Gårding's Theory of Hyperbolic Polynomials

This paper presents a simple, self‐contained account of Gårding's theory of hyperbolic polynomials, together with a recent convexity result of Bauschke‐Güler‐Lewis‐Sendov and an inequality of Gurvits. This account begins by establishing some new results. The first concerns the existence of a pointwise arrangement of the eigenvalues so that they become global real analytic functions. The second asserts that the associated “branches” are independent of the choice of hyperbolic direction. © 2013 Wiley Periodicals, Inc.     

Synthesis and crystal structures of two novel 3,4,5- trimethoxyphenyl derivatives from (Z)-1-[(2′,3′-dinitro-4′-methoxy)-phenyl]-2-[(3″,4″,5″-trimethoxy)-phenyl] ethene

The title compounds, (Z)-1-[(2′,4′-dimethoxy-3′-nitro)-phenyl]-2-[(3″,4″,5″-trimethoxy)-phenyl]ethene, C₁₉H₂₁O₇N (I), and 2-amino-4-methyl-6-(3,4,5-trimethoxy-phenyl)-pyrimidine, C₁₄H₁₇O₃N₃ (II), were obtained unexpectedly from a reaction involving (Z)-1-[(2′,3′-dinitro-4′-methoxy)-phenyl]-2-[(3″,4″,5″-trimethoxy)-phenyl]ethene (IV). The molecular structures of these compounds were obtained by single-crystal X-ray diffraction. Crystallization of I occurs in the centrosymmetric monoclinic space group P2₁/c (No. 14) with a=7.7311(5), b=19.9239(13), c=11.5725(8); and β=92.193(3) and Z=4. Crystallization of II occurs in the centrosymmetric monoclinic space group C2/c (No. 15) with a=21.296(2), b=6.8963(7), c=20.001(2); and β=114.121(6) and Z=8. Details of the synthesis and the structural characterization of the title compounds are presented and discussed.     

THE NATURE OF ULTRAVIOLET LIGHT-INDUCED STRAND BREAKAGE IN DNA CONTAINING BROMOURACIL

Abstract— Single-strand breaks are produced in the phosphodiester backbone of ultraviolet-light-irradiated 5–bromodeoxyuridine-containing DNA (BU-DNA) after treatment with alkali. No radiation dependent breakage is observed in thymine-containing DNA (thy-DNA). The relative yields of breaks terminated by 5'-hydroxyl and 5'-phosphate groups was determined by measuring the rate of phosphorylation achieved with polynucleotide kinase in BU-DNA single strands before and after treatment with alkaline phosphatase. The ratio of 5'-phosphate to 5' hydroxyl groups ranged from 2.3 to 2.9 in different experiments. When cysteamine was present during irradiation no new end groups were produced.
In order to identify the nucleoside(s) at the 5'-termini, phosphate groups were removed with alkaline phosphatase and the 5'-hydroxyl groups were phosphorylated with polynucleotide kinase. Electrophoresis of enzymatic digests showed a single ³²P-labeled component migrating more rapidly than any of the four usual 5'-mononucleotides. Upon column chromatography this component resolved into a major peak coincident with 5'-dUMP and a lesser unidentified constituent. No 5'-dBUM³²P was observed among these nucleotides.     

Infrared spectral changes with crystallization in poly(vinylchloride): Correlations with X-ray and density data

The influence of crystallinity and stereoregularity on the infrared (IR) spectrum of atactic PVC in the solid state has been studied by many researchers [1-12]. Although the molecules in commercial PVC consist of both syndiotactic and isotactic sequences, the bulk polymer is not highly stereoregular, having approximately 50% syndiotacticity. Its infrared spectrum is different from that of highly syndiotactic PVC [3,5,7,9,10-12], particularly in the carbon-to-chlorine stretching region where there are three bands located at 610(615), 635, and 690 cm^?1. These three bands are known to be of complex origin, since each band consists of more than one absorption frequency and its relative intensity depends on the physical state or history of the specimen [3,5,7,9,10-12]. The spectrum in this region is most rigorously interpreted in terms of chain conformational structure, the spatial arrangement of the atoms around the C-C1 bond. Thus, while changes in absorbance intensities for the bands with history do not necessarily reflect changes in crystallinity, their history dependence renders these bands potentially useful as crystallinity indicators.     

Raman Scattering Tensors in Biological Molecules and Their Assemblies

INTRODUCTION

The tensor associated with a Raman band plays an important role in determining the band intensity and its structural significance. Each Raman tensor interrelates two electric vectors, that of the exciting radiation (i.e. laser photon) and that of the Raman scattered radiation (i.e. the inelastically scattered photon which results from the exchange of a vibrational quantum between the exciting photon and the molecule). The Raman tensor is obtained formally as the first derivative of the molecular polarizability tensor, the derivative being taken with respect to the vibrational normal coordinate. In other words, the Raman tensor associated with a vibrational Raman band is an indicator of how the polarizability of the molecule oscillates with the molecular normal mode of vibration.     

