Vojta's Main Conjecture for blowup surfaces

In this paper, we prove Vojta's Main Conjecture for split blowups of products of certain elliptic curves with themselves. We then deduce from the conjecture bounds on the average number of rational points lying on curves on these surfaces, and expound upon this connection for abelian surfaces and rational surfaces.

     

Automated separation and measurement of radioxenon for the Comprehensive Test Ban Treaty

A fully automatic radioxenon sampler/analyzer (ARSA) has been developed and demonstrated for the collection and quantitative measurement of the four xenon radionuclides,^131mXe(11.9 d),^133mXe(2.2 d),¹³³Xe(5.2 d), and¹³⁵Xe(9.1 hr), in the atmosphere. These radionuclides are important signatures in monitoring for compliance to a Comprehensive Test Ban Treaty (CTBT). Activity ratios of these radionuclides permit source attribution. Xenon, continuously and automatically separated from the atmosphere, is automatically analyzed by electron-photon coincidence spectrometry providing a lower limit of detection of about 100 μBq/m³. The demonstrated detection limit is about 100 times better than achievable with reported laboratory-based procedures for the short-time collection intervals of interest.     

High-performance liquid chromatographic analysis of basic drugs on silica columns using non-aqueous ionic eluents. II. Application of UV, fluorescence and electrochemical oxidation detection

Unmodified silica columns together with non-aqueous ionic eluents give stable yet flexible systems for the analysis of basic drugs by high-performance liquid chromatography. Low-wavelength UV and fluorescence detection may be used, and fluorescence may be optimised by, for example, post-column pH change or derivatisation of some primary aliphatic amines with o-phthaldialdehyde. A novel feature is that electrochemical oxidation can be used for the detection of most analytes and this detection mode is thus discussed in detail. Retention and relative response data (UV, 254 nm and electrochemical, +1.2 V) have been generated for 462 compounds using a 125-mm Spherisorb S5W silica column and methanolic ammonium perchlorate (10 mM, pH 6.7) as eluent. This system can be used isocratically in qualitative analyses and also for quantitative work, when either the wavelength or the applied potential can be adjusted to optimise the response.     

Hydrogen atom mediated Stone-Wales rearrangement of pyracyclene: a model for annealing in fullerene formation

We have investigated the Stone-Wales (SW) rearrangement of pyracyclene (C(14)H(12)) using quantum mechanical molecular modeling. Of particular interest in this study is the effect of an added hydrogen atom on the barriers to SW rearrangement. Hydrogen atoms are found in high abundance during combustion, and their effect upon isomerization of aromatic compounds to more stable species may play an important role in the combustion synthesis of fullerenes. We have calculated the barriers for the SW rearrangement in pyracyclene using density functional theory B3LYP/6-31G(d) and B3LYP/6-311G(d,p). Two mechanisms have been investigated: (i) a mechanism with two identical transition states of C(1) symmetry and a cyclobutyl intermediate and (ii) a mechanism with one transition state containing an sp(3) carbon (J. Am. Chem. Soc. 2003, 125, 5572-5580; Nature 1993, 366, 665-667). We find that the barriers for these mechanisms are 120.0 kcal mol(-1) for the cyclobutyl mechanism and 130.1 kcal mol(-1) for the sp(3) mechanism. Adding a hydrogen atom to the internal bridge carbon atoms of pyracyclene reduces the barrier of the cyclobutyl mechanisms to 67.0 kcal mol(-1) and the sp(3) mechanism to 73.1 kcal mol(-1). The bonding of carbon atoms in pyracyclene is similar to those found in isomers of C(60), and the barriers are low enough so that these reactions can become significant during fullerene synthesis in flames. Adding hydrogen atoms to the external bridge atoms on pyracyclene produces a smaller reduction in the SW barrier and adding hydrogen atoms to nonbridge external carbon atoms results in no reduction of the barrier.     

Straight line embeddings of cubic planar graphs with integer edge lengths

We prove that every simple cubic planar graph admits a planar embedding such that each edge is embedded as a straight line segment of integer length. © 2008 Wiley Periodicals, Inc. J Graph Theory 58:270‐274, 2008     

On the Generation of Markov Decision Processes

Comparisons of the performance of solution algorithms for Markov decision processes rely heavily on problem generators to provide sizeable sets of test problems. Existing generation techniques allow little control over the properties of the test problems and often result in problems which are not typical of real-world examples. This paper identifies the properties of Markov decision processes which affect the performance of solution algorithms, and also describes a new problem generation technique which allows all of these properties to be controlled.     

DYNGA: a general purpose QM-MM-MD program. I. Application to water

We present a general purpose QM-MM-MD engine (DYNGA) designed to test alternative hybrid Hamiltonians geared towards the treatment of problems of interest in structural biology including the use of experimental data constraints. In this first presentation we use DYNGA to explore the behaviour of a traditional QM-MM approach in the treatment of the water—water interaction. We find the potential energy hypersurface for the water dimer computed with the HF 4–31G*/TIP3P hybrid Hamiltonian tends to be too flat. We also explore the effect of using traditional QM-MM techniques on proton wires and conclude there is a need for improvement, possibly addressed by using polarizable force fields.     

Constructing integer programming models by the predicate calculus

A modelling language for Integer Programming (IP) based on the Predicate Calculus is described. This is particularly suitable for building models with logical conditions. Using this language a model is specified in terms of predicates. This is then converted automatically by a series of transformation rules into a normal form from which an IP model can be created. There is also some discussion of alternative IP formulations which can be incorporated into the system as options. Further practical considerations are discussed briefly concerning implementation language and incorporation into practical Mathematical Programming Systems.