On the transition from a Markov chain to a continuous time process

Starting from a real-valued Markov chain X₀,X₁,…,X_n with stationary transition probabilities, a random element {Y(t);t[0, 1]} of the function space D[0, 1] is constructed by letting Y(k/n)=X_k, k= 0,1,…,n, and assuming Y (t) constant in between. Sample tightness criteria for sequences {Y(t);t[0,1]};_n of such random elements in D[0, 1] are then given in terms of the one-step transition probabilities of the underlying Markov chains. Applications are made to Galton-Watson branching processes.     

Chemistry of the neophyl radical. The reaction of neophylmagnesium chloride with carbon tetrachloride and 1,2-dibromoethane in the solution

Neophylmagnesium chloride reacts via an ionic pathway with CCl₄ which is a very reactive halide towards Grignard reagents. On the other hand with the less reactive dibromoethane, the lowest energy pathway seems to be electron transfer to yield neophyl radicals.     

Ratio matching: A statistical aid for discovering generic relationships among samples

A technique of matching the ratios of elemental concentrations of a sample with the equivalent ratios of other samples is described. The resulting correlations are indications of potential generic relationships among the samples. Experimental data based on 91 sediments analyzed for eight elements by neutron activation analysis is used to demonstrate the ability of the method. Three typical examples show the relatively high correlations achieved between samples for which close generic relationships could be explained, post facto, by geographical evidence.     

On the decay of the Higgs particle into two lepton pairs

The decay of the standard Higgs into two lepton pairs is found to have a very small branching ratio, contrary to a recent result in the literature. The physical reasons for this discrepancy are discussed.     

The Stereoselective Acylation of Racemic Secondary Alcohols with Phenyltrifluoromethylketene as an Experimental Test of the Stereochemical Analogy Model

Validity of the stereochemical analogy model^[1,2] for stereoselective reactions is tested on acylations of racemic chiral secondary alcohols with phenyltrifluoromethylketene. The product ratios for the diastereomeric esters formed can be calculated using a formula derived from the general model for the special case, the results agreeing with the experimental data within the accuracy of the measuring method (integration of the ¹⁹F-NMR signals).     

Vortex glass transition in a random pinning model

We study the vortex glass transition in disordered high temperature superconductors using Monte Carlo simulations. We use a random pinning model with strong point-correlated quenched disorder, a net applied magnetic field, long-range vortex interactions, and periodic boundary conditions. From a finite size scaling study of the helicity modulus, the rms current, and the resistivity, we obtain critical exponents at the phase transition. The new exponents differ substantially from those of the gauge glass model, but are close to those of the pure three-dimensional XY model.