Caratheodory interpolation kernels

Kernels over the unit disk for which a version of Carathéodory interpolation is true are characterized in a simple computationally verifiable manner.     

Orientation-reversing involutions on handlebodies

The observation that the quotient orbifold of an orientation- reversing involution on a 3-dimensional handlebody has the structure of a compression body leads to a strong classification theorem, and general structure theorems. The structure theorems decompose the action along invariant discs into actions on handlebodies which preserve the -fibers of some -bundle structure. As applications, various results of R. Nelson are proved without restrictive hypotheses.

     

Accurate orbital amplitudes at nuclei frog gaussian basis sets

A simple extrapolation procedure combining wavefunctions obtained from gaussian basis sets with exact solutions of the nuclear cusp equations is proposed for computing orbital amplitudes at nuclei. Comparison with exact results for atoms and diatomic molecules indicates that the procedure is capable of giving Hartree—Fock amplitudes with errors of at most 10^?2 for the low amplitude outer orbitals and errors of less than 10^?3 for the important inner orbitals. The resulting errors in the total densities are around 10^?2. These accuracies are comparable with those obtained with energy-optimized Slater basis sets.     

An energetics approach to the analysis of molecular motions in polymeric solids

The feasibility of certain modes of intra-and intermolecular motion in polymeric solids are examined in terms of interaction energetics and geometrical constraints. Energy methods for determining equilibrium chain structures and stable deformation structures are reviewed. A systematic approach to the specification of explicit geometrical constraints in condensed phase polymeric systems is developed by matrix techniques. Combination rules are derived which provide straightforward means of constructing deformation structures for oriented polymers.

Applications of these general methods are illustrated for paraffinic systems. Structure-energy maps, based on empirically justified potential functions, are presented for assemblies of paraff inic chains. The potential energy surface in the vicinity of the minima associated with the orthorhombic crystal structure is described by a Taylor's series in the unit cell parameters. Applications of this approximate representation of the energy surface to the prediction of the moduli, thermal expansion coefficients, and bulk compressibility of crystalline paraffins and polyethylene are discussed. Detailed energy maps for coupled rotations of rigid chains and coupled translation-rotation motions are developed. Feasible modes of motion are identified as low-energy structural conversion paths; activation energies are determined from the saddle points in the structure-energy map. The temperature dependence of barriers to motion is estimated by introducing empirical functions which relate average chain spacings to temperature.     

Generating pairs and group actions

An action of a finite group on a closed 2-manifold is called almost free if it has a single orbit of points with nontrivial stabilizers. It is called large when the order of the group is greater than or equal to the genus of the surface. We prove that the orientation-preserving large almost free actions of G on closed orientable surfaces correspond to the Nielsen equivalence classes of generating pairs of G  . We classify the almost free actions on the surfaces of genera 3 and 4, find the large almost free actions of the alternating group _A5$A_5$, and give various other examples.