Toward Non Commutative Numerical Analysis: High Order Integration in Time

We review some methods for high precision time integration: it is not easy to ensure stability, precision and numerical efficiency at the same time. Operator splitting—when it works—can be a good way to satisfy all these constraints; in some cases, the order of the splitting schemes can be enhanced by extrapolation; nevertheless, the applicability of splitting is limited due to non commutativity. As an alternative to splitting, we introduce preconditioned Runge–Kutta (PRK) schemes: the preconditioning is included in the scheme, instead of being put aside for implementation. Examples of PRK schemes are given including the extrapolation of the residual smoothing scheme, and sufficient conditions for stability are described.     

Penalty Approximation for Dynamical Systems Submitted to Multiple Non-Smooth Constraints

We consider discrete mechanical systems subject to perfect unilateral constraints. Moreau's impact law uses the decomposition of the velocity on the normaland tangent cones to the set of admissible positions at the impact point, and it iswell-known that this gives the only possible rule in the case of a singleperfect unilateral constraint. In the multi-constraint case, there areother possible energetically and geometrically consistant impact laws. Weshow here that in a number of cases, the limiting behavior of impact asits rigidity tends to infinity is given by Moreau's rule, i.e., in a more mathematical language, we justify this impact law by a penalty approach.First we describe the penalty method, then we apply it to amulti-constraint model problem. We choose an overdamped approximationand we obtain Moreau's rule for inelastic shocks in the limit. Finally,we present the computational drawbacks of the penalty method.     

Induction of p34cdc2 in mouse parotid glands upon activation of beta1-adrenergic receptors

The element pSAM2 from Streptomyces ambofaciens integrates into the chromosome through site-specific recombination between the element (attP) and the chromosomal (attB) sites. These regions share an identity segment of 58bp extending from the anti-codon loop through the 3' end of a tRNA(Pro) gene. To facilitate the study of the attB site, the int and xis genes, expressed from an inducible promoter, and attP from pSAM2 were cloned on plasmids in Escherichia coil. Compatible plasmids carrying the different attB regions to be tested were introduced in these E. coli strains. Under these conditions, Int alone could promote site-specific integration; Int and Xis were both required for site-specific excision. This experimental system was used to study the sequences required in attB for efficient site-specific recombination. A 26 bp sequence, centred on the anti-codon loop region and not completely included in the identity segment, retained all the functionality of attB; shorter sequences allowed integration with lower efficiencies. By comparing the 26-bp-long attB with attP, according to the Lambda model, we propose that B and B', C and C' core-type Int binding sites consist of 9 bp imperfect inverted repeats separated by a 5 bp overlap region.