Microstrain in hydroxyapatite carbon nanotube composites

Synchrotron radiation diffraction data were collected from hydroxyapatite–carbon nanotube bioceramic composites to determine the crystallite size and to measure changes in non‐uniform strain. Estimates of crystallite size and strain were determined by line‐profile fitting of discrete peaks and these were compared with a Rietveld whole‐pattern analysis. Overall the two analysis methods produced very similar numbers. In the commercial hydroxyapatite material, one reflection in particular, (0 2 3), has higher crystallite size and lower strain values in comparison with laboratory‐synthesized material. This could indicate preferential crystal growth in the [0 2 3] direction in the commercial material. From the measured strains in the pure material and the composite, there was a degree of bonding between the matrix and strengthening fibres. However, increasing the amount of carbon nanotubes in the composite has increased the strain in the material, which is undesirable for biomedical implant applications.     

Polyether antibiotic CP44,161

The crystal structure of antibiotic CP44,161, 6-(7-{2-ethyl-2-[5-(1-hydroxy­methyl)-5-methyl-2,3,4,5-tetra­hydro-2-furyl]-4,10,-­12-tri­methyl-1,6,8-trioxadi­spiro­[4.1.5.3]­pentadec-13-en-9-yl}-4-hydroxy-3,5-di­methyl-6-oxononyl)-2-hydroxy-3-methyl­benzoic acid monohydrate, C₄₃H₆₆O₁₀·H₂O, has been determined by X-ray crystallography. The mol­ecule adopts a cyclic conformation, with a centrally located water mol­ecule contributing to the stability of the conformation through hydrogen-bonding interactions.     

A general dual-bolus approach for quantitative DCE-MRI

Purpose

To present a dual-bolus technique for quantitative dynamic contrast-enhanced MRI (DCE-MRI) and show that it can give an arterial input function (AIF) measurement equivalent to that from a single-bolus protocol.

Methods

Five rabbits were imaged using a dual-bolus technique applicable for high-resolution DCE-MRI, incorporating a time resolved imaging of contrast kinetics (TRICKS) sequence for rapid temporal sampling. AIFs were measured from both the low-dose prebolus and the high-dose main bolus in the abdominal aorta. In one animal, TRICKS and fast spoiled gradient echo (FSPGR) acquisitions were compared.

Results

The scaled prebolus AIF was shown to match the main bolus AIF, with 95% confidence intervals overlapping for fits of gamma-variate functions to the first pass and linear fits to the washout phase, with the exception of one case. The AIFs measured using TRICKS and FSPGR were shown to be equivalent in one animal.

Conclusion

The proposed technique can capture even the rapid circulation kinetics in the rabbit aorta, and the scaled prebolus AIF is equivalent to the AIF from a high-dose injection. This allows separate measurements of the AIF and tissue uptake curves, meaning that each curve can then be acquired using a protocol tailored to its specific requirements.     

Connections Between Single-Level and Bilevel Multiobjective Optimization

The relationship between bilevel optimization and multiobjective optimization has been studied by several authors, and there have been repeated attempts to establish a link between the two. We unify the results from the literature and generalize them for bilevel multiobjective optimization. We formulate sufficient conditions for an arbitrary binary relation to guarantee equality between the efficient set produced by the relation and the set of optimal solutions to a bilevel problem. In addition, we present specially structured bilevel multiobjective optimization problems motivated by real-life applications and an accompanying binary relation permitting their reduction to single-level multiobjective optimization problems.     

Preservice Teachers' Use of Multiple Representations In Solving Arithmetic Mean Problems

The development of preservice teachers' views of various mathematical concepts involves building a repertoire of flexible representations of the concepts they teach. In this study, science and mathematics preservice teachers (n = 19) were asked to solve graphical and numerical problems involving the arithmetic mean and to provide two different solutions for each problem. Background information about the preservice teachers was obtained, including subject area specialty, type of statistics courses previously taken, type of science laboratory courses previously taken, and prior experience with real data outside the classroom. In solving the problems, some participants presented two different methods: algorithmic computation and balancing deviations about the mean. A significant difference was found between science and mathematics preservice teachers in the use of balancing deviations to solve the problems but not in the use of the computational algorithm.     

A double alkylation—ring closing metathesis approach to spiroimines

As part of a programme directed towards the synthesis of the marine toxins, the spirolides and gymnodimine, a convenient synthesis of the key bicyclic spiroimine ring systems has been developed. The method involves double alkylation of a simple lactam, Grubbs ring closing metathesis of the resultant dialkylated lactam then reduction of the lactam to an imine.