Some results on quasipolyhedral convexity

The objective of this paper is to analyze under what well-known operations the class of quasipolyhedral convex functions, which can be regarded as an extension of that of polyhedral convex functions, is closed. The operations that will be considered are those that preserve polyhedral convexity, such that the image and the inverse image under linear transformations, right scalar multiplication (including the case where λ=0⁺) and pointwise addition.      

Optical absorption of lithium metal vapor at high temperatures

Experimental results are reported for a unique spectroscopic device called the Plasma Spectroscopy Cell. Optical absorption of lithium metal vapor was observed at high density and temperature. Absorption spectra are analyzed using theoretical calculations of absorption cross sections for lithium-helium interactions, and singlet and triplet state transitions of diatomic lithium in the visible spectral range. This is believed to be the most complex example yet calculated in which absolute bound-bound, bound-free, free-bound, and free-free contributions for all possible optically allowed transitions are all included, in quite respectable agreement with experiment.     

What is a design? How should we classify them?

Design theory crosses the boundary between mathematics and statistics, and includes a wide range of disparate types of design. In this paper we present a classification scheme which aims to include as many important types as possible, based on a balance among concept, representation and use.     

Synthesis of perfluorinated functionalized, branched ethers

We wish to report synthesis of perfluorinated functionalized, branched ethers from their hydrocarbon analogues by direct fluorination. Yields up to 90%, with high purities, have been obtained at ambient temperature and pressure. This technique will likely develop into a new general method for producing perfluorinated, hyperbranched and dendritic polymers.     

Embedding partial Steiner triple systems so that their automorphisms extend

It is shown that there is a function g on the natural numbers such that a partial Steiner triple system U on u points can be embedded in a Steiner triple system V on ν points, in such a way that all automorphisms of U can be extended to V, for every admissible ν satisfying ν > g(u). We find exponential upper and lower bounds for g. © 2005 Wiley Periodicals, Inc. J Combin Designs.     

On the structure of a random sum-free set

Summary There is a natural probability measure on the set of all sum-free sets of natural numbers. If we represent such a set by its characteristic functions, then the zero-one random variabless(i) are far from independent, and we cannot expect a law of large numbers to hold for them. In this paper I conjecture a decomposition of into countably many more tractible pieces (up to a null set). I prove that each piece has positive measure, and show that, within each piece, a random set almost surely has a density which is a fixed rational number depending only on the piece. For example, the first such piece is made up of sets consisting entirely of odd numbers; it has probability 0.218 ..., and its members almost surely have density 1/4.     

Polymerised bicontinuous microemulsions as stationary phases for capillary electrochromatography

Summary Polymerisation of bicontinuous microemulsions yields porous monolithic structures with well defined pore sizes that are potentially suitable for use as stationary phases for capillary electrochromatography (CEC). A variety of pore sizes can be achieved by altering the composition of the microemulsion, which typically consists of butyl methacrylate (BMA) and ethylene glycol dimethacrylate (EGDMA) as the polymerisable oil phase. The aqueous phase consists of water, a surfactant (sodium dodecyl sulphate, SDS) and a co-surfactant (1-propanol). 2-acrylamido-2-methyl-1-propane sulfonic acid (AMPS) is also added to provide charges along the polymer backbone to allow electroosmotic flow (EOF) to occur. SEM analysis shows that in-situ polymerisation yields a monolithic structure with a porous topography. Investigations have shown that these monoliths are easy to prepare, robust and suitable for the separation of phthalates. They generate higher linear velocities than are achieved using the silica based HPLC packings normally used for CEC.