Global fit analysis including the ν9 + ν4 − ν4 hot band of ethane: Evidence of an interaction with the ν12 fundamental

The ν₉ fundamental band of ethane occurs in the 12 μm region. It is the strongest band of ethane in a terrestrial window and is commonly used for the identification of ethane in the Jovian planets. The ν₉ + ν₄ − ν₄ band occurs in the same region; neither can be analysed as an isolated band, since both are embedded in the torsional bath of the ground vibrational state. We report here two global fit models including data from both of these bands as well as the ν₃ fundamental and the ν₄, 2ν₄ − ν₄, and 3ν₄ torsional transitions. The first is restricted to −5 ? KΔK ? 15 in the hot band and gives an excellent fit to the included data. Three resonant interactions are identified in this fit—a Coriolis interaction with two resonant cases between the ν₉ torsional stack and that of the ground vibrational state (gs) and a resonant Fermi interaction between the ν₃ fundamental and the gs. Hot band lines with KΔK < −5 are influenced by a fourth perturbation, with a crossing at −11 < KΔK < −10, which has been attributed to an interaction with the ν₁₂ fundamental. A second fit, demonstrating a promising treatment of this interaction, is also presented.     

Choice of modelling technique for evaluating health care interventions

Economic evaluation, such as cost effectiveness analysis, provides a method for comparing healthcare interventions. These evaluations often use modelling techniques such as decision trees, Markov processes and discrete event simulations (DES). With the aid of examples from coronary heart disease, the use of these techniques in different health care situations is discussed. Guidelines for the choice of modelling technique are developed according to the characteristics of the health care intervention.The choice of modelling technique is shown to depend on the acceptance of the modelling technique, model ‘error’, model appropriateness, dimensionality and ease and speed of model development. Generally decision trees are suitable for acute interventions but they cannot model recursion and Markov models are suitable for simple chronic interventions. It is further recommended that population based models be used in order to provide health care outcomes for the likely cost, health benefits and cost effectiveness of the intervention. The population approach will complicate the construction of the model. DES will allow the modeller to construct more complex, dynamic and accurate systems but these may involve a corresponding increase in development time and expense. The modeller will need to make a judgement on the necessary complexity of the model in terms of interaction of individuals and model size and whether queuing for resources, resource constraints or the interactions between individuals are significant issues in the health care system.     

On the invariant measure for the quasi‐linear Lasota equation

The problem of the existence of the invariant measure is important considering its connections with chaotic behaviour. In the papers (Zesz. Nauk. Uniw. Jagiellońskiego, Pr. Mat. 1982; 23 :117–123; Ann. Pol. Math. 1983; XLI :129–137; J. Differential Equations 2004; 196 :448–465) the existence of invariant and ergodic measures according to the dynamical system generated by the Lasota equation was proved, i.e. the equation describing the dynamics and becoming different of the population of cells. In this paper, the existence of such measure for the quasi‐linear Lasota equation is proved. This measure is the carriage of the measure described by Dawidowicz (Zesz. Nauk. Uniw. Jagiellońskiego, Pr. Mat. 1982; 23 :117–123). Copyright © 2006 John Wiley & Sons, Ltd.     

Relevance of Reflection in Static and Dynamic Light Scattering Experiments

Using a monodisperse PMMA dispersion, it was shown that light reflection at the sample cuvette walls may greatly influence the results of both static (SLS) and dynamic (DLS) light scattering experiments. Considering SLS, this reflection phenomenon mostly causes an overestimation of the scattered intensity at high scattering angles, which may give rise to the emergence of an additional, artificial peak in the lower region of the particle size distribution. On the other hand, the influcence of reflection on DLS measurements was shown to be particularly important in the upper region of the particle size distribution. The experimentally observed phenomena were explained from the basic principles of both particle sizing methods. Finally, it was shown that the disturbing effect of reflection could be avoided by modifying either the hardware or the software of the static and dynamic light scattering technique.     

A duality relation for busy cycles inGI/G/1 queues

Using a generalization of the classical ballot theorem, Niu and Cooper [7] established a duality relation between the joint distribution of several variables associated with the busy cycle inM/G/1 (with a modified first service) and the corresponding joint distribution of several related variables in its dualGI/M/1. In this note, we generalize this duality relation toGI/G/1 queues with modified first services; this clarifies the original result, and shows that the generalized ballot theorem is superfluous for the duality relation.     

The implementation of ab initio quantum chemistry calculations on transputers

Summary The RHF and geometry optimization sections of the ab initio quantum chemistry code, GAMESS, have been optimized for a network of parallel microprocessors, Inmos T800-20 transputers, using both indirect and direct SCF techniques. The results indicate great scope for implementation of such codes on small parallel computer systems, very high efficiencies having been achieved, particularly in the cases of direct SCF and geometry optimization with large basis sets.The work, although performed upon one particular parallel system, the Meiko Computing Surface, is applicable to a wide range of parallel systems with both shared and distributed memory.     

De Bruijn cycles for covering codes

A de Bruijn covering code is a q‐ary string S so that every q‐ary string is at most R symbol changes from some n‐word appearing consecutively in S. We introduce these codes and prove that they can have size close to the smallest possible covering code. The proof employs tools from field theory, probability, and linear algebra. Included is a table of the best known bounds on the lengths of small binary de Bruijn covering codes, up to R = 11 and n = 13, followed by several open questions in this area. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004