Boundedness and Dissipativity of Truncated Rotations on Uniform Planar Lattices

The finiteness of computer arithmetic can lead to some dramatic differences between the behaviour of a continuous dynamical system and a computer simulation. A thorough rigorous theoretical analysis of what may or what does happen is usually extremely difficult and to date little has been done even in relatively simple contexts. The comparative behaviour of a rotation mapping in the plane and on a uniform lattice in the plane is one such example. Simulations show that the rounding operator applied to a planar rotation mapping more or less preserves the qualitative behaviour of the original mapping, whereas the application of the truncation operator to a planar rotation can lead to quite different dynamical features. In this paper a theoretical justification of the properties of the planar rotation mappings under truncation to a, uniform integer lattice is provided, in particular properties of boundedness and dissipativity are investigated.     

Determination of total mercury in environmental and biological samples by flow injection cold vapour atomic absorption spectrometry

A simple and accurate method has been developed for the determination of total mercury in environmental and biological samples. The method utilises an off-line microwave digestion stage followed by analysis using a flow injection system with detection by cold vapour atomic absorption spectrometry.

The method has been validated using two certified reference materials (DORM-1 dogfish and MESS-2 estuarine sediment) and the results agreed well with the certified values. A detection limit of 0.2 ng g⁻¹ Hg was obtained and no significant interference was observed. The method was finally applied to the determination of mercury in river sediments and canned tuna fish, and gave results in the range 0.1–3.0 mg kg⁻¹.     

Measuring intracellular calcium fluxes in high throughput mode

The measurement of intracellular calcium fluxes in real time is widely applied within the pharmaceutical industry to measure the activation of G-protein coupled receptors (GPCRhyp;s), either for pharmacological characterisation or to screen for new surrogate ligands. Initially restricted to G(q) coupled GPCRs, the introduction of promiscuous and chimeric G-proteins has further widened the application of these assays. The development of new calcium sensitive dyes and assays has provided sensitive, homogeneous assays which can be readily applied to high throughput screening (HTS). In this paper we describe the full automation of this assay type using a fluorometric imaging plate reader (FLIPR ) integrated into a Beckman/Sagian system to establish a simple robotic system that is well suited for the current medium throughput screening in this area of lead discovery. Using a recently completed HTS we discuss important determinants for FLIPR based screening, highlight some limitations of the current approach, and look at the requirements for future automated systems capable of keeping up with expanding compound files.     

Highly efficient Pd-catalyzed carbonylative cross-coupling reactions with tetraorganoindates

Tetraorganoindates, which were prepared easily from the reaction of 1 equiv of InCl(3) with 4 equiv of organometallics, could be employed as effective nucleophilic cross-coupling partners in Pd-catalyzed carbonylative cross-coupling reactions with a variety of organic electrophiles. The present method gave unsymmetrical ketones and 1,4-diacylbenzenes in good yields with highly efficient transfer of almost all the organic groups attached to the indium under a carbon monoxide atmosphere in THF at 60 degrees C.     

Surface tension of a Lennard-Jones liquid under supersaturation

A formally exact Kirkwood-Buff virial formula for the surface tension of a supersaturated interface is derived. A modified Gibbs ensemble method is given that allows the creation of interacting supersaturated phases of equal chemical potential, and which enables the Kirkwood-Buff formula to be applied. The methods are tested by Monte Carlo simulation of a supersaturated Lennard-Jones fluid with a planar liquid-vapor interface. The Kirkwood-Buff results for the supersaturated surface tension are found to be in reasonable agreement with new results obtained here using the recently developed, formally exact, ghost interface method, [M. P. Moody and P. Attard, J. Chem. Phys., 2002, 117, 6705]. The surface tension is obtained as a function of supersaturation at four temperatures, and it is found to decrease with increasing supersaturation, and to vanish at the vapor spinodal. The relevance of the present results to the nucleation of droplets in a supersaturated vapor is discussed.     

Indium-mediated beta-allylation,beta-propargylation,and beta-allenylation onto alpha,beta-unsaturated ketones: reactions of in-situ-generated 3-tert-butyldimethylsilyloxyalk-2-enylsulfonium salts with in-situ-generated organoindium reagents

3-tert-Butyldimethylsilyloxyalk-2-enylsulfonium salts, generated in situ from the reaction of alpha,beta-enones with dimethyl sulfide in the presence of TBSOTf, underwent a novel nucleophilic substitution with allylindiums to give silyl enol ethers of delta,epsilon-alkenyl ketones in good yields, which correspond to formal Michael addition products. In a similar manner, 1,4-propargylation of propargylindiums onto the sulfonium salts produced the corresponding silyl enol ethers of delta,epsilon-alkynyl ketones in good yields. Organoindium reagents derived from gamma-substituted propargyl bromide and indium afforded the corresponding silyl enol ethers of beta-allenyl ketones in good yields. The reaction proceeds via an addition-substitution mechanism involving the formation of allylic sulfonium salts. The presence of the intermediate sulfonium salt was confirmed by observation of the low-temperature (1)H NMR spectra.     

Cyclization of 1-bromo-2,7- and 1-bromo-2,8-enynes mediated by indium

[reaction: see text] The cyclization of 1-bromo-2,7- and 1-bromo-2,8-enynes mediated by indium in DMF produced five- and six-membered cyclic compounds. Although KI was a necessary additive in the cyclization of terminal 1-bromo-2,7-enynes to give the desired products at 25 degrees C, reactions of terminal 1-bromo-2,8-enynes and internal 1-bromo-2,7-enynes with indium proceeded at 100 degrees C in DMF without KI. After cyclizations, subsequent cross-coupling reaction and iodolysis increase the usefulness of this reaction.     

W(CO)5(L)-catalyzed endo-selective cyclization of allenyl silyl enol ethers: an efficient method for the cyclopentene annulation onto alpha,beta-unsaturated ketones

[reaction: see text] Indium-mediated allenylation of alpha,beta-unsaturated ketones in the presence of tert-butyldimethylsilyl triflate and dimethyl sulfide gives 6-siloxy-1,2,5-trienes, which undergo W(CO)(5)(L)-catalyzed 5-endo cyclization to give the corresponding cyclopentene derivatives in good yield. Furthermore, this novel W(CO)(5)(L)-catalyzed cyclization of allenyl silyl enol ethers proceeds in a 6-endo manner when 5-siloxy-1,2,5-trienes are employed as a substrate. In these reactions, effective electrophilic activation of allenyl compounds for attack by silyl enol ethers is achieved using a catalytic amount of W(CO)(6).