Subcycling first- and second-order generalizations of the trapezoidal rule

Subcycling algorithms which employ multiple timesteps have been previously proposed for explicit direct integration of first- and second-order systems of equations arising in finite element analysis, as well as for integration using explicit/implicit partitions of a model. The author has recently extended this work to implicit/implicit multi-timestep partitions of both first- and second-order systems. In this paper, improved algorithms for multi-timestep implicit integration are introduced, that overcome some weaknesses of those proposed previously. In particular, in the second-order case, improved stability is obtained. Some of the energy conservation properties of the Newmark family of algorithms are shown to be preserved in the new multi-timestep extensions of the Newmark method. In the first-order case, the generalized trapezoidal rule is extended to multiple timesteps, in a simple way that permits an implicit/implicit partition. Explicit special cases of the present algorithms exist. These are compared to algorithms proposed previously. (C) 1998 John Wiley & Sons, Ltd.

First- and second-order stimulus length selectivity in New World monkey striate cortex

Motion is a powerful cue for figure-ground segregation, allowing the recognition of shapes even if the luminance and texture characteristics of the stimulus and background are matched. In order to investigate the neural processes underlying early stages of the cue-invariant processing of form, we compared the responses of neurons in the striate cortex (V1) of anaesthetized marmosets to two types of moving stimuli: bars defined by differences in luminance, and bars defined solely by the coherent motion of random patterns that matched the texture and temporal modulation of the background. A population of form-cue-invariant (FCI) neurons was identified, which demonstrated similar tuning to the length of contours defined by first- and second-order cues. FCI neurons were relatively common in the supragranular layers (where they corresponded to 28% of the recorded units), but were absent from layer 4. Most had complex receptive fields, which were significantly larger than those of other V1 neurons. The majority of FCI neurons demonstrated end-inhibition in response to long first- and second-order bars, and were strongly direction selective, Thus, even at the level of V1 there are cells whose variations in response level appear to be determined by the shape and motion of the entire second-order object, rather than by its parts (i.e. the individual textural components). These results are compatible with the existence of an output channel from V1 to the ventral stream of extrastriate areas, which already encodes the basic building blocks of the image in an invariant manner.

Folding, calcium binding, and structural characterization of a concatemer of the first and second ligand-binding modules of the low-density lipoprotein receptor

The ligand-binding domain of the low-density lipoprotein (LDL) receptor is comprised of seven tandemly repeated ligand-binding modules, each being approximately 40 amino acids long and containing six conserved cysteine residues. We have expressed and characterized a concatemer of the first two modules (LB1 and LB2) of the human LDL receptor. Oxidative folding of the recombinant concatemer (rLB(1-2)), in the presence of calcium ions, gave a single dominant isomer with six disulfide bonds. Peptic cleavage of the short Linker region that connects the last cysteine residue of LB1 and the first cysteine residue of LB2 yielded two discrete fragments, thus excluding the presence of intermodule disulfide bonds. The N-terminal module, LB1, reacted with a conformation-specific monoclonal antibody (IgG-C7) made to LB1 in the native LDL receptor. From this, we concluded that the first module was correctly folded, with the same set of disulfide bonds as LB1 of the LDL receptor. The disulfide bond connections of LB2 were identified from mass spectral analysis of fragments formed by digestion of the C-terminal peptic fragment with elastase. These data showed that the disulfide bonds of LB2 connected Cys(I) and Cys(III), Cys(II) and Cys(V), and Cys(IV) and Cys(VI). This pattern is identical to that found for recombinant LB1 and LB2. The concatemer has two high-affinity calcium-binding sites, one per module. An analysis of the secondary chemical shifts of C alpha protons shows that the conformations of LB1 and LB2 in the concatemer are very similar to those of the individual modules, with no evidence for strong interactions between the two modules.

A comparison of the responses of first and second year veterinary science students to group project work

A change in curriculum permitted a direct and simultaneous comparison between first and second year responses to group project work while assuming similar prior experience with this method of learning. Responses were obtained by a survey form and by meetings with individual groups. Overall, there were no differences between first and second year responses, although analyses of gender responses suggested trends whereby males indicated they had developed greater creativity and felt they had contributed more to the group. The majority of students responded that group project work was a positive experience and a useful learning experience.

Quantum interference in optical fields and atomic radiation

We discuss the connection between quantum interference effects in optical beams and radiation fields emitted from atomic systems. We illustrate this connection by a study of the first- and second-order correlation functions of optical fields and atomic dipole moments. We explore the role of correlations between the emitting systems and present examples of practical methods to implement two systems with non-orthogonal dipole moments. We also derive general conditions for quantum interference in a two-atom system and for a control of spontaneous emission. The relation between population trapping and dark states is also discussed. Moreover, we present quantum dressed-atom models of cancellation of spontaneous emission, amplification on dark transitions, fluorescence quenching and coherent population trapping.

