Reductive heterocoupling mediated by Cp*2U(2,2'-bpy)

Trivalent Cp*(2)U(2,2'-bpy) (2) (Cp* = C(5)Me(5), 2,2'-bpy = 2,2'-bipyridine), which has a monoanionic bipyridine, was treated with p-tolualdehyde (a), furfuraldehyde (b), acetone (c), and benzophenone (d). Reduction of the C[double bond, length as m-dash]O bond followed by radical coupling with bipyridine forms the U(iv) derivatives [Cp*(2)U(2,2'-bpy)(OCRR')] (3a-d).     

Cobalt complexes with tripodal ligands: implications for the design of drug chaperones

Extensive research is currently being conducted into metal complexes that can selectively deliver cytotoxins to hypoxic regions in tumours. The development of pharmacologically suitable agents requires an understanding of appropriate ligand-metal systems for chaperoning cytotoxins. In this study, cobalt complexes with tripodal tren (tris-(2-aminoethyl)amine) and tpa (tris-(2-pyridylmethyl)amine) ligands were prepared with ancillary hydroxamic acid, β-diketone and catechol ligands and several parameters, including: pK(a), reduction potential and cytotoxicity were investigated. Fluorescence studies demonstrated that only tpa complexes with β-diketones showed any reduction by ascorbate in situ and similarly, cellular cytotoxicity results demonstrated that ligation to cobalt masked the cytotoxicity of the ancillary groups in all complexes except the tpa diketone derivative [Co(naac)tpa](ClO(4))(2) (naac = 1-methyl-3-(2-naphthyl)propane-1,3-dione). Additionally, it was shown that the hydroxamic acid complexes could be isolated in both the hydroxamate and hydroximate form and the pK(a) values (5.3-8.5) reveal that the reversible protonation/deprotonation of the complexes occurs at physiologically relevant pHs. These results have clear implications for the future design of prodrugs using cobalt moieties as chaperones, providing a basis for the design of cobalt complexes that are both more readily reduced and more readily taken up by cells in hypoxic and acidic environments.     

Direct submolecular scale imaging of mesoscale molecular order in supported dipalmitoylphosphatidylcholine bilayers

Supported dipalmitoylphosphatidylcholine (DPPC) bilayers are widely used membrane systems in biophysical and biochemical studies. Previously, short-range positional and orientational order of lipid headgroups of supported DPPC bilayers was observed at room temperature using low deflection noise frequency modulation atomic force microscopy (FM-AFM). While this ordering was supported by X-ray diffraction studies, it conflicted with diffusion coefficient measurements of gel-phase bilayers determined from fluorescence photobleaching experiments. In this work, we have directly imaged mica-supported DPPC bilayers with submolecular resolution over scan ranges up to 146 nm using low deflection noise FM-AFM. Both orientational and positional molecular ordering were observed in the mesoscale, indicative of crystalline order. We discuss these results in relation to previous biophysical studies and propose that the mica support induces mesoscopic crystalline order of the DPPC bilayer at room temperature. This study also demonstrates the recent advance in the scan range of submolecular scale AFM imaging.     

Synthesis, characterization and crystal structures of the boratranes: 2,10,11-trioxa-6-aza-1-boratricyclo[4.4.4.0] tetradecane (tri-n-propanolamine borate), and 3-(4-methoxy)phenoxymethyl-7,10-dimethyl-2,8,9-trioxa-5-aza-1-boratricyclo[3.3.3.0]-undecane

The crystal structures of boratranes 2,10,11-trioxa-6-aza-1-boratricyclo[4.4.4.0^1,6] tetradecane (tri-n-propanolamine borate) 1 as the tri-hydrate, and 3-(4-methoxy)phenoxymethyl-7,10-dimethyl-2,8,9-trioxa-5-aza-1-boratricyclo[3.3.3.0^1,5]-undecane 2 as the partial (0.2) hydrate have been determined. Compound 1 has a near-tetrahedral coordination of both the N (108.8°) and B atoms (111.2°), N → B bond length 1.656 Å and all-chair tricyclic conformation, whereas 2 has a slightly-longer N → B dative bond length (1.667 Å) and the O-B-O angle, 114.8°, was slightly distorted from near-tetrahedral to adopt a flatter conformation. Theoretical calculations on 1 and 2 showed that the B-N distance in each shortened markedly between isolated gas phase molecules and ‘solvated’ models. Neither structural results, nor calculated parameters, were able to explain the propensity towards slow hydrolysis of boratranes with five-membered rings compared with the relative hydrolytic stability of boratranes with six-membered rings.     

