Magnetic properties of erbium iron garnet in high magnetic fields up to 150kOe

The magnetic properties of single crystals of erbium iron garnet (ErIG) were studied in applied fields up to 150kOe between 1.4 and 300K. At low temperature, the macroscopic easy direction of the bulk magnetization is [100]; below the compensation temperature (80±2K), the magnetization presents non-linear field evolution. On the assumption of an isolated ground doublet, the anisotropy constantsK _i (i=1,2) of ErIG are given byK _i (Er)+K _i (YIG); theK _i are calculated as a function of theG andg tensor components. It is worthwhile noting that theK _i (Er) are strongly temperature dependent; so at low temperature the anisotropy of the garnet is determined by the rare earth ions, while in the 50 K regionK ₁(Er) becomes comparable toK ₁(YIG) with the opposite sign which results in a very weak anisotropy of the garnet. Above 50 K,K ₁(YIG) is predominant and the Fe³⁺ ions determine the garnet anisotropy.     

Geometry of equilibrium configurations in the Ising model

We derive microscopically precise identities for the geometry of small clusters in the equilibrium states of the two-dimensional Ising model with emphasis on near-critical phenomena.     

Crystal structures of three substituted pentacyclo[5.4.0.02,6.03,10.05,9]undecanes

The crystal structures of three compounds formed via ultimate nucleophilic attack of unsaturated hydrocarbon fragments are reported. Geometries of the bis(vinyl)-, mono(vinyl), and bis(ethynyl)-substituted PCU species are unexceptional. The crystal structures are dictated by the availability of intermolecular hydrogen bonding.     

Cutting planes for integer programs with general integer variables

We investigate the use of cutting planes for integer programs with general integer variables. We show how cutting planes arising from knapsack inequalities can be generated and lifted as in the case of 0–1 variables. We also explore the use of Gomory's mixed-integer cuts. We address both theoretical and computational issues and show how to embed these cutting planes in a branch-and-bound framework. We compare results obtained by using our cut generation routines in two existing systems with a commercially available branch-and-bound code on a range of test problems arising from practical applications. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.Corresponding author.This research was partly performed when the author was affiliated with CORE, Université Catholique de Louvain.     

Statistical inference and quantum mechanical measurement

We analyze the quantum mechanical measuring process from the standpoint of information theory. Statistical inference is used in order to define the most likely state of the measured system that is compatible with the readings of the measuring instrument and the a priori information about the correlations between the system and the instrument. This approach has the advantage that no reference to the time evolution of the combined system need be made. It must, however, be emphasized that the result is to be interpreted as the statistically inferred state of the original system rather than the state of the system after measurement. The phenomenon of “reduction of states” appears in this light as a consequence of incomplete information rather than the physical interaction between measured system and measuring instrument.     

Electrospray ionization mass spectrometric detection of self-assembly of a crown ether complex directed by π-stacking interactions

The self-assembly of ligand-metal-ligand sandwich complexes involving a novel quinoxaline-containing crown ether, 1, was studied by electrospray ionization mass spectrometry (ESI-MS). Donor-acceptor π-stacking interactions between the electron-poor quinoxaline group of 1 and electron-rich benzene groups from benzo- or dibenzo-18-crown-6 were found to significantly enhance the formation of mixed-ligand sandwich complexes with a free energy gain of up to 17 kJ/mol relative to sandwich formation involving macrocycles without such aromatic functionalities. The relative intensities of the sandwich complexes were greatest with the alkali metals Na⁺, K⁺, and Rb⁺ as well as with the ammonium ion in equimolar concentrations with the macrocycles. The preferential formation of the mixed-ligand sandwich complexes demonstrated that donor-acceptor π-stacking interactions contribute to the assembly of molecular structures and can be monitored by ESI-MS.