreted as due to the increasing protonation of VI as μ goes up. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1683–1693, 2007     

Synthesis of polysiltrimethylenes with trimethylsilyl groups in the branch of the main chain

The thermally initiated and platinum-catalyzed polymerization of 1-silacyclobutanes with substitutents containing a trimethylsilyl group was carried out. Soluble, high-molecular-weight, heterochain siltrimethylene polymers were obtained, containing trimethylsilyl groups removed from the main chain by various bridges.A. V. Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, 117912 Moscow. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 1, pp. 223–225, January, 1992.     

Corner spontaneous magnetization

Details are given of a new method allowing an exact calculation of the spontaneous magnetization in the corner as well as along the edge at an arbitrary distance of the corner for a rectangular planar Ising ferromagnet.     

Rotational temperature and density measurements in a hypersonic flow by dual-line CARS

Rotational temperature and nitrogen number density are measured in the shock wave/boundary layer interaction region in the vicinity of a two-dimensional compression corner disposed in a low pressure, 55 K, Mach 10 hypersonic air flow. Spatially-resolved data are recorded using a nonlinear optical technique named dual-line coherent anti-Stokes Raman scattering (DLCARS). Averaged temperature and density profiles are compared with those predicted by a Navier-Stokes solver. Good agreement is found.     

Riccati-based preconditioner for computing invariant subspaces of large matrices

Summary. This paper introduces and analyzes the convergence properties of a method that computes an approximation to the invariant subspace associated with a group of eigenvalues of a large not necessarily diagonalizable matrix. The method belongs to the family of projection type methods. At each step, it refines the approximate invariant subspace using a linearized Riccati's equation which turns out to be the block analogue of the correction used in the Jacobi-Davidson method. The analysis conducted in this paper shows that the method converges at a rate quasi-quadratic provided that the approximate invariant subspace is close to the exact one. The implementation of the method based on multigrid techniques is also discussed and numerical experiments are reported. Received June 15, 2000 / Revised version received January 22, 2001 / Published online October 17, 2001     

Intramolecular hemiacetals. The acid-base-catalyzed ring-chain interconversion of 2-substituted 2-hydroxy-4,4-dimethylmorpholinium cations in aqueous solution.

The ring-chain tautomerism in aqueous solution of some aryl-substituted morpholinium salts (bromides), has been studied and equilibrium constants are reported. In the crystals the substrates exist entirely in their cyclic forms as hemiacetals, but in aqueous solution NMR measurements reveal that an equilibrium is established between the cyclic (hemiacetal) and the noncyclic (ketone) form, the degree of ring-opening being more pronounced with electron-donating aryl substituents at the carbonyl carbon. The kinetics of the ring-chain interconversion in water has been investigated spectrophotometrically by a 'pH jump' stopped-flow technique. General base catalysis is observed with a Br?nsted beta value apparently independent of substituent and equal to 0.60. The Hammett rho values for various base catalysts are close to those for very similar intermolecular reactions involving hemiacetal breakdown, leading to the suggestion of a 'normal' class n mechanism for base catalysis. For acid catalysis, however, a quite different situation is encountered, since no general acid but only (weak) catalysis by the hydronium ion can be detected. We believe this deviation from 'normal' general acid catalysis is caused by an electrostatic interaction, and we suggest that it might result from a change in the usual class e mechanism for general acid catalysis by a situation in which rate-limiting concerted proton transfer is replaced by rate-limiting preprotonation. This is supported by the observed drastic change in Hammett rho value for catalysis by the hydronium ion, compared with the 'normal' case. An interesting case is encountered for the 4-aminophenyl-substituted substrate, in which the amino group becomes protonated in acid solution, thus representing a new substituent. Despite this complication, the various equilibrium and rate constants may also be evaluated experimentally for this substrate.     

π π andK¯K channel coupling

We investigate the origin of the attraction in theK¯K channel around the threshold by introducing an additional channel to theππ andK¯K channels in a separable potential formalism assuming, in general, no direct interaction in theK¯K channel. To reproduce the features of the data, we find that the threshold of the additional channel is much above thef ₀(975) meson position. We show that this three-channel problem can be reduced to an effective two-channel problem where thef ₀(975) behaves as if it were aK¯K molecule bound by the coupling to the exotic channel. This picture is also supported by the fact that a single pole only, in the complexK¯K momentum plane, is associated to thef ₀(975) meson. Various physical observables, like the decay branching ratio and theK¯K scattering length, are then discussed in an effective two-channel framework.