Smart Geodesic Tracing in GRworkbench

We have developed a new tool for numerical work in General Relativity: GRworkbench. We discuss how GRworkbench's implementation of a numerically-amenable analogue to Differential Geometry facilitates the development of robust and chart-independent numerical algorithms. We consider, as an example, geodesic tracing on two charts covering the exterior Schwarzschild space-time.     

Activity of microemulsion-based nanoparticles at the human bio-nano interface: concentration-dependent effects on thrombosis and hemolysis in whole blood

Background: Although microemulsion-based nanoparticles (MEs) may be useful for drug delivery or scavenging, these benefits must be balanced against potential nanotoxicological effects in biological tissue (bio-nano interface). We investigated the actions of assembled MEs and their individual components at the bio-nano interface of thrombosis and hemolysis in human blood. Methods: Oil-in-water MEs were synthesized using ethylbutyrate, sodium caprylate, and pluronic F-68 (ME4) or F-127 (ME6) in 0.9% NaCl_w/v. The effects of MEs or components on thrombosis were determined using thrombo-elastography, platelet contractile force, clot elastic modulus, and platelet counting. For hemolysis, ME or components were incubated with erythrocytes, centrifuged, and washed for measurement of free hemoglobin by spectroscopy. Results and conclusions: The mean particle diameters (polydispersity index) for ME6 and ME4 were 23.6 ± 2.5 nm (0.362) and 14.0 ± 1.0 nm (0.008), respectively. MEs (0, 0.03, 0.3, 3 mM) markedly reduced the thromboelastograph maximal amplitude in a concentration-dependent manner (49.0 ± 4.2, 39.0 ± 5.6, 15.0 ± 8.7, 3.8 ± 1.3 mm, respectively), an effect highly correlated (r2 = 0.94) with similar changes caused by pluronic surfactants (48.7 ± 10.9, 30.7 ± 15.8, 20.0 ± 11.3, 2.0 ± 0.5) alone. Neither oil nor sodium caprylate alone affected the thromboelastograph. The clot contractile force was reduced by ME (27.3 ± 11.1–6.7 ± 3.4 kdynes/cm², P = 0.02, n = 5) whereas the platelet population not affected (175 ± 28–182 ± 23 10⁶/ml, P = 0.12, n = 6). This data suggests that MEs reduced platelet activity due to associated pluronic surfactants, but caused minimal changes in protein function necessary for coagulation. Although pharmacological concentrations of sodium caprylate caused hemolysis (EC₅₀ = 213 mM), MEs and pluronic surfactants did not disrupt erythrocytes. Knowledge of nanoparticle activity and potential associated nanotoxicity at this bio-nano interface enables rational ME design for in vivo applications.     

On Levels in Arrangements of Curves, II: A Simple Inequality and Its Consequences

We give a surprisingly short proof that in any planar arrangement of n curves where each pair intersects at most a fixed number (s) of times, the k-level has subquadratic (O(n^2-1/2s) complexity. This answers one of the main open problems from the author’s previous paper [DCG 29, 375-393 (2003)], which provided a weaker upper bound for a restricted class of curves only (graphs of degree-s polynomials). When combined with existing tools (cutting curves, sampling, etc.), the new idea generates a slew of improved k-level results for most of the curve families studied earlier, including a near-O(n^3/2 bound for parabolas.     

Investigation into the absolute stereochemistry of the marine sponge alkaloid pyrinodemin A

The absolute configuration of the marine sponge alkaloid pyrinodemin A is established by organic synthesis.     

Novel dinitroxide mediating agent for stable free‐radical polymerization

A novel dinitroxide mediating agent that was suitable for stable free‐radical polymerization was synthesized and used in the block copolymerization of styrene and t‐butyl styrene. Quantitative yields of a novel dinitroxide based on 1,6‐hexamethylene diisocyanate and 4‐hydroxy‐2,2,6,6‐tetramethyl‐1‐piperidinyloxy were obtained. Various experimental parameters, including the nitroxide‐to‐initiator molar ratio, were examined, and it was determined that the polymerization was most controlled under conditions similar to those of conventional 2,2,6,6‐tetramethyl‐1‐piperidinyloxy‐mediated stable free‐radical polymerization. Moreover, the dinitroxide mediator proved to be a viable route for the facile two‐step synthesis of triblock copolymers of styrene and t‐butyl styrene. However, the dinitroxide mediation process resulted in a higher than expected level of nitroxide decomposition, which resulted in polymers possessing a terminal alkoxyamine and an adjacent hydroxylamine rather than a preferred internal bisalkoxyamine. This decomposition resulted in the formation of diblock copolymer species during the triblock copolymer synthesis. Gel permeation chromatography was used to monitor the chain‐end decomposition kinetics, and the determined observed rate constant (5.89 × 10^?5 s^?1) for decomposition agreed well with previous studies for other dinitroxide mediating agents. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1547–1556, 2004     

Nano-electrochemical detection of hydrogen or protons using palladium nanoparticles: distinguishing surface and bulk hydrogen.

The benefits of using nanoparticle-modified electrodes are exemplified through the electrochemical detection of protons and/or hydrogen. It is shown that a palladium-nanoparticle-modified boron-doped diamond allows voltammetric information relating to the relative roles played by the surface and the bulk metal to be obtained for the proton-hydrogen system at palladium surfaces which is not accessible using palladium macroelectrodes or microelectrodes.     

Latin Squares without Orthogonal Mates

In 1779 Euler proved that for every even n there exists a latin square of order n that has no orthogonal mate, and in 1944 Mann proved that for every n of the form 4k + 1, k ≥ 1, there exists a latin square of order n that has no orthogonal mate. Except for the two smallest cases, n = 3 and n = 7, it is not known whether a latin square of order n = 4k + 3 with no orthogonal mate exists or not. We complete the determination of all n for which there exists a mate-less latin square of order n by proving that, with the exception of n = 3, for all n = 4k + 3 there exists a latin square of order n with no orthogonal mate. We will also show how the methods used in this paper can be applied more generally by deriving several earlier non-orthogonality results.