Boundary value problems for systems of difference equations associated with systems of second-order ordinary differential equations

We study difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order ordinary differential equations. We formulate conditions which guarantee a priori bounds on first differences of solutions to the discretized problem. We establish existence results for solutions to the discretized boundary value problems subject to nonlinear boundary conditions. We apply our results to show that solutions to the discrete problem converge to solutions of the continuous problem in an aggregate sense. (C) 2002 Elsevier Science Ltd. All rights reserved.

Synthesis, antiprotozoal and antibacterial activity of nitro- and halogeno-substituted benzimidazole derivatives

Two series of benzimidazole derivatives were sythesised. The first one was based on 5,6-dinitrobenzimidazole, the second one comprises 2-thioalkyl- and thioaryl-substituted modified benzimidazoles. Antibacterial and antiprotozoal. activity of the newly obtained compounds was studied. Some thioalkyl derivatives showed remarkable activity against nosocomial strains of Stenotrophomonas malthophilia, and an activity comparable to that of metronidazole against Gram-positive and Gram-negative bacteria. Of the tested compounds, 5,6-dichloro-2-(4-nitrobenzylthio)-benzimidazole showed the most distinct antiprotozoal activity.

Existence of Multiple Solutions for Second Order Boundary Value Problems

We give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y" + f(x, y, y') = 0, x epsilon [0, 1], y(0) = 0 = y(1). In the special case f(x, y, y') = f(y) greater than or equal to 0 we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and of Lakshmikantham et al.

Three-point boundary value problems for second-order, ordinary, differential equations

We establish existence results for solutions to three-point boundary value problems for nonlinear, second-order, ordinary differential equations with nonlinear boundary conditions. (C) 2001 Elsevier Science Ltd. All rights reserved.

EphB2 and two of its ligands have dynamic protein expression patterns in the developing olfactory system

Primary olfactory neurons are located in the olfactory neuroepithelium lining the nasal cavity. Their axons converge and form glomeruli with the dendrites of second-order neurons in the olfactory bulb. The molecular basis of primary olfactory axon guidance, targeting and subsequent arborisation is largely unknown. In this study we examined the spatio-temporal expression of the Eph receptor EphB2 and its ligands, ephrin-B1 and ephrin-B2, during development of the rat primary olfactory system. Unlike in other regions of the nervous system where receptor and ligand expression patterns are usually non-overlapping, EphB2, ephrin-B1 and ephrin-B2 were all expressed by primary and second-order olfactory neurons. In the embryonic animal we found that these three proteins had distinct and different expression patterns. EphB2 was first expressed at E18.5 by the perikarya of primary olfactory neurons. In contrast, ephrin-B1 was expressed from E13.5 and was localised to the axons of these cells up to E18.5 but was then restricted to the perikarya. Ephrin-B2, however, was expressed by olfactory ensheathing cells. EphB2, ephrin-B1 and ephrin-B2 were also expressed in the prenatal olfactory bulb and were restricted to the perikarya of mitral cells. In the post-natal olfactory bulb there was a shift in the localisation of both EphB2 and ephrin-B1 to the dendritic arborisations of mitral cells. The dynamic and tightly regulated spatio-temporal expression patterns of EphB2, ephrin-B1 and ephrin-B2 by specific olfactory cell populations suggest that these molecules have the potential to regulate important developmental events in the olfactory system. (C) 2001 Elsevier Science B.V. All rights reserved.

Adsorption kinetics for the removal of chromium(VI) from aqueous solution by adsorbents derived from used tyres and sawdust

The batch removal of hexavalent chromium (Cr(Vl)) from wastewater under different experimental conditions using economic adsorbents was investigated in this study. These adsorbents were produced from the pyrolysis and activation of the waste tyres (TAC) and from the pyrolysis of sawdust (SPC). The performance of these adsorbents against commercial activated carbon F400 (CAC) has also been carried out. The removal was favoured at low pH, with maximum removal at pH = 2 for all types of carbon. The effects of concentration, temperature and particle size have been reported. All sorbents were found to efficiently remove Cr(VI) from solution. The batch sorption kinetics have been tested for a first-order reversible reaction, a first-order and second-order reaction. The rate constants of adsorption for all these kinetic models have been calculated. The applicability of the Langmuir isotherm for the present system has been tested at different temperatures. The thermodynamic parameters (AGO, K,) obtained indicate the endothermic nature of Cr(Vl) adsorption on TAC, SPC and CAC. (C) 2001 Elsevier Science B.V. All rights reserved.