Parallel variable distribution for total least squares

A novel parallel method for determining an approximate total least squares (TLS) solution is introduced. Based on domain decomposition, the global TLS problem is partitioned into several dependent TLS subproblems. A convergent algorithm using the parallel variable distribution technique (SIAM J. Optim. 1994; 4 :815–832) is presented. Numerical results support the development and analysis of the algorithms. Copyright © 2005 John Wiley & Sons, Ltd.     

Pentavalent organoantimonial derivatives: two simple and efficient synthetic methods for meglumine antimonate

Two simple and efficient procedures for the preparation of pentavalent antimony derivatives are described, using either antimony pentachloride (SbCl₅) or potassium hexahydroxoantimonate (KSb(OH)₆) as sources of antimony(V). These two new methods are evaluated for the synthesis of an important anti‐leishmanial drug: meglumine antimonate. Using elemental (carbon, hydrogen, nitrogen) and thermal analysis, atomic absorption (antimony), proton NMR spectroscopy and high‐resolution positive‐ion electrospray ionization mass spectrometry (ESI(+)‐MS), products for the reaction with N‐methyl‐D ‐glucamine (NMG) using both the SbCl₅ and KSb(OH)₆ methods were characterized and found to be similar to a commercial sample of the drug. The only notable difference was observed for the ESI‐MS spectrum of the KSb(OH)₆ product; it displays the same pattern of ESI‐generated ions as those of both the SbCl₅ product and the commercial drug, but with significantly different abundance ratios. NMR data indicate that the NMG molecules coordinate antimony in two different fashions, which suggests either the coexistence of two different complexes or the existence of a single major complex in which two NMG molecules are coordinated with antimony in an asymmetrical geometry. Copyright © 2003 John Wiley & Sons, Ltd.     

Optical absorption spectra of PtO and Pt2 in rare-gas matrices

The diatomic molecules, PtO and Pt₂, as well as atomic Pt, were isolated in Ar and Kr matrices at a temperature of ca.12K. The absorption spectra of these species were photographed in the wavelength region 2500–9000 Å. Probably three systems of PtO were observed but none of them seemed to correspond to the earlier analyzed intense systems of gaseous PtO having a ¹Σ state, designated X¹Σ, as their common lower state. The assumption that this state should be the ground state of PtO is thus rather uncertain. A single progression of sharp bands in the near-infrared spectrum was ascribed to the dimer Pt₂. In addition, some absorption lines due to Pt atoms were found in the ultraviolet region.     

Evidence from fluorine and proton NMR spectra for restricted rotation about the P?O bond in some steroidal phosphorofluoridates

The salient features of the ¹⁹F and ¹H NMR spectra of seven steroidal phosphorofluoridates are presented and evidence for restricted rotation, obtained from high temperature studies and deuteration experiments, is discussed.     

Adult learners' criteria for explanations

This article explores adult learners’ preferences for explanations of mathematical statements in terms of kinds of reasoning and formats of presentation. Based on data from questionnaires and interviews it is concluded thatfamiliarity andclarity influenced students’ preferences more than the format or reasoning used. A contrast between the factors influencing students’ choices and those of instructors is also reported. Implications for teaching and research are drawn from the study.     

N-(Alkylsulfamoyl)aldimines: easily deprotected precursors for diarylmethylamine synthesis

The sequential reaction of chlorosulfonyl isocyanate with t-BuOH, t-BuNH₂ and TFA allows formation of H₂NSO₂NHBu^t. Condensation of the latter with Ar¹CHO in the presence of Ti(OEt)₄ provides the activated imines Ar¹CHNSO₂NHBu^t (59–89%). Commercially available boronic acids add to these imines with good stereoselectivity (76–98% ee) using readily available diene ligands. Simple deprotection with 5% w/w water in pyridine affords free Ar¹CHNH₂Ar².     

