An approach to deciding the observational equivalence of Algol-like languages

We prove that the observational equivalence of third-order finitary (i.e. recursion-free) Idealized Algol (IA) is decidable using Game Semantics. By modelling the state explicitly in our games, we show that the denotation of a term M of this fragment of IA is a compactly innocent strategy-with-state, i.e. the strategy is generated by a finite view function f_M. Given any such f_M, we construct a real-time deterministic pushdown automaton (DPDA) that recognizes the complete plays of the knowing-strategy denotation of M. Since such plays characterize observational equivalence, and there is an algorithm for deciding whether any two DPDAs recognize the same language, we obtain a procedure for deciding the observational equivalence of third-order finitary IA. Restricted to second-order terms, the DPDA representation cuts down to a deterministic finite automaton; thus our approach gives a new proof of Ghica and McCusker’s regular-expression characterization for this fragment. Our algorithmic representation of program meanings, which is compositional, provides a foundation for model-checking a wide range of behavioural properties of IA and other cognate programming languages. Another result concerns second-order IA with full recursion: we show that observational equivalence for this fragment is undecidable.     

On a class of preconditioners for solving the Helmholtz equation

In 1983, a preconditioner was proposed [J. Comput. Phys. 49 (1983) 443] based on the Laplace operator for solving the discrete Helmholtz equation efficiently with CGNR. The preconditioner is especially effective for low wavenumber cases where the linear system is slightly indefinite. Laird [Preconditioned iterative solution of the 2D Helmholtz equation, First Year's Report, St. Hugh's College, Oxford, 2001] proposed a preconditioner where an extra term is added to the Laplace operator. This term is similar to the zeroth order term in the Helmholtz equation but with reversed sign. In this paper, both approaches are further generalized to a new class of preconditioners, the so-called “shifted Laplace” preconditioners of the form Δφ−k²φ with . Numerical experiments for various wavenumbers indicate the effectiveness of the preconditioner. The preconditioner is evaluated in combination with GMRES, Bi-CGSTAB, and CGNR.     

Electron transfer induced dissociations of 2- and 4-alkyl cyclohexadienones

Several 2- and 4-alkylcyclohexadienones were prepared and shown to accept electrons to produce ketyl radical anions that dissociated rapidly at room temperature to release carbon-centered radicals and an aromatic phenoxide type anion. In the PET process with benzyl-substituted cyclohexadienones, initiated with triethylamine, the benzyl radicals dimerised or abstracted an H-atom from solvent. In electrochemical reductions, and in reductions with alkali metals in liquid ammonia, the benzyl radicals were further reduced to anions.     

The evolution of a truncated gaussian probability density through time—modelling animal liveweights after selection

The form of the probability density derived from the evolution in time of a previously truncated frequency distribution of animal Liveweights is of interest in animal husbandry. Truncated frequency distributions arise when the heavier animals are sold for slaughter and the lighter animals retained. The demands of modern quality assurance schemes require that, given information on animal growth, the farmer is able to estimate the number of animals that would meet the specifications at some time in the future after truncation. Assuming that animal growth can be described by a linear stochastic differential equation, we derive an explicit expression for the probability density of animal Liveweights at any time after the truncation of an initial Gaussian density. It is shown that this probability density converges rapidly to a Gaussian density, so that after about 20 days of typical growth rates for lambs, the resulting density is practically indistinguishable from Gaussian.     

Three-dimensional structure of Saccharomyces cerevisiae inorganic pyrophosphatase complexed with cobalt and phosphate ions

Crystals of Saccharomyces cerevisiae inorganic pyrophosphatase suitable for X-ray diffraction study were grown by cocrystallization of the enzyme with cobalt chloride and imidodiphosphate. Saccharomyces cerevisiae is a metal-dependent enzyme which catalyzes hydrolysis of inorganic pyrophosphate to orthophosphate. The three-dimensional structure of this enzyme was solved by the molecular-replacement method and refined at 1.8 Å resolution to an R factor of 19.5%. Cobalt and phosphate ions were revealed in the active centers of both identical subunits (A and B) of the pyrophosphatase molecule. In subunit B, a water molecule was found between two cobalt ions. It is believed that this water molecule acts as an attacking nucleophile in the enzymatic cleavage of the pyrophosphate bond. It was demonstrated that cobalt ions and a phosphate group occupy only part of the potential binding sites (two chemically identical and crystallographically independent subunits have different binding sites). The arrangement of ligands and the structure of the nucleophile-binding site are discussed in relation to the mechanism of action of the enzyme and the nature of the metal activator.     

Performance of a CW pumped Nd:YVO4 amplifier with kHz pulses

Until recently, simple and reliable high repetition-rate laser sources with nanosecond pulses much shorter than from conventional A-O Q-switch lasers were not available. However over the past 2 years we have developed such lasers based on proprietary fast E-O switching technology, which allows designs delivering 1 ns pulses and subnanosecond jitter for good synchronisation. The technology provides pulses with multi-kW peak power and repetition-rates to >100 kHz.Most recently, the performance of these short pulse lasers has been developed further by implementing oscillator/amplifier (master oscillator and power amplifier, MOPA) technology which increases the output to >1 W average power. Here we report on a simple model that has been used to predict the performance of the CW pumped Nd:YVO₄ amplifier used in the MOPA laser. The model is based on the well-known expressions for the saturated gain applying to laser pulses, but more usually applied to pulse-excited amplifiers. The model is shown to allow a good interpretation of the amplifier behaviour for kHz pulses and to be a useful tool for predicting the performance of the MOPA laser.     

Determination of flutter derivatives via a neural network approach

A neural-network-based method is offered to determine the flutter derivatives of section models under smooth and turbulent flows. The approach uses the observed dynamic responses to train an appropriate neural network. Subsequently, the modal parameters of the model for different mean velocities of wind flow are directly estimated using weight matrices in the neural network. The flutter derivatives can then be determined accurately. The validity of the present method is verified through numerical studies. Finally, the procedure is employed to process experimental data from an inverted-U-type section model, obtained from wind tunnel tests.     

Multi-Item Scheduling by Benders' Decomposition

Scheduling the production of several items requires the determination of production quantities in different periods in the presence of resource constraints. Several approximate and heuristic algorithms have been proposed to solve this problem. However, no method for finding an optimal solution has as yet been developed. It is shown that the problem may be solved advantageously using Benders' decomposition. The subproblem in Benders' decomposition is shown to be a transportation problem, and some strategies for solving the master problem are indicated. The paper concludes with a sample problem demonstrating the application of the method.     

Ionization potentials and geometrical structure of pure and oxygenated barium clusters

In this article, we present results obtained on structures of small bare and oxygenated barium clusters produced by the laser vaporization technique. Contrary to the very weak Ba—Ba binding (0.202 eV), the Ba—O binding is rather strong (5.8 eV). As a consequence, extremely small amounts of oxygen in the cluster source are sufficient to induce the nucleation of oxygenated barium clusters. Surprisingly, at least for substoechiometric systems, Ba_nO_m clusters exhibit the same icosahedral structure as bare clusters do. Mass spectra seem to indicate that replacing a barium atom with a strongly polar BaO molecule does not affect the geometrical structure of the cluster. This aspect is more easily understandable if we assume that the oxygen atom takes place inside the structure of the Ba_n cluster without significant distortions. Ab-initio calculations have been undertaken in order to give a satisfactory account of this hypothesis.