Investigating the mechanisms of diamond polishing using Raman spectroscopy

Recent research has shown that a phase transformation of diamond to a different form of carbon is involved when diamonds are polished in the traditional fashion. The question as to how this phase transformation is activated and maintained to produce high wear rates is of great technological interest since it may radically change the way we view the processing of diamond. This paper describes the use of Raman spectroscopy to examine debris produced on the diamond polishing wheel, both during its preparation and during polishing. In addition, polished diamond surfaces were examined for the possible existence of non-diamond surface layers in an attempt to identify material removal mechanisms. Raman spectroscopy proves ideal for these analyses because its relatively high spatial resolution is well suited to the analysis of small wear features and debris particles, and because of the wealth of information it reveals about chemical structure. This level of structural information has been lacking in previous analyses of diamond polishing debris. In addition to the non-diamond carbon found in the wear debris, significant quantities of two iron oxides, magnetite (Fe₃O₄) and haematite (α-Fe₂O₃), were also found. An interesting observation was that a transformation from magnetite to haematite could be induced either by using high power laser excitation or by frictional heating during polishing. It is suggested that some of the Raman peaks previously attributed to lonsdaleite might better be explained by the presence of these oxides.     

Benchmark calculations with correlated molecular wavefunctions. XIII. Potential energy curves for He2, Ne2 and Ar2 using correlation consistent basis sets through augmented sextuple zeta

The potential energy curves of the rare gas dimers He2, Ne2, and Ar2 have been computed using correlation consistent basis sets ranging from singly augmented aug-cc-pVDZ sets through triply augmented t-aug-cc-pV6Z sets, with the augmented sextuple basis sets being reported herein. Several methods for including electron correlation were investigated, namely Møller—Plesset perturbation theory (MP2, MP3 and MP4) and coupled cluster theory [CCSD and CCSD(T)]. For He2 CCSD(T)/d-aug-cc-pV6Z calculations yield a well depth of 7.35 cm-1 (10.58 K), with an estimated complete basis set (CBS) limit of 7.40 cm-1 (10.65 K). The latter is smaller than the 'exact' well depth (Aziz, R. A., Janzen, A. R., and Moldover, M. R., 1995, Phys. Rev. Lett., 74, 1586) by about 0.2 cm-1 (0.35 K). The Ne2 well depth, computed with the CCSD(T)/d-aug-cc-pV6Z method, is 28.31 cm-1 and the estimated CBS limit is 28.4 cm-1, approximately 1 cm-1 smaller than the empirical potential of Aziz, R. A., and Slaman, M., J., 1989, Chem. Phys., 130, 187. Inclusion of core and core—valence correlation effects has a negligible effect on the Ne2 well depth, decreasing it by only 0.04 cm-1. For Ar2, CCSD(T)/d-aug-cc-pV6Z calculations yield a well depth of 96.2 cm-1. The corresponding HFDID potential of Aziz, R. A., 1993, J. chem. Phys., 99, 4518 predicts of De of 99.7 cm-1. Inclusion of core and core-valence effects in Ar2 increases the well depth and decreases the discrepancy by approximately 1 cm-1.     

Polymerizable derivatives of long-chain fatty acids. IV. Vinyl esters

Contrary to some published reports, the vinyl esters of saturated fatty acids polymerize readily and rapidly. Vinyl oleate, when present in excess of 5%, and oxygen exert marked retarding effects. Techniques are described for the free-radical-initiated polymerization of the vinyl esters of caprylic, capric, lauric, myristic, palmitic, and stearic acids in bulk, dispersion, solution, and emulsion. Some data are given for polymerization in the presence of chain-transfer agents, such as carbon tetrachloride, dodecylmercaptan, and ethylbenzene. Conditions are reported for obtaining degrees of polymerization from about 2 (when chain-transfer agents are employed) to 10,000 (weight average). The weight average degree of polymerization increases markedly as the conversion increases, particularly above 80%. Even up to extremely high conversions, soluble polymers are obtained in most cases. Solubility characteristics, transition point data, molecular weights (osmometric and light-scattering), and isolation and purification techniques are also reported.     

Data Formats for Elementary Gas Phase Kinetics,Part 1: Unique Representations of Species at the Molecular Level

Standardized electronic formats for data are needed to efficiently and transparently communicate the results of scientific studies. A format for the unique identification of chemical species is a requirement in the field of chemistry, and the IUPAC International Chemical Identifier (InChI) has been widely adopted for this purpose. The InChI identifier has proved to be very useful. The InChI identifier, however, is currently insufficient to uniquely specify some types of molecular entities at a detailed molecular level needed to fully characterize their chemical nature, to differentiate between chemically distinct conformers, to uniquely identify structures used in quantum chemical calculations, and to completely describe elementary chemical reactions. To address this limitation, we propose an augmented form of InChI, denoted as InChI–ER, which contains additional optional layers that allow the unique and unambiguous identification of molecules at a detailed molecular level. The new layers proposed herein are optional extensions of the existing InChI formalism and, like all other InChI layers, would not interfere with InChI identifiers currently in use. The focus of the present work is the better specification of required molecular entities such as rotational conformations, ring conformations, and electronic states. In companion articles, we propose additional reaction layers using an extended InChI format that will enable the unique identification of elementary chemical reactions, including specification of associated transition states, specification of the changes in bonds that occur during reaction, and classification of reaction types.