The 2-characters of a group and the group determinant

A new look at Frobenius' original papers on character theory has produced the following: (a) the group determinant determines the group (Formanek-Sibley); (b) the group is determined by the 1-, 2- and 3-characters of the irreducible representations (Hoehnke-Johnson); and (c) pairs of non-isomorphic groups exist with the same irreducible 1- and 2-characters (Johnson-Sehgal). The examples produced in Johnson and Sehgal have large orders but, recently, McKay and Sibley have proved that the ten Brauer pairs of order 256 have the same irreducible 2-characters. It is shown here that the pairs of non-isomorphic groups of order p³, p and odd prime, have the same irreducible 2-characters. Further results are given on the k-characters of the regular representation/rod a shorter proof of the result mentioned in (c) is indicated. A criterion is given which is sufficient for the 3-character of an arbitrary representation to determine the group.     

Nilpotent elements in group rings

The main theorem gives necessary and sufficient conditions for the rational group algebra QG to be without (nonzero) nilpotent elements if G is a nilpotent or F·C group. For finite groups G, a characterisation of group rings RG over a commutative ring with the same property is given. As an application those nilpotent or F·C groups are characterised which have the group of units U(KG) solvable for certain fields K.This work has been supported by N.R.C. Grant No. A-5300.     

Measurement of the acoustic nonlinearity parameter B/A in human tissues by a thermodynamic method

A thermodynamic method for measuring the acoustic nonlinearity parameter B/A in tissues is presented. It is based on the measurement of change in phase velocity as a function of time as the hydrostatic pressure of the sample is quickly reduced from a known value. This technique circumvents the effect of the attenuation in the medium and does not require a prior knowledge of the thermodynamic parameters of the tissues. The method is used to estimate nonlinearity parameters for normal and malignant tissues in the temperature range 20 degrees to 37 degrees C. The values and the temperature dependence of these parameters are found to vary with the nature of the tissues.     

Torsion units in integral group rings of metacyclic groups

It is proved that if G is a split extension of a cyclic p-group by a cyclic p′-group with faithful action then any torsion unit of augmentation one of $\text{Z}$G is rationally conjugate to a group element. It is also proved that if G is a split extension of an abelian group A by an abelian group X with (|A|, |X|) = 1 then any torsion unit of $\text{Z}$G of augmentation one and order relatively prime to |A| is rationally conjugate to an element of X.     

Photoinduced cycloadditions of electron deficient nitrones to alkenes

Oxaziridines are proposed as intermediates in the photoinduced cycloadditions of electron deficient nitrones to dipolarophiles.     

Stable oxide nanoparticle clusters obtained by complexation

We report on the electrostatic complexation between polyelectrolyte-neutral copolymers and oppositely charged 6-nm crystalline nanoparticles. For two different dispersions of oxide nanoparticles, the electrostatic complexation gives rise to the formation of stable nanoparticle clusters in the range 20-100 nm. It is found that inside the clusters, the particles are "pasted" together by the polyelectrolyte blocks adsorbed on their surface. Cryo-transmission electronic microscopy allows visualization of the clusters and determination of the probability distribution functions in size and in aggregation number. The comparison between light scattering and cryo-microscopy results suggests the existence of a polymer brush around the clusters.     

Interactions between anionic mixed micelles and α-cyclodextrin and their inclusion complexes: conductivity, NMR and fluorescence study

Mixed micelle formation of anionic surfactants sodium dodecyl sulfate (SDS) and sodium lauroyl sarcosine (SLAS) have been studied in water and in 5, 10, and 15 mM concentrations of α-cyclodextrin (α-CD) over mole fraction range of α _SDS from 0 to 1. From the conductivity curves, the critical micellar concentration (CMC) for the pure and binary mixtures were evaluated. The degree of counterion association (χ) or counterion dissociation (δ), the equivalent ionic conductivities of the monomeric species (Λ _m), the associated species (Λ _assc), and the micelle (Λ _mic) were evaluated from the slope of the conductivity vs concentration plots. The CMC values have been used to calculate the thermodynamic parameters such as the standard free energy of micelle formation and a transfer of standard free energy of micelle from the aqueous medium to additive medium computed. The apparent CMC of the surfactants varies linearly with α-CD concentrations. From the dependence of CMC of the surfactants on α-CD concentration, we are able to determine the association constant (K) of surfactant-α-CD inclusion complexes assuming 1:1 stoichiometry. Mixed micelle behaves ideally in the pure water as well as at the different concentrations of α-CD, which was evaluated by using the Clint equation, the regular solution approximation, and Motomura’s formulation. Self-diffusion coefficients of the micelle increased upon the induction of SDS into the micelle. 2D-rotating frame Overhauser effect spectroscopy spectra of SDS and SLAS were recorded in the presence of α-CD to investigate the interaction between H-atoms of the alkyl chain of the surfactants and H-atoms of the hydrophobic cavity of α-CD indicating multiple complexation. The fluorescence anisotropy of rhodamine B has been measured to observe the structural behavior of mixed micelle.