On a new class of dynamic Hardy-type inequalities and some related generalizations

Aequationes mathematicae - In this paper, we establish a new class of dynamic inequalities of Hardy’s type which generalize and improve some recent results given in the literature. More...     

Teaching the Chemistry of Platinum

Following colonisation of South America by the Spanish, many new naturally occurring substances were sent to Europe. One of these was the silvery, unreactive metal, platinum, discovered in New Grenada in the mid-eighteenth century. It was often found in granular form, associated with gold, and the challenge to chemists was to refine it, produce it as wire or sheet, and determine its chemical properties. This interested the professor of chemistry at the University of Edinburgh, Joseph Black, who was able to obtain samples from London-based Spanish contacts, particularly Ignacio Luzuriaga. This paper examines how Black transmitted his knowledge of the metal to large numbers of students attending his annual course.     

Diffeomorphism finiteness for manifolds with ricci curvature andL n/2-norm of curvature bounded

Partially supported by NSF Grants.     

Mod 2 cohomology of combinatorial Grassmannians

Matroid bundles, introduced by MacPherson, are combinatorial analogues of real vector bundles. This paper sets up the foundations of matroid bundles. It defines a natural transformation from isomorphism classes of real vector bundles to isomorphism classes of matroid bundles. It then gives a transformation from matroid bundles to spherical quasifibrations, by showing that the geometric realization of a matroid bundle is a spherical quasifibration. The poset of oriented matroids of a fixed rank classifies matroid bundles, and the above transformations give a splitting from topology to combinatorics back to topology. A consequence is that the mod 2 cohomology of the poset of rank k oriented matroids (this poset classifies matroid bundles) contains the free polynomial ring on the first k Stiefel-Whitney classes.     

Assessment of two‐equation turbulence modelling for high Reynolds number hydrofoil flows

This paper presents an evaluation of the capability of turbulence models available in the commercial CFD code FLUENT 6.0 for their application to hydrofoil turbulent boundary layer separation flow at high Reynolds numbers. Four widely applied two‐equation RANS turbulence models were assessed through comparison with experimental data at Reynolds numbers of 8.284×106 and 1.657×107. They were the standard k–εmodel, the realizable k–εmodel, the standard k–ωmodel and the shear‐stress‐transport (SST) k–ωmodel. It has found that the realizable k–εturbulence model used with enhanced wall functions and near‐wall modelling techniques, consistently provides superior performance in predicting the flow characteristics around the hydrofoil. Copyright © 2004 John Wiley & Sons, Ltd.     

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     

How to Build Robust Shared Control Systems

Previous researchers have designed shared control schemes with a view to minimising the likelihood that participants will conspire to perform an unauthorised act. But, human nature being what it is, systems inevitably fail; so shared control schemes should also be designed so that the police can identify conspirators after the fact. This requirement leads us to search for schemes with sparse access structures. We show how this can be done using ideas from coding theory. In particular, secret sharing schemes based on geometric codes whose dual [n,k,d] codes have d and n as their only nonzero weights are suitable. We determine their access structures and analyse their properties. We have found almost all of them, and established some relations among codes, designs and secret-sharing schemes.     

Evolution in complex systems

What features characterize complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena. Here we argue that slow, directed dynamics, during which the system's properties change significantly, is fundamental. The underlying dynamics is related to a slow, decelerating but spasmodic release of an intrinsic strain or tension. Time series of a number of appropriate observables can be analyzed to confirm this effect. The strain arises from local frustration. As the strain is released through “quakes,” some system variable undergoes record statistics with accompanying log‐Poisson statistics for the quake event times. We demonstrate these phenomena via two very different systems: a model of magnetic relaxation in type II superconductors and the Tangled Nature model of evolutionary ecology and show how quantitative indications of aging can be found. © 2004 Wiley Periodicals, Inc. Complexity 10: 49–56, 2004