A Comparison of Splittings and Integral Equation Solvers for a Nonseparable Elliptic Equation

Iterative numerical schemes for solving the electrostatic partial differential equation with variable conductivity, using fast and high-order accurate direct methods for preconditioning, are compared. Two integral method schemes of this type, based on previously suggested splittings of the equation, are proposed, analyzed, and implemented. The schemes are tested for large problems on a square. Particular emphasis is paid to convergence as a function of geometric complexity in the conductivity. Differences in performance of the schemes are predicted and observed in a striking manner. AMS subject classification (2000) 31A10, 35C15, 65R20.Received May 2004. Accepted September 2004. Communicated by Anders Szepessy.Johan Helsing: This work was supported by the Swedish Science Research Council under contract 621-2001-2799.     

Hydrogenolysis of [PhBP3]Fe[triple bond]N-p-tolyl: probing the reactivity of an iron imide with H2

This paper describes the reductive hydrogenolysis of a low-spin (S = 1/2) iron(III) imide. Pseudotetrahedral [PhBP3]FeIIIN-p-tolyl is reduced by hydrogen at ambient temperature and pressure in benzene solution. The reduction appears to proceed in a stepwise fashion. An intermediate S = 2 iron(II) anilide, [PhBP3]Fe(N(H)-p-tolyl), is observed and has been independently generated and structurally characterized. Prolonged hydrogenolysis in benzene results in the complete hydrogenolysis of the Fe-N linkage to release H2N-p-tolyl. The major iron-containing product formed from this step is the diamagnetic cyclohexadienyl complex, [PhBP3]Fe(eta5-cyclohexadienyl), which has also been independently prepared and structurally characterized. Evidence is presented to suggest that the final [PhBP3]Fe(eta5-cyclohexadienyl) product is formed via benzene insertion into a reactive [PhBP3]FeII-H intermediate.     

Optical tweezers applied to a microfluidic system

We will demonstrate how optical tweezers can be combined with a microfluidic system to create a versatile microlaboratory. Cells are moved between reservoirs filled with different media by means of optical tweezers. We show that the cells, on a timescale of a few seconds, can be moved from one reservoir to another without the media being dragged along with them. The system is demonstrated with an experiment where we expose E. coli bacteria to different fluorescent markers. We will also discuss how the system can be used as an advanced cell sorter. It can favorably be used to sort out a small fraction of cells from a large population, in particular when advanced microscopic techniques are required to distinguish various cells. Patterns of channels and reservoirs were generated in a computer and transferred to a mask using either a sophisticated electron beam technique or a standard laser printer. Lithographic methods were applied to create microchannels in rubber silicon (PDMS). Media were transported in the channels using electroosmotic flow. The optical system consisted of a combined confocal and epi-fluorescence microscope, dual optical tweezers and a laser scalpel.     

Multiwavelength pulse generator using time-lens compression

We demonstrate a novel method of generating a multiwavelength pulse train by use of time-lens compression. In addition to pulse compression, this time lens simultaneously displaces the pulses according to their center wavelengths, resulting in a temporally evenly spaced multiwavelength pulse train. We further demonstrate a new aberration-correction technique based on the temporal analog of a spatial correction lens to improve the quality of the compressed pulses. Through the use of cw distributed-feedback lasers and electro-optic phase modulators, the all-fiber system allows complete tunability of temporal spacing, spectral profile, and repetition rate.     

Relations between 77Se NMR chemical shifts of (phenylseleno)-benzenes and their molecular structures derived from nine X-ray crystal structures

An extensive library of 77Se chemical shifts have been generated from the NMR measurements on substituted (phenylseleno)benzenes, including 33 new compounds. The variation in chemical shifts cover 265 ppm ranging from 446 to 181 ppm. Crystal structures have been determined for nine selected representatives of the substituted (phenylseleno)-benzenes. The analysis of the crystal structures supported that through-space interactions between selenium and the ortho-substituent observed in the crystal structures also are likely to be present in solution. The variation in the 77Se NMR chemical shifts can be rationalised from the intramolecular interactions with the substituent in the ortho-position. Furthermore it appears that these ortho-effects are roughly additive, and that it is the actual interactions and not the resulting conformational constraints that are responsible for the variations in the 77Se NMR chemical shifts.     

Dinitrogen chemistry from trigonally coordinated iron and cobalt platforms

This report establishes that trigonally coordinated "[PhBPiPr3]M" platforms (M = Fe, Co) will support both pi-acidic (N2) and pi-basic (NR) ligands at a fourth binding site. The N2 complexes of iron that are described are the first thoroughly characterized examples to exhibit a 4-coordinate geometry. Methylation of monomeric {Fe0(N2)-} and {Co0(N2)-} species successfully derivatizes the beta-N atom of the coordinated N2 ligand and affords the diazenido products {FeII(N2Me)} and {CoII(N2Me)}, respectively. One-electron oxidation of the mononuclear M0(N2)- species produces dinuclear and synthetically versatile MI(N2)MI complexes. These latter species provide clean access to the chemistry of the "[PhBPiPr3]MI" subunit. For example, addition of RN3 to MI(N2)MI results in oxidative nitrene transfer to generate [PhBPiPr3]MNR with concomitant N2 release.     

Dissociative cycloelimination,a new selenium based pericyclic reaction

The stereospecific oxidation of hydrazine into cis-diimide and the catalytic disproportionation of hydrogen peroxide effected by selenoxides are suggested to involve a dissociative cycloelimination from an intermediary selenurane.     

A generalization of a theorem on biseparating maps

In J. Math. Anal. Appl. 12 (1995) 258–265, Araujo et al. proved that for any linear biseparating map  from C(X) onto C(Y), where X and Y are completely regular, there exist ω in C(Y) and an homeomorphism h from the realcompactification vX of X onto vY, such that

The compact version of this result was proved before by Jarosz in Bull. Canad. Math. Soc. 33 (1990) 139–144. In Contemp. Math., Vol. 253, 2000, pp. 125–144, Henriksen and Smith asked to what extent the result above can be generalized to a larger class of algebras. In the present paper, we give an answer to that question as follows. Let A and B be uniformly closed Φ-algebras. We first prove that every order bounded linear biseparating map from A onto B is automatically a weighted isomorphism, that is, there exist ω in B and a lattice and algebra isomorphism ψ between A and B such that

(a)=ωψ(a) for all aA.

We then assume that every universally σ-complete projection band in A is essentially one-dimensional. Under this extra condition and according to a result from Mem. Amer. Math. Soc. 143 (2000) 679 by Abramovich and Kitover, any linear biseparating map from A onto B is automatically order bounded and, by the above, a weighted isomorphism. It turns out that, indeed, the latter result is a generalization of the aforementioned theorem by Araujo et al. since we also prove that every universally σ-complete projection band in the uniformly closed Φ-algebra C(X) is essentially one-dimensional.