A facile tandem carbene-ylide route to 2-fluoropyrrole derivatives

2-Fluoropyrroles were synthesised via 1,3-dipolar cycloaddition of iminiodifluoromethanides derived from corresponding imines and difluorocarbene to dimethyl acetylenedicarboxylate.     

Systolic inequalities and Massey products in simply-connected manifolds

We show that the existence of a nontrivial Massey product in the cohomology ring H* (X) imposes global constraints upon the Riemannian geometry of a manifold X. Namely, we exhibit a suitable systolic inequality, associated to such a product. This generalizes an inequality proved in collaboration with Y. Rudyak, in the case when X has unit Betti numbers, and realizes the next step in M. Gromov’s program for obtaining geometric inequalities associated with nontrivial Massey products. The inequality is a volume lower bound, and depends on the metric via a suitable isoperimetric quotient. The proof relies upon W. Banaszczyk’s upper bound for the successive minima of a pair of dual lattices. Such an upper bound is applied to the integral lattices in homology and cohomology of X. The possibility of applying such upper bounds to obtain volume lower bounds was first exploited in joint work with V. Bangert. The latter work deduced systolic inequalities from nontrivial cup-product relations, whose role here is played by Massey products. Supported by the Israel Science Foundation (grants no. 620/00, 84/03, and 1294/06)     

Investigation of uremic analytes in hemodialysate and their structural elucidation from accurate mass maps generated by a multi‐dimensional liquid chromatography/mass spectrometry approach

Historically, structural elucidation of unknown analytes by mass spectrometry alone has involved tandem mass spectrometry experiments using electron ionization. Most target molecules for bioanalysis in the metabolome are unsuitable for detection by this previous methodology. Recent publications have used high‐resolution accurate mass analysis using an LTQ‐Orbitrap with the more modern approach of electrospray ionization to identify new metabolites of known metabolic pathways. We have investigated the use of this methodology to build accurate mass fragmentation maps for the structural elucidation of unknown compounds. This has included the development and validation of a novel multi‐dimensional LC/MS/MS methodology to identify known uremic analytes in a clinical hemodialysate sample. Good inter‐ and intra‐day reproducibility of both chromatographic stages with a high degree of mass accuracy and precision was achieved with the multi‐dimensional liquid chromatography/tandem mass spectrometry (LC/MS/MS) system. Fragmentation maps were generated most successfully using collision‐induced dissociation (CID) as, unlike high‐energy CID (HCD), ions formed by this technique could be fragmented further. Structural elucidation is more challenging for large analytes >270 Da and distinguishing between isomers where their initial fragmentation pattern is insufficiently different. For small molecules (<200 Da), where fragmentation data may be obtained without loss of signal intensity, complete structures can be proposed from just the accurate mass fragmentation data. This methodology has led to the discovery of a selection of known uremic analytes and two completely novel moieties with chemical structural assignments made. Copyright © 2009 John Wiley & Sons, Ltd.     

Elastic SH wave propagation in a layered anisotropic plate with interface damage modelled by spring boundary conditions

Elastic SH wave propagation in a layered anisotropic plate withinterface damage is modelled in several steps. A single interfacecrack between two half-spaces is first studied and an explicitsolution for the crack-opening displacement is obtained at lowfrequencies. This is then generalised to a random distributionof cracks at the interface and the result is reformulated asa spring boundary condition. As an example of its usefulness,this boundary condition is then used in the derivation of aplate equation by expanding the displacements in power seriesin the thickness coordinate.     

Novel types of boronated chlorin e6 conjugates via ‘click chemistry’

Conjugates of chlorin e₆ with closo‐dodecaborate and cobalt bis(dicarbollide) anions were synthesized for the first time in high yields using the advanced ‘click’ methodology. In vitro study on A549 human lung adenocarcinoma cells revealed that the synthesized boronated conjugates are able to penetrate and accumulate in cancer cells, but their intracellular concentration is not sufficient for effective photodynamic and boron neutron capture therapy of cancer. Copyright © 2009 John Wiley & Sons, Ltd.     

On a problem by Beidar concerning the central closure

We give an example of a prime ring with zero center such that its central closure is a simple ring with an identity element. It solves a problem posed by Beidar.     

Modeling the Behavior of Heat-Shrinkable Thin Films

We describe an asymptotic model for the behavior of PET-like heat-shrinkable thin films that includes both membrane and bending energies when the thickness of the film is positive. We compare the model to Koiter’s shell model and to models in which a membrane energy or a bending energy are obtained by Γ-convergence techniques. We also provide computational results for various temperature distributions applied to the films.