The consecutive [2+2] cycloaddition-ring expansion route to diastereomeric 1,4-diazepin-5-ones from imino-ketenimines. Alternative intramolecular transamidation of β-lactams

Azeto[1,2-a]imidazoles are prepared by a formal intramolecular [2+2] cycloaddition of imino-ketenimines in which an ethylene chain is linking the nitrogen atoms of both functionalities, bearing a methyl and a phenyl group on the terminal carbon atom of the heterocumulene. By acid-catalyzed hydrolysis these azeto[1,2-a]imidazoles are converted into 6,6,7-trisubstituted hexahydro-1,4-diazepin-5-ones, which have been alternatively prepared via intramolecular transamidation of N-(2-aminoethyl)-β-lactams.     

Crystalline calmagite and a study of sulphonation effects on azo dye metal-ion indicators

Calmagite was introduced in 1960 as a stable substitute for Eriochrome Black T in EDTA titrations of calcium plus magnesium. The colour changes were the same but somewhat sharper. Indicator stock solutions were stable indefinitely. The new indicator was designed as an indicator and not as a wool dye. Azo dye impurities which may be present in some commercial supplies tend to lengthen the end-points. A simple means of removing these impurities to yield crystalline indicator has been developed. The effects of sulphonation on the performance of azo dyes as indicators have been studied.     

Synthesis,Characterization and Magnetic Properties of New Dinuclear Copper(II) Complexes with N,N′‐Disubstituted Dithiooxamides derived from α‐Amino Acids

Four new dinuclear copper(II) complexes have been synthesized and have the general formula [Cu₂(L)(H₂O)₂], where L = GLYDTO [N,N′‐bis(carboxymethyl)dithiooxamide], ALADTO [N,N′‐bis(carboxyethyl)dithiooxamide], VALDTO [N,N′‐bis(1‐carboxy‐2‐methylpropyl)dithiooxamide] and LEUDTO [N,N′‐bis(1‐carboxy‐3‐methylbutyl)dithiooxamide]. The complexes were characterized by elemental analysis as well as by IR, electronic and EPR spectroscopy. These techniques provided evidence for the presence of the CuNO₂S chromophore. Magnetic susceptibility measurements on all the complexes in the range 4–300 K show the existence of a dominant antiferromagnetic interaction with ?J values greater than 300 cm^?1. Thermal decomposition behaviour of the complexes was studied by thermogravimetry.     

Recent Advances in Electropolymerized Conducting Polymers in Amperometric Biosensors

Conducting electroactive polymers (CPs) are materials discovered just over 20 years ago which have aroused considerable interest on account of their electronic conducting properties and unique chemical and biochemical properties. Consequently, they have numerous (bio)analytical and technological applications. CPs are easily synthesized and deposited onto the conductive surface of a given substrate from monomer solutions by electrochemical polymerization with precise electrochemical control of their formation rate and thickness. Coating electrodes with CPs under mild conditions opens up enormous possibilities for the immobilization of biomolecules and bioaffinity or biorecognizing reagents, the improvement of their electrocatalytic properties, rapid electron transfer and direct communication to produce a range of analytical signals and new analytical applications. Co-immobilization of other molecules (enzymatic co-factors or charge-transfer mediators) by entrapment within electropolymerized films or by covalent binding on these films permits straightforward fabrication of reagentless biosensors. The characteristics of CPs and their uses, mainly in amperometric biosensors, are reviewed. The most recent applications and lines of research related to CP films are summarized in the different sections of the paper, and probable future trends are discussed.     

Stereoselective synthesis of trans-2,3-disubstituted pyrrolidines via addition to N-acyliminium ions

An efficient and stereoselective synthesis of trans-2,3-disubstituted pyrrolidines is described. The intermolecular alkylation of racemic N-acyliminium ions generated in situ from the corresponding 3-substituted lactams proceeds stereoselectively and in high yield.     

Stéréosélectivité et régiosélectivité de la réduction des cyclopropènes-2,3 et méthylène-2 cyclopropanes fonctionalisés en position 1

Reduction of 2 cyclopropenyl esters and alcohols with lithium aluminium hydride is selective; at low temperatures (0°) the double bond is not reduced, but at higher temperatures (65°) the reduction is complete and only the cyclopropylmethanol is obtained. The reduction of the double bond is regioselective (the most stable carbanion is formed) and stereospecific (the hydride attack on the double bond occurs cis to the functional group). This stereospecificity can be explained through the initial formation of an alkoxylaluminium hydride followed by an intramolecular reduction of the double bond. Similar results have been obtained in the reduction of functionalised methylenecyclopropanes.     

On the Hilbert Evolution Algebras of a Graph

Evolution algebras are a special class of nonassociative algebras exhibiting connections with various fields of mathematics. Hilbert evolution algebras generalize the concept in the framework of Hilbert spaces. This allows us to deal with a wide class of infinite-dimensional spaces. We study Hilbert evolution algebras associated to a graph. Inspired by the definitions of evolution algebras we define the Hilbert evolution algebra that is associated to a given graph and the Hilbert evolution algebra that is associated to the symmetric random walk on a graph. For a given graph, we provide the conditions for these structures to be or not to be isomorphic. Our definitions and results extend to the graphs with infinitely many vertices. We also develop a similar theory for the evolution algebras associated to finite graphs.

     

Co-monotone allocations,Bickel-Lehmann dispersion and the Arrow-Pratt measure of risk aversion

For every integrable allocation (X ₁,X ₂, ...,X _n ) of a random endowmentY= _i ^=1/n X _i amongn agents, there is another allocation (X ₁*,X ₂*, ...,X _n *) such that for every 1in,X _i * is a nondecreasing function ofY (or, (X ₁*,X ₂*, ...,X _n *) areco-monotone) andX _i * dominatesX _i by Second Degree Dominance.If (X ₁*,X ₂*, ...,X _n *) is a co-monotone allocation ofY= _i ^=1/n X _i *, then for every 1in, Y is more dispersed thanX _i * in the sense of the Bickel and Lehmann stochastic order.To illustrate the potential use of this concept in economics, consider insurance markets. It follows that unless the uninsured position is Bickel and Lehmann more dispersed than the insured position, the existing contract can be improved so as to raise the expected utility of both parties, regardless of their (concave) utility functions.