Interactions between octyl-β-D-glucoside and α-amino acids or small peptides

The interactions between octyl--D-glucoside and glycine in water have been investigated by surface tension, viscosity, and density measurements. The results show that the -amino acid causes an unexpected lowering of the critical micellar concentration of octyl--D-glucoside. Such a finding has been interpreted in temss of dipole-dipole interactions between the hydrophilic site of the surfactant and the peptidic cosluttes. From three to seven amino acid molecules have been estimated to be coordinated with each glucoside unity in the micellar state. The research has been extended to glycine oligopeptides and L-lysine. The latter compound has effects similar to those observed with glycine whereas diglycine and triglycine show weaker effects on the micellization process.     

Recurrence relations for the evaluation of electron repulsion integrals over spherical Gaussian functions

Recurrence relations are derived for the evaluation of two-electron repulsion integrals (ERIs) over Hermite and spherical Gaussian functions. Through such relations, a generic ERI or ERI derivative may be reduced to “basic” integrals, i.e., true and auxiliary integrals involving only zero angular momentum functions. Extensive use is made of differential operators, in particular, of the spherical tensor gradient ??(?). Spherical Gaussians, being nonseparable in the x, y, and z coordinates, were not included in previous formulations. The advantages of using spherical Gaussians instead of Cartesian or Hermite Gaussians are briefly discussed. © 1993 John Wiley & Sons, Inc.     

On a new method for constructing good point sets on spheres

We use quadrature formulas with equal weights in order to constructN point sets on spheres ind-space (d 3) which are almost optimal with respect to a discrepancy concept, based on distance functions (potentials) and distance functionals (energies). By combining this approach with the probabilistic method, we obtain almost best possible approximations of balls by zonotopes, generated byN segments of equal length.Editors' note: We learned with sadness of Gerold Wagner's untimely death as a result of an avalanche in the Alps shortly after the submission of this paper. When one of the referees, Joram Lindenstrauss, suggested that Wagner's results might be extended to dimensions >6, we invited Professor Lindenstrauss to submit a paper containing that extension which we would publish alongside the Wagner paper. The result is the paper by Bourgain and Lindenstrauss that follows the present one.