Quotient polytopes of cyclic polytopes part I: Structure and characterization

We investigate the quotient polytopesC/F, whereC is a cyclic polytope andF is a face ofC. We describe the combinatorial structure of such quotients, and show that under suitable restrictions the pair (C, F) is determined by the combinatorial type ofC/F. We describe alternative constructions of these quotients by “splitting vertices” of lower-dimensional cyclic polytopes. Using Gale diagrams, we show that every simpliciald-polytope withd+3 vertices is isomorphic to a quotient of a cyclic polytope.     

Deconvolution of scanning transmission electron microscopy images of ionomers

Previously, we studied a variety of ionomer morphologies with scanning transmission electron microscopy (STEM). Other groups have found that deconvoluting STEM images dramatically improve the overall image quality and the detection of sub‐nanometer‐scale features. In this study, STEM images of nanometer‐scale ion‐rich aggregates were deconvolved via the Pixon method with a simulated electron probe. The image models are considerably sharper with significantly decreased noise levels, thus making the size and shape of the ionic aggregates easier to distinguish relative to those in the raw STEM images. Raw and deconvoluted images of Zn‐neutralized poly(styrene‐ran‐methacrylic acid) ionomers containing spherical ionic aggregates indicate that the electron density varies smoothly from the edge to the center of the aggregates. Deconvolution also clarifies the issue of aggregate overlap in the STEM images. Furthermore, line scans across deconvoluted STEM images suggest that the three‐dimensional density distribution of these nanoaggregates compares favorably with a radially symmetric Gaussian distribution as opposed to a uniformly dense sphere. The overall result of this work is that deconvolution of STEM images provide ways in which to better investigate the morphologies of ionomers. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 319–326, 2003     

Lattice characterization of convex 3-polytopes and of polygonizations of 2-manifolds

LetC be a polygonization of a 2-dimensional closed manifold without boundary, andL(C) the set of all the faces ofC, partially ordered by inclusion, with adjoinment of a minimal and a maximal element. ThenL(C) is a lattice, and its characterization is given here. Also a characterization of the lattice of the faces of a convex 3-polytope is given. This is a part of the author’s Ph.D. dissertation, written under the supervision of Professor H. Furstenberg, and submitted to the Hebrew University in June, 1969.     

Thin-layer chromatography in the heavy organic industries

The technique of thin-layer chromatography, as practised in the organic industrial laboratory, is described and its applications to the analysis of petroleum hydrocarbons, fuels, lubricants, polymers, plastics and their additives, non-ionic surfactants and explosives are reviewed. The role of thin-layer chromatography in the conservation of the environment is also considered.     

A study of the C(p, p′) reactions at 135 MeV

A relativistic mean field approach is used to determine and compare the single-particle Dirac potentials for nuclei and hypernuclei (Λ, Σ, Ξ). A simple model is used and the Dirac-Hartree-Fock equations are reduced to a Schrödinger-like equation. The subsequent central and spin-orbit shell-model potentials are compared to those of phenomenological approach and other recent microscopic approaches. In the case of hypernuclei the Hartree approximation works already quite well without any need of taking into account the strangeness exchange part coming from strange mesons. The influence of the anomalous magnetic moment of the baryon on the spin-orbit term is found to be rather important for both Λ- and Σ-hyperons.     

A configuration-interaction study of the polarizability derivatives of carbon monoxide

The components of the dipole polarizability and of the dipole-quadrupole polarizability A of the carbon monoxide molecule have been calculated as a function of the internuclear distance using both SCF and CI wavefunctions. The resulting values of , A and then derivatives should be the most accurate ab initio estimates available for these quantities. A comparison of the SCF and CI results shows significant differences in the values obtained.     

Total synthesis of (±)-desepoxy-4,5-didehybromethylenomycin A

The total synthesis of (±)-desepoxy-4,5-didehydromethylenomycin A employing a retrolactonization strategy has been achieved.