Shear banding and interfacial instability in planar Poiseuille flow

Motivated by the need for a theoretical study in a planar geometry that can easily be implemented experimentally, we study the pressure driven Poiseuille flow of a shear banding fluid. After discussing the “basic states” predicted by a one-dimensional calculation that assumes a flat interface between the bands, we proceed to demonstrate such an interface to be unstable with respect to the growth of undulations along it. We give results for the growth rate and wavevector of the most unstable mode that grows initially, as well as for the ultimate flow patterns to which the instability leads. We discuss the relevance of our predictions to the present state of the experimental literature concerning interfacial instabilities of shear banded flows, in both conventional rheometers and microfluidic channels.     

Latent class models for time series analysis

Latent class analysis of time series designed to classify and compare sets of series is discussed. For a particular time series in latent class the data are independently normally distributed with a vector of means, and common variance , that is, . The function of time, , can be represented by a linear combination of low-order splines (piecewise polynomials). The probability density function for the data of a time series is posited to be a finite mixture of spherical multivariate normal densities. The maximum-likelihood function is optimized by means of an EM algorithm. The stability of the estimates is investigated using a bootstrap procedure. Examples of real and artificial data are presented. Copyright © 1999 John Wiley & Sons, Ltd.     

Optimal control of boundary habitat hostility for interacting species

We consider boundary control for a parabolic system describing the evolution of two interacting species in a bounded habitat. The control models the hostility of the boundary environment to the maintenance of the species. The objective functional represents the balance between the ecological benefit (modelled by the size of the two populations) and the economic cost of maintaining an ecologically favorable boundary environment (modelled by the boundary friendliness). The unique optimal control is characterized in terms of the solution of the optimality system, which consists of the state system coupled with an adjoint system. Copyright © 1999 John Wiley & Sons, Ltd.     

Assessing Students' Mathematical Communication

Assessment of students' mathematical communication through the use of open-ended tasks and scoring procedures is addressed, as is the use of open-ended tasks to assess students' mathematical communication by providing students opportunities to display their mathematical thinking and reasoning. Also, two scoring procedures (quantitative holistic scoring procedure and qualitative analytic scoring procedure) are described for examining students' communication skills.     

Heterodimerization studies of calix[4]arene derivatives in polar solvents

[reaction: see text] Several calix[4]arene derivatives propylated on the lower rim and substituted on the upper rim with amino or carboxyl groups have been synthesized. Examples include calixarenes substituted with alanino (C- and N-linked), amino, carboxy, carboxyphenyl, and amidino groups. The self-assembly of these derivatized calixarenes into heterodimers has been studied by NMR in DMSO-d(6) or CD(3)OD with 5% aqueous phosphate buffer.     

A bootstrap procedure for mixture models: applied to multidimensional scaling latent class models

A bootstrap procedure useful in latent class, or more general mixture models has been developed to determine the sufficient number of latent classes or components required to account for systematic group differences in the data. The procedure is illustrated in the context of a multidimensional scaling latent class model, CLASCAL. Also presented is a bootstrap technique for determining standard errors for estimates of the stimulus co‐ordinates, parameters of the multidimensional scaling model. Real and artificial data are presented. The bootstrap procedure for selecting a sufficient number of classes seems to correctly select the correct number of latent classes at both low and high error levels. At higher error levels it outperforms Hope's (J. Roy. Statist. Soc. Ser B 1968; 30 : 582) procedure. The bootstrap procedures to estimate parameter stability appear to correctly re‐produce Monte Carlo results. Copyright © 2002 John Wiley & Sons, Ltd.