Canonical forms of pseudo-orthogonal matrices

Canonical forms are found for all real four-dimensional matrices of the pseudo-orthogonal group which differs from the Lorentz group only in that its metric has twoplus signs and twominus signs.     

Metalloid derivatives for synthesis the preparation of macrocyclic tetrathiolactones

The preparation of macrocyclic thiolactones by condensation of diacyl chlorides with siladithianes is described.     

Determination of substituent chemical shifts in the proton resonance spectra of the porphyrins

Reproducible proton chemical shifts in the porphyrin series are obtained when the spectrum is measured in chloroform using the zinc (II) complex of the porphyrin in the presence of an excess of pyrrolidine. This method is specifically demonstrated for the case of 2,4-dicyanodeuteroporphyrin-IX dimethyl ester which, as the free base, shows dramatic effects due to aggregation phenomena. The shifts obtained using the zinc (II) complex plus pyrrolidine method, which allow compilation of substituent chemical shifts in the porphyrin series, are shown to be the same as the less easily accessible infinite dilution shifts of the porphyrin free bases.     

Intensity fluctuations of amplified spontaneous emission

The intensity fluctuations of a linearly polarized component of the amplified spontaneous emission at 3.51 μm from a single, variable-length xenon-helium source have been measured. The fluctuations are only slightly reduced despite heavy saturation and the results are found to be in qualitative agreement with theoretical models based on the coupling of the fluctuations in the beams travelling in different directions.     

Radiolytic decomposition of methanesulfonyl chloride in liquid cyclohexane. A kinetic determination of the bond dissociation energies D(ME-SO2) and D(c-C6H11-SO2)

The gamma radiation induced decomposition of MeSO₂Cl in cyclohexane (RH) was studied between 60 and 150°C. Throughout this temperature range the reaction proceeds by a free radical chain mechanism. Its propagation is described by the following reactions: The kinetic analysis of the results of the experiments with added SO₂, which were carried out in the temperature range of 80 to 150°C, gives 14.94 ± 0.92 and 11.91 ± 0.82 kcal/mole for D(Me-SO₂) and D(c-C₆H₁₁-SO₂), respectively. These bond dissociation energies are considerably lower than the gas-phase values, and the possible cause of this difference is discussed. Present results also seem to indicate that D(MeSO₂-H) does not exceed 95 kcal/mole. Competitive experiments with added tetrachloroethylene result in where θ = 2.303RT in kcal/mole.     

On the Transfer Matrix for the Two-Dimensional Ising Model

The eigenvalue problem for the transfer matrix of the two-dimensional Ising lattice, with free boundaries perpendicular to the transfer direction, is solved. The mathematical mechanism which produces the asymptotic degeneracy of the eigenvalue spectrum below the bulk transition temperature is different from the case with cyclic boundary conditions. The results are used to calculate the two-spin correlation function between two spins in the same edge of the lattice, and between two spins in opposite edges.     

The structure and thermodynamics of binary microclusters: A Monte Carlo simulation

The Monte Carlo computer simulation technique of classical statistical mechanics is employed to determine the structure and thermodynamics of binary microclusters of Lennard-Jones atoms as a function of cluster size, composition and temperature. Further, amorphous microclusters are prepared by a Monte Carlo quench, and their structural properties are examined. The properties of interest include the internal energy, instantaneous “snapshot” pictures of the microcluster's atomic configuration, and the single-particle and pair distribution functions. The Lennard-Jones potential parameters are chosen to model Ar₁₃, Ar₇Kr₆, Ar₃₆Kr₁₉ and Ar₁₉Kr₃₆, as well as to crudely model the bimetallic clusters of Cu₁₉Ni₃₆, Cu₁₉Ru₃₆ and Cu₁₉Os₃₆. A large variety of interesting features associated with these systems are described.     

Pair function for the rectangular Ising ferromagnet

A representation of the pair correlation function for the rectangular Ising model in zero magnetic field is derived using a new spinor technique; this enables the scaling limit to be established, as well as several analytical properties of the scaling functions.Supported by the Fonds National Suisse de la Recherche Scientifique, by the National Science Foundation Grant No. PHY76-17191, and by the National Research Council of Canada Grant No. NRC A9344