Orders of Indescribable Sets

We extract some properties of Mahlo’s operation and show that some other very natural operations share these properties. The weakly compact sets form a similar hierarchy as the stationary sets. The height of this hierarchy is a large cardinal property connected to saturation properties of the weakly compact ideal.     

Spin-transfer switching in MgO magnetic tunnel junction nanostructures

Spin-transfer driven switching was observed in MgO based magnetic tunnelling junctions (MTJ) with tunnelling magnetoresistance ratio of up to 160% and the average intrinsic switching current density (J_c0) down to 2 MA/cm², which are the best known results reported in spin-transfer switched MTJ nanostructures. Based on a comparison of results both from MgO and AlO_x MTJs, further switching current decrease via MgO dual structures with two pinned layers is discussed.     

Deacetalisation-bicyclisation routes to novel polycyclic heterocycles using stannous chloride dihydrate

The stannous chloride dihydrate-mediated deprotection-bicyclisation of a range of amides possessing a pendant acetal group is reported. These mild reaction conditions have been used to prepare a number of ring-fused heterocyclic compounds, some in enantiomerically pure form, which should be of interest both in their own right and as building blocks for the production of more complex target molecules.     

Property (<Emphasis Type="Italic">T</Emphasis>) and rigidity for actions on Banach spaces

We study property (T) and the fixed-point property for actions on L ^p and other Banach spaces. We show that property (T) holds when L ² is replaced by L ^p (and even a subspace/quotient of L ^p ), and that in fact it is independent of 1≤p<∞. We show that the fixed-point property for L ^p follows from property (T) when 1<p< 2+ε. For simple Lie groups and their lattices, we prove that the fixed-point property for L ^p holds for any 1< p<∞ if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive spaces. Bader partially supported by ISF grant 100146; Furman partially supported by NSF grants DMS-0094245 and DMS-0604611; Gelander partially supported by NSF grant DMS-0404557 and BSF grant 2004010; Monod partially supported by FNS (CH) and NSF (US).     

A Genetic Algorithm for Solving a Capacitated p-Median Problem

Facility-location problems have several applications, such as telecommunications, industrial transportation and distribution. One of the most well-known facility-location problems is the p-median problem. This work addresses an application of the capacitated p-median problem to a real-world problem. We propose a genetic algorithm (GA) to solve the capacitated p-median problem. The proposed GA uses not only conventional genetic operators, but also a new heuristic “hypermutation” operator suggested in this work. The proposed GA is compared with a tabu search algorithm.     

Logarithmic corrections in a quantization rule. The polaron spectrum

A nonlinear integrodifferential equation that arises in polaron theory is considered. The integral nonlinearity is given by a convolution with the Coulomb potential. Radially symmetric solutions are sought. In the semiclassical limit, an equation for the self-consistent potential is found and studied. The potential has a logarithmic singularity at the origin, and also a turning point at 1. The phase shifts at these points are determined. The quantization rule that takes into account the logarithmic corrections gives a simple asymptotic formula for the polaron spectrum. Global semiclassical solutions of the original nonlinear equation are constructed.Moscow Institute of Electronic Engineering; Moscow Power Institute. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 97, No. 1, pp. 78–93, October, 1993.     

O− and OH− chemical ionization of some fatty acid methyl esters and triacylglycerols

O^? and OH^? react with fatty acid methyl esters (FAMES) under chemical ionization conditions both as Bronsted bases to form [M - H]^? and as nucleophiles to form the carboxylate ion RCOO^?. O^? shows a much greater tendency to react as a nucleophile than does OH^?. The [M - H]^? ions fragment by elimination of CH³OH, with unsaturation in certain positions in the fatty acid hydrocarbon chain promoting this elimination for unknown reasons. The reaction of O^? and OH^? with triacylglycerols leads to [M - H]^?, characteristic of the molecular mass, and to carboxylate ions characteristic of the fatty acid(s) present in the lipid. The presence of the three ester functions in the lipids greatly enhances the formation of carboxylate ions compared to the FAMES.