Talbot quadratures and rational approximations

Many computational problems can be solved with the aid of contour integrals containing $e^z$ in the the integrand: examples include inverse Laplace transforms, special functions, functions of matrices and operators, parabolic PDEs, and reaction-diffusion equations. One approach to the numerical quadrature of such integrals is to apply the trapezoid rule on a Hankel contour defined by a suitable change of variables. Optimal parameters for three classes of such contours have recently been derived: (a) parabolas, (b) hyperbolas, and (c) cotangent contours, following Talbot in 1979. The convergence rates for these optimized quadrature formulas are very fast: roughly $O(3^{-N})$, where $N$ is the number of sample points or function evaluations. On the other hand, convergence at a rate apparently about twice as fast, $O(9.28903^{-N})$, can be achieved by using a different approach: best supremum-norm rational approximants to $e^z$ for $z\in (-\infty,0]$, following Cody, Meinardus and Varga in 1969. (All these rates are doubled in the case of self-adjoint operators or real integrands.) It is shown that the quadrature formulas can be interpreted as rational approximations and the rational approximations as quadrature formulas, and the strengths and weaknesses of the different approaches are discussed in the light of these connections. A MATLAB function is provided for computing Cody--Meinardus--Varga approximants by the method of Carathèodory-Fejèr approximation

Preliminary Investigation on the Physiology and Ecology of Luminescence in the Copepod, Metridia lucens

1. Skin glands believed to be the source of luminescence were found on the anterior portion of the head, on the last thoracic segment, and on the posterior margins of each segment of the abdomen. 2. The maximum intensity of the luminescent flash was 1.2 x 10-3 µw./cm.2 (at 18 cm.). The flash rose rapidly to peak intensity and then decayed slowly. The total duration of the flashes with peaks greater than 10-4 µw./cm.2 ranged from 3 to 50 seconds. 3. The peak of the luminescence spectrum occcurred at 482 mµ and the curve fell off to one-half the maximum value at 440 mµ and 525 mµ. 4. The ability of Metridia to luminesce on stimulation was found to be largely unaffected by prolonged laboratory culture. Starvation had little effect on the luminescence for the first three weeks and there was never any inhibition by previous light- or dark-adaptation. 5. With an increase in the strength of the electric stimulus from 0.3 amp. to 0.7 amp., the intensity of the luminescent flash was found to increase. With pulses stronger than 0.7 amp. no change in intensity was recorded but the number of successive responses to repeated stimuli was reduced. Duration of the pulse had little effect on the intensity or the number of successive responses. 6. Metridia showed a lag time of 8-10 msc. to the beginning of the luminescent response. The lag time to the peak of the luminescent response varied from 20 to 60 msc. 7. There was no spontaneous luminescence produced by groups of Metridia under conditions of constant darkness. However, the presence of certain planktonic predators, most notably Meganyctiphanes norvegica, caused a brilliant display of luminescence. The number of flashes attributable to Metridia was always greater than the number of Metridia eaten by the predator. There was little evidence that the luminescent euphausiid, Meganyctiphanes, flashed spontaneously either in the presence or absence of its prey. 8. Observations on the behavior of Metridia during and just after luminescence suggest that the flashing may be involved in an escape mechanism, but the precise effect of the light on the predator has not been determined

Les institutions sans but lucratif en France ; principales évolutions (1995-2005) et nouveaux enjeux

Major trends (1995-2005) in the French Nonprofit sectors are the following: An increased awareness of the importance , an increased support of central and local governments and more professionalized organizations and more anti-establishment new voluntary organizations. Three major issues : ambiguous results of the new phase of decentralisation, increased competition with the business sector and the accountability and evaluation issueParmi les traits qui ont caractérisé l'évolution des institutions sans but lucratif sur la dernière décennie, on a privilégié la prise de conscience de leur importance croissante , le partenariat renforcé avec les pouvoirs publics et, enfin, la professionnalisation rapide et l'avènement de nouvelles associations contestataires. Parmi les enjeux futurs, on a choisi les conséquences ambigües de la seconde phase de la décentralisation, la compétition accrue à laquelle font face les associations et l'exigence renforcée de transparence et d'évaluation dans les années à venir

Garbage collector interface

The purpose of the presented garbage collector interface is to provide a universal interface for many different implementations of garbage collectors. This is to simplify the integration and exchange of garbage collectors, but also to support incremental, non-conservative, and thread safe implementations. Due to the complexity of the interface, it is aimed at code generators and preprocessors. Experiences from ongoing implementations indicate that the garbage collector interface successfully provides the necessary functionality in an efficient way

Des vertus des personnages du Tirant lo Blanc et de leur appétit : réflexions sur le rôle de la nourriture dans l'oeuvre de Joanot Martorell

International audienceRéflexions autour du rôle de la nourriture dans Tirant lo Blanc. D'après Miguel de Cervantes, le roman de Joanot Martorell se distingue des autres romans de chevalerie parce que, notamment, les chevaliers mangent beaucoup. Nous avons pris Cervantes au mot et nous avons essayé de voir quelle était la forme et la signification de ces repas

The Stokes operator with Robin boundary conditions in solenoidal subspaces of L^1({\mathbb R}^n_+) and L^\infty({\mathbb R}^n_+)

We prove that the Stokes operator with Robin boundary conditions is the generator of a bounded holomorphic semigroup on L^\infty_\sigma({\mathbb R}^n_+), which is even strongly continuous on the space \BUC_\sigma({\mathbb R}^n_+). Contrary to that result it is also proved that there exists no Stokes semigroup on L^1_\sigma({\mathbb R}^n_+), except if we assume the special case of Neumann boundary conditions. Nevertheless, we also obtain gradient estimates for the solution of the Stokes equations in L^1_\sigma({\mathbb R}^n_+) for all types of Robin boundary conditions

Evolutions of personal networks and life events

http://www.sciencedirect.com/science/journal/03788733International audienceNetworks of personal relations evolve over time. They reflect and go with processes of socialization. Their history and dynamics contribute to their present structure. The number of people involved in them and their composition change, as does the quality of the links that constitute them. What life events might influence these changes, or possibly even explain them? Drawing on a qualitative survey of a panel of 66 young people living originally in Normandy (France), who were questioned every three years, we attempt here to find a relation between the evolution of their personal networks and the events marking their entry into adult life. Do their networks expand or contract, do they move regularly or in stages? What are the links that appear, disappear or change? What events are likely to influence changes in these links and in the networks as a whole? We begin by examining the changes in the young people's networks during the survey's three waves. We then identify the life events that took place in the intervals, focusing in particular on entry into the labour market, geographical mobility, setting up house with a partner and the birth of children in the household. This enables us to advance some hypotheses about the impact of these events on the evolution of networks and to illustrate our argument with a few significant examples

An Evaluation of the Effect of Instrument Geometry on Color Management for Printed Textiles

The present study analyzes spectrophotometers with two different optical geometries, namely unidirectional 45° instruments and spherical 8°instruments, for building ICC profiles of inkjet-printed textiles. Unidirectional 45° instruments are utilized extensively in the graphic arts, while spherical 8° instruments are more commonly used in the textile industry. One limitation to using spherical 8° instruments for ICC profiling is that profiles built of printing conditions typically require readings of hundreds of patches, and there is only one known instrument configuration that can automate this process, while choices abound for automated instrumentation with unidirectional 45° for ICC profiling. Using a ColorScout A+, a robotic x,y table that is instrument agnostic and able to accommodate both handheld unidirectional 45° instruments and spherical 8°instruments in automating multiple readings, profiles are built and analyzed for two different inkjet-printed textile substrates