Isomorphism types of Aronszajn trees

We study the isomorphism types of Aronszajn trees of height ω₁ and give diverse results on this question (mainly consistency results). The second author would like to thank the United States-Israel Binational Science Foundation for partially supporting this research by a grant.     

Linear transformations that preserve certain positivity classes of matrices

For each of several S ? R^n,n, those linear transformations $\text{L}\text{: R}{}^{\mathrm{n,n}}\text{→ R}{}^{\mathrm{n,n}}$ which map S onto S are characterized. Each class is a familiar one which generalizes the notion of positivity to matrices. The classes include: the matrices with nonnegative principal minors, the M-matrices, the totally nonnegative matrices, the D-stable matrices, the matrices with positive diagonal Lyapunov solutions, and the H-matrices, as well as other related classes. The set of transformations is somewhat different from case to case, but the strategy of proof, while differing in detail, is similar.     

The 1H NMR spectra of some norbornene derivatives,a LIS study

The ¹H NMR spectra of 2-exo-hydroxymethyl-3-endo-methylnorbornene and the corresponding 2-endo-3-exo isomer have been completely assigned with the aid of lanthanide reagents. This enabled a full analysis of the unusual spectrum of 2-exo-hydroxy-methyl-3-endo-methylnorbornene to be undertaken, confirming the proposed structure. The ΔEu values for 2-exo-hydroxymethyl-3-endo-methylnorbornene and the 2-endo-3-exo-isomer have been used to test the effect of rotational averaging on the calculated pseudo contact shifts. Good agreement is obtained for a dynamic model in which the Eu atom exchanges between two sites on the oxygen atom of the OH bond, and in which the rotational equilibrium about the CH? CH₂OH bond is explicitly considered.     

Boson mappings for schematic nuclear models with the symmetry of SO(5)

In the past, several schematic nuclear models have been proposed with the symmetry of the Lie algebra SO(5). We derive a set of mappings from the shell model spaces in which these models are defined to suitable boson spaces. The derivations are carried out by two distinct algebraic methods, which are customarily associated with the names Holstein-Primakoff and Dyson, respectively. The relative utility of the two is seen to depend on the particular mapping. The mappings are useful for the study of the collective properties of the various models and of generalizations of each of them. This is illustrated with one of the models. Some algebraic details, some ideas concerning schematic model building, and an extension of the results of this paper are presented in appendices.     

A novel use of cobalt(III) meso-tetraphenylporphyrin as a chiral shift reagent

The NMR spectra of the diastereomeric complexes formed by the coordination of nitrogenous enantiomeric bases with cobalt(III) meso-tetraphenylporphyrin (CoTPP) allow the immediate differentiation of these complexes. The spectra are interpreted on the basis of symmetry (RR and SS) and pseudo-chirality (RS and SR) considerations. The effects are observed in both the proton and carbon spectra and the complexes are stable in both CDCl₃ and DMSO-d₄ solution. This technique, in principle, allows the ready determination of the optical purity of multifunctional ligands.     

The rigidity of the surface of phase separation in the ising ferromagnet

A model due to Onsager and Temperley for the interface between thermodynamic phases in classical lattice gases is examined. It is found that a field is needed for stabilisation in two dimensions; in three dimensions, on the other hand, the interface is localised, unlike the drumhead model without cutoff.     

An ultramicromethod for the determinations of phosphatase activity in serum or plasma

An ultramicromethod has been described for the determination of alkaline and acid phosphatase using dicyclohexylammonium salt of p-nitrophenylphosphate as substrate. The ammonium salt shares the advantages of the sodium salt, but it is more stable, which results in more stable working reagent. This has been incorporated into the Unopette System. All of the premeasured, individually packaged reagents are stable at room temperature for at least 1 year. The method has been validated by comparing the results obtained with clinical samples analyzed with the Auto-Analyzer.     

Thomas rotation and the parametrization of the Lorentz transformation group

Two successive pure Lorentz transformations are equivalent to a pure Lorentz transformation preceded by a 3×3 space rotation, called a Thomas rotation. When applied to the gyration of the rotation axis of a spinning mass, Thomas rotation gives rise to the well-knownThomas precession. A 3×3 parametric, unimodular, orthogonal matrix that represents the Thomas rotation is presented and studied. This matrix representation enables the Lorentz transformation group to be parametrized by two physical observables: the (3-dimensional) relative velocity and orientation between inertial frames. The resulting parametrization of the Lorentz group, in turn, enables the composition of successive Lorentz transformations to be given by parameter composition. This composition is continuously deformed into a corresponding, well-known Galilean transformation composition by letting the speed of light approach infinity. Finally, as an application the Lorentz transformation with given orientation parameter is uniquely expressed in terms of an initial and a final time-like 4-vector.