Structural studies on 9-hydrazono-6,7,8,9-tetrahydro-4-oxo-4H-pyrido[1,2-a]pyrimidines by 1H, 13C and 15N NMR spectroscopy

¹H, ¹³C and ¹⁵N NMR studies demonstrated that 9-hydrazono-6,7,8,9-tetrahydro-4-oxo-4H-pyrido-[1,2-a] pyrimidlnes exist as an equilibrium mixture of Z-E isomers in the hydrazono–imino tautomeric form having an exocyclic double bond. Proton-catalysed Z-E interconversion is fast. Substituent and solvent effects revealed that the decisive factors controlling the Z:E ratio are internal hydrogen bonding in the Z-isomer, stabilization by solvation and steric interaction.     

Iron plasma: Sensitivity of photoelectric cross sections to different models and general features of the Fermi-Amaldi-Modified model

Photoelectric cross sections in several atomic models are presented as a function of temperature and density. The models discussed are Thomas-Fermi (TF), Fermi-Amaldi-Modified (FAM), and Debye-Hückel-Thomas-Fermi (DHTF). We also present some systematic results for the less known FAM potential model regarding predictions for: electrostatic potentials, bound electron level energies, pressures, and branching ratios of photoelectric cross sections. The pure iron plasma which we explored had a temperature in the range of 0.2–3 keV and a density in the range of 50–1000 g/cm³. Our conclusion is that except near threshold the photoelectric cross sections per fully occupied subshell are less sensitive to changes in density and temperature, at least in the ranges of our investigation, than other factors, such as occupation numbers.     

Motivic orthogonal two-dimensional representations of Gal(ℚ/ℚ)

Given a two-dimensional compatible family of ℓ-adic representations which is motivic and which respects an orthogonal form up to similitudes, we show how to express itsL-function in terms of a Hecke character. We give several examples and in particular we analyze a representation associated to a certainK3 surface which arose in the study of Kloosterman sums.     

On multivariate approximation by integer translates of a basis function

Approximation properties of the dilations of the integer translates of a smooth function, with some derivatives vanishing at infinity, are studied. The results apply to fundamental solutions of homogeneous elliptic operators and to “shifted” fundamental solutions of the iterated Laplacian. Following the approach from spline theory, the question of polynomial reproduction by quasi-interpolation is addressed first. The analysis makes an essential use of the structure of the generalized Fourier transform of the basis function. In contrast with spline theory, polynomial reproduction is not sufficient for the derivation of exact order of convergence by dilated quasi-interpolants. These convergence orders are established by a careful and quite involved examination of the decay rates of the basis function. Furthermore, it is shown that the same approximation orders are obtained with quasi-interpolants defined on a bounded domain. Supported in part by the United States under contract No. DAAL-87-K-0030, and by Carl de Boor’s Steenbock Professorship, University of Wisconsin-Madison.     

A set of geometric programming test problems and their solutions

This paper attempts to provide a set of standard test examples for researchers working in the area of geometric programming and general nonlinear, continuous, nonconvex programming algorithms. The examples consist partly of applications of nonlinear programming that have appeared in the literature and partly of original geometric programming applications. Solutions to all the problems are provided as well as the starting points from which these solutions were computed. Other computationally important aspects such as tolerances and degree of accuracy with which these problems were solved, are also included.This work was supported in part by Canada Council Grant #S74-0148 and National Research Council of Canada Grant #084-6319-32.     

Investigating the reaction of N-carbobenzoxy-O-carbobenzoxy- hydroxylamine with dimethyl sulfoxide: formation of S,S-dimethyl-N-[(phenylmethoxy)- carbonyl]sulfoximine

[Reaction: see text]. N-carbobenzoxy-O-carbobenzoxyhydroxylamine (1a) underwent a thermally induced reaction in DMSO in which there is net N-alpha-eliminative oxidation with tandem oxidative incorporation of DMSO to yield S,S-dimethyl-N-[(phenylmethoxy)carbonyl]sulfoximine. Mechanisms for the formation of the sulfoximine are presented as well as the product characterizations, including the X-ray crystal structure.     

Simple modification of a protein database for mass spectral identification of N-linked glycopeptides

We describe an algorithm which modifies a protein database such that during a database search deamidation is limited to asparagines strictly contained within the N-glycosylation consensus sequence. The modified database was evaluated using a dataset created from the shotgun proteomic analysis of N-linked glycopeptides from human blood serum. We demonstrate that the application of the modified database eliminates incorrect glycopeptide assignments, reduces the peptide false-discovery rate, and eliminates the need for manual validation of glycopeptide identifications.     

Molecular recognition in a thermoplastic elastomer

Selective incorporation of bisurea guests in thermoplastic elastomers with poly(tetrahydrofuran) soft blocks and bisurea containing hard blocks is observed when the distances between the urea groups of host and guest match. The incorporation leads to significant modulation of mechanical properties. With bisurea-functionalized dyes as guests, a strong difference in extractability by detergent solution was shown between dyes differing by just one methylene unit between urea groups. Upon elongation of elastomer films, strong differences in alignability of matching and nonmatching dyes were observed.     

The Classification of Flats in {\boldsymbol {PG}}({\bf 9,2}) which are External to the Grassmannian {\cal G}_{\bf 1,4,2}

Constructions are given of different kinds of flats in the projective space $PG(9,2)={\mathbb P}(\wedge^{2}V(5,2))$ which are external to the Grassmannian ${\cal G}_{\bf 1,4,2}$ of lines of PG(4,2). In particular it is shown that there exist precisely two GL(5,2)-orbits of external 4-flats, each with stabilizer group ?31:5. (No 5-flat is external.) For each k=1,2,3, two distinct kinds of external k-flats are simply constructed out of certain partial spreads in PG(4,2) of size k+2. A third kind of external plane, with stabilizer ?2³:(7:3), is also shown to exist. With the aid of a certain ‘key counting lemma’, it is proved that the foregoing amounts to a complete classification of external flats.     

Agropine,a new amino acid derivative from crown gall tumours

Agropine, an unusual compound produced in plant tumours was shown by mass spectrometry and proton and carbon-13 nmr spectroscopy to be a bicyclic derivative of glutamic acid and a hexitol sugar.