The numerical evaluation of the error term in a quadrature formula of Clenshaw-Curtis type for the Gegenbauer weight function

A method is derived for the numerical evaluation of the error term arising in a quadrature formula of Clenshaw-Curtis type for functions of the form (1-x²)^{l- \frac12}f(x)(1-x^{2})^{\lambda - \frac{1}{2}}f(x) over the interval [−1,1]. The method is illustrated by an example.     

Doubly diastereoselective conjugate addition of enantiopure lithium amides to enantiopure N-enoyl oxazolidin-2-ones: a mechanistic probe

The doubly diastereoselective conjugate addition of the antipodes of lithium N-benzyl-N-(α-methylbenzyl)amide to a range of enantiopure N-enoyl oxazolidin-2-ones has been used as a mechanistic probe to determine that the reactive conformation is the anti-s-cis form. The β-amino carbonyl products resulting from these conjugate addition reactions are useful templates for further elaboration into an α,β,α-pseudotripeptide.     

The Hydrogen-Bonded Coordination Polymer Tetracesium Bis(5-nitroisophthalate) Heptahydrate

Abstract  

The coordination polymer complex tetracesium bis(5-nitroisophthalate) heptahydrate [Cs₄(C₈H₃NO₆)₂ (H₂O)₇] _n has been synthesized and characterized using single-crystal X-ray diffraction. Crystals are monoclinic, space group P2₁/c, with Z = 4 in a cell with dimensions a = 12.3213(3), b = 6.7557(2), c = 36.2020(9) ?, β = 90.548(2)^o. The complex is based on a repeating unit comprising four independent and different Cs coordination centres, two 6-coordinate, and two 8-coordinate [Cs–O, range 2.959(5)–3.386(5) ?], and seven water molecules, two of which are monodentate and the other five bridging, while all other oxygen atoms in the structure, including those of the nitro groups form inter-Cs bridges. Extensive water O–H···O hydrogen-bonding interactions give a three-dimensional framework. This structure represents the first of an alkali metal compound of 5-nitroisophthalic acid that has been reported.     

A tits alternative for groups that are residually of bounded rank

In this short note a Tits alternative for certain kinds of groups which are residually of rank at mostr is obtained. The main theorem states that ifG is a group that is residually (locally (soluble-by-finite) of rankr), then eitherG is locally (soluble-by-finite) orG contains a non-abelian free subgroup. The third author would like to thank the School of Mathematics at the University of Wales, Cardiff for its hospitality whild part of this work was being done.     

Rapid quantitative measurements of proteomes by Fourier transform ion cyclotron resonance mass spectrometry.

The patterns of gene expression, post-translational modifications, protein/biomolecular interactions, and how these may be affected by changes in the environment, cannot be accurately predicted from DNA sequences. Approaches for proteome characterization are generally based upon mass spectrometric analysis of in-gel digested two dimensional polyacrylamide gel electrophoresis (2-D PAGE) separated proteins, allowing relatively rapid protein identification compared to conventional approaches. This technique, however, is constrained by the speed of the 2-D PAGE separations, the sensitivity limits intrinsic to staining necessary for protein visualization, the speed and sensitivity of subsequent mass spectrometric analyses for identification, and the limited ability for accurate quantitative measurements based on differences in spot intensity. We are presently developing alternative approaches for proteomics based upon the combination of fast capillary electrophoresis, or other suitable chromatographic separations, and the high mass accuracy and sensitivity obtainable with unique Fourier transform ion cyclotron resonance (FTICR) mass spectrometers available at our laboratory. Several approaches are presently being pursued; one based upon the analysis of intact proteins and the second upon approaches for global protein digestion and accurate peptide mass analysis. Quantitation of protein/peptide levels are based on using two or more stable-isotope labeled versions of proteomes which are combined to obtain precise quantitation of relative protein abundances. We describe the status of our efforts towards the development of a high-throughput proteomics capability and present initial results for application to several microorganisms and discuss our efforts for extending the developed capability to mammalian proteomes.     

Penny-shaped crack in a linear viscoelastic medium under shear

The problem of a linear viscoelastic body, containing a penny-shaped crack subjected to the shear parallel to the edge of the crack is considered in this paper. Closed form expressions for the displacements over the surface of the crack, the shear components in the plane of the crack and the stress intensity factors are determined. The various expressions are then specialized for two particular linear viscoelastic materials and the effect of viscoelasticity, wherever possible, is pointed out.     

Poly(2-imidazolin-5-ones)—A new class of heterocyclic polymers

The reaction of bisazlactones (2-oxazolin-5-ones) with primary diamines containing additional secondary or tertiary amine functionality (e.g., diethylenetriamine, triethylenetetramine, or N-methyliminobispropylamine) readily produces polyamides which serve as precursors to a new class of heterocyclic polymers. Thermal cyclodehydration takes place under relatively mild conditions (180–200°C) to produce water-soluble polymers containing the 2-imidazolin-5-one heterocycle. Model reactions have been studied to verify this mode of cyclization and confirm the proposed polymer structure.