Modelling for the robust design of layered resonators for ultrasonic particle manipulation

Several approaches have been described for the manipulation of particles within an ultrasonic field. Of those based on standing waves, devices in which the critical dimension of the resonant chamber is less than a wavelength are particularly well suited to microfluidic, or "lab on a chip" applications. These might include pre-processing or fractionation of samples prior to analysis, formation of monolayers for cell interaction studies, or the enhancement of biosensor detection capability. The small size of microfluidic resonators typically places tight tolerances on the positioning of the acoustic node, and such systems are required to have high transduction efficiencies, for reasons of power availability and temperature stability. Further, the expense of many microfabrication methods precludes an iterative experimental approach to their development. Hence, the ability to design sub-wavelength resonators that are efficient, robust and have the appropriate acoustic energy distribution is extremely important. This paper discusses one-dimensional modelling used in the design of ultrasonic resonators for particle manipulation and gives example of their uses to predict and explain resonator behaviour. Particular difficulties in designing quarter wave systems are highlighted, and modelling is used to explain observed trends and predict performance of such resonators, including their performance with different coupling layer materials.     

Observation of internal electron transfer in bulky allyl ytterbium complexes with substituted terpyridine ligands

A series of new bulky allyl terpyridyl-ytterbium complexes have been synthesized to determine the effect of allyl ligands on the internal charge-transfer process that exists in these materials. Compared to the pentamethylcyclopentadienyl-ytterbocene compound Cp*2Yb(tpyCN) (nu(C(triple bond)N) = 2172 cm(-1)), the symmetrically substituted allyl complex [1,3-(SiMe3)2C3H3]2Yb(tpyCN) possesses a markedly lowered C(triple bond)N frequency of 2130 cm(-1). Furthermore, the electronic nature of these bulky allyl complexes can be tuned, as demonstrated by the C(triple bond)N frequency of the asymmetric derivatives [1-(SiMe3)C3H4]2Yb(tpyCN) and [1-(SiPh3)-3-(SiMe3)C3H3]2Yb(tpyCN) (2171 and 2164 cm(-1), respectively). The differences in these frequencies can be attributed to differences in the ligands' steric and electronic character. Single-crystal X-ray characterization of [1,3-(SiMe3)2C3H3]2Yb(tpy) reveals that the allyl moiety possesses shorter Yb-C and Yb-N bond distances than the Cp* analogue. The magnetic susceptibility data for [1,3-(SiMe3)2C3H3]2Yb(tpy) departs dramatically from the Curie law, with a room-temperature magnetic moment of 2.95 mu(B).     

Multisplitting for regularized least squares with Krylov subspace recycling

The method of multisplitting (MS), implemented as a restricted additive Schwarz type algorithm, is extended for the solution of regularized least squares problems. The presented non‐stationary version of the algorithm uses dynamic updating of the weights applied to the subdomains in reconstituting the global solution. Standard convergence results follow from extensive prior literature on linear MS schemes. Additional convergence results on nonstationary iterations yield convergence conditions for the presented nonstationary MS algorithm. The global iteration uses repeated solves of local problems with changing right hand sides but a fixed system matrix. These problems are solved inexactly using a conjugate gradient least squares algorithm which provides a seed Krylov subspace. Recycling of the seed system Krylov subspace to obtain the solutions of subsequent nearby systems of equations improves the overall efficiency of the MS algorithm, and is apparently novel in this context. The obtained projected solution is not always of sufficient accuracy to satisfy a reasonable inner convergence condition on the local solution. Improvements to accuracy may be achieved by reseeding the solution space either every few steps, or when the successive right hand sides are sufficiently close as measured by a provided tolerance. Restarting and augmenting the solution space are also discussed. Any time a new space is generated it is used for subsequent steps. Numerical simulations validate the use of the recycling algorithm. These numerical experiments use the standard reconstruction of the two dimensional Shepp–Logan phantom, as well as a two dimensional problem from seismic tomography. Copyright © 2011 John Wiley & Sons, Ltd.