Spectra and structure of silicon containing compounds

The Raman (50 to 3200 cm^–1) and infrared (50 to 3500 cm^–1) spectra of chlorodimethylmethoxysilane, Cl(CH₃)₂SiOCH₃, in the vapor and solid phases have been recorded. Raman spectra of the liquid including depolarization ratios have also been recorded. Optimized geometries and conformational stabilities have been obtained from ab initio calculations utilizing the RHF/3–21G* and RHF/6–31G* basis sets. The calculations from both of these basis sets indicated the gauche conformer to be significantly more stable than the trans conformer. Since the gauche has twice the multiplicity of the trans form it is unlikely that the trans conformer will be detected in the fluid phases at room temperature. This is supported by the fact that no infrared or Raman bands were found to vanish in the spectra of the crystalline solid. The vibrational frequencies have been calculated using appropriate scaling factors, and the vibrational spectra are interpreted in detail. The results have been compared with those obtained for some related molecules.Dedicated to Professor Dr. H. Kriegsmann on the occasion of his 70th birthdayFor part XX, see J Raman Spectrosc 26:in press (1995)Analytical R/D Department, Organic Products Division, Miles Inc., Bushy Park Plant. Charleston, SC 9411, USAChemistry Department, Mu'tah University, P.O.Box 7, Mu'tah-Karak, JordanDepartment of Chemistry, Moscow State University, Moscow, B-234, RussiaDepartment of Ceramic Engineering, Inha University, Nam-Ku, Incheon 160, KoreaDepartment of Chemistry, University of Oslo, P.O.Box 1033, 0315 Oslo, Norway     

Rates and mechanisms of the intermolecular cation-exchange reactions of sodium tetraphenylboron with sodium–nitrobenzene and with sodium–p-nitrobenzonitrile

The rates of the exchange of sodium ions between sodium tetraphenylborate and sodium–nitrobenzene or sodium–p-nitrobenzonitrile were measured from analysis of the line broadening effect on the ESR spectra off the paramagnetic ion pairs. The rate is significantly lower for the substituted nitro compound, and it is suggested that this reflects a difference in mechanism for the two systems.     

Affine-Invariant Distances, Envelopes and Symmetry Sets

Affine invariant symmetry sets of planar curves are introduced and studied in this paper. Two different approaches are investigated. The first one is based on affine invariant distances, and defines the symmetry set as the closure of the locus of points on (at least) two affine normals and affine-equidistant from the corresponding points on the curve. The second approach is based on affine bitangent conics. In this case the symmetry set is defined as the closure of the locus of centers of conics with (at least) 3-point contact with the curve at two or more distinct points on the curve. This is equivalent to conic and curve having, at those points, the same affine tangent, or the same Euclidean tangent and curvature. Although the two analogous definitions for the classical Euclidean symmetry set are equivalent, this is not the case for the affine group. We present a number of properties of both affine symmetry sets, showing their similarities with and differences from the Euclidean case. We conclude the paper with a discussion of possible extensions to higher dimensions and other transformation groups, as well as to invariant Voronoi diagrams.     

Heegner points,cycles and Maass forms

We derive for Hecke-Maass cusp forms on the full modular group a relation between the sum of the form at Heegner points (and integrals over Heegner cycles) and the product of two Fourier coefficients of a corresponding form of half-integral weight. Specializing to certain cycles we obtain the nonnegativity of theL-function of such a form at the center of the critical strip. These results generalize similar formulae known for holomorphic forms. Partially supported by NSF grant # DMS-9096262. Partially supported by NSF grant # DMS-9102082.     

High-order adaptive finite element-singly implicit Runge-Kutta methods for parabolic differential equations

We describe an adaptive mesh refinement finite element method-of-lines procedure for solving one-dimensional parabolic partial differential equations. Solutions are calculated using Galerkin's method with a piecewise hierarchical polynomial basis in space and singly implicit Runge-Kutta (SIRK) methods in time. A modified SIRK formulation eliminates a linear systems solution that is required by the traditional SIRK formulation and leads to a new reduced-order interpolation formula. Stability and temporal error estimation techniques allow acceptance of approximate solutions at intermediate stages, yielding increased efficiency when solving partial differential equations. A priori energy estimates of the local discretization error are obtained for a nonlinear scalar problem. A posteriori estimates of local spatial discretization errors, obtained by order variation, are used with the a priori error estimates to control the adaptive mesh refinement strategy. Computational results suggest convergence of the a posteriori error estimate to the exact discretization error and verify the utility of the adaptive technique.This research was partially supported by the U.S. Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Number AFOSR-90-0194; the U.S. Army Research Office under Contract Number DAAL 03-91-G-0215; by the National Science Foundation under Grant Number CDA-8805910; and by a grant from the Committee on Research, Tulane University.     

Natural product chemistry. Part 160. Synthesis of 8-, 9-, 10- and 11-methylacronycines to improve the cytostatic activity of acronycine

With the help of drug design, 8-, 9-, 10- and 11-methylacronycines 24, 25, 26 and 27 have been selected and synthesised to improve the cytostatic potency of acronycine ( 31 ). The condensation of phloroglucinol with 6-methylanthranilic acid gave 7-hydroxy-1,9-dimethyldibenzo[b,j][1,7]phenanthroline-8,14(5H,13H)-dione ( 32 ) as the main product.     

The density of rational functions in Markov systems: A counterexample to a conjecture of D. J. Newman

We construct a family of infinite Markov systems on [?1, 1] with the property that the rational functions from these systems are not dense inC[?1, 1]. This gives counterexamples to a long-standing conjecture of D. J. Newman.     

Reaction of lithium dimethylcuprate with conformationally biased β-acyloxy enol esters - regio and stereocontrolled access to functionalized six-carbon chiral synthons

Alkyl 2-acyloxy α-D-erythro-hex-2-enopyranoside diesters, readily available from D-hexoses, are versatile intermediates fro the expeditious preparation of six-carbon chiral synthons containing alternating and/or consecutive C-methyl and hydroxyl groups.     

Synthesis and characterization of layered tetravalent metal terphenyl mono- and bis-phosphonates

The syntheses of p-terphenylphosphonic acid and p,p″-terphenyl-bis-phosphonic acid have been developed, and the resulting products were used to prepare layered Th(IV) and Zr(IV) phosphonates. The monoacidic terphenyl species formed a bilayered structure while the diacid created a pillared geometry. Mixed component phases were also produced. Synthesis, characterization, X-ray and thermal properties of these materials are discussed.