TiOBr; Darstellung,Eigenschaften und Struktur*

TiOBr was prepared by reaction of Ti with TiO₂ and Br₂. The compound forms fiat reddish-brown needles and shows a temperature independent weak paramagnetism. It crystallises in the orthorhombic system (Pmmn; a = 3.787, b = 3.487, c = 8.529 Å) with the FeOCl type of structure. The interatomic distances are Ti?O = 1.952; 2.245 Å (2X) and Ti?Br = 2.544 Å (2X).     

A study of the effects of curvature and compression on the behavior of a supersonic turbulent boundary layer

The influences of concave streamline curvature and bulk compression on a turbulent boundary layer in a supersonic flow were studied. The effects of curvature and compression were identified by comparing two flows with identical pressure distributions but different amounts of curvature. The effect of the pressure rise was to increase the wall stress and amplify the Reynolds stresses. The influence of curvature complemented the destabilizing effect of the compression, and the larger the curvature the greater the increase in the wall friction and Reynolds stresses in the boundary layer.This work was supported by AFOSR grant 90-0261, monitored by Dr. L. Sakell     

A second-order accurate material-order-independent interface reconstruction technique for multi-material flow simulations

A new, second-order accurate, volume conservative, material-order-independent interface reconstruction method for multi-material flow simulations is presented. First, materials are located in multi-material computational cells using a piecewise linear reconstruction of the volume fraction function. These material locator points are then used as generators to reconstruct the interface with a weighted Voronoi diagram that matches the volume fractions. The interfaces are then improved by minimizing an objective function that smoothes interface normals while enforcing convexity and volume constraints for the pure material subcells. Convergence tests are shown demonstrating second-order accuracy. Static and dynamic examples are shown illustrating the superior performance of the method over existing material-order-dependent methods.     

Rational Unfoldings of ± X k and their relation with geometric equilibrium theory

In this paper, two theorems determine the locus B (buoyancy locus) of the centre of gravity of the displaced water of a ship with any number of 2n sides, as a function of the arbitrary continuous curves that make up those sides, and that generalize the classical wall-sided case (n=1). Although the theorems may have interest from the pure geometrical point of view, they have been obtained with a view to simulate processes in biology that, in analogy to the self-righting of ships, are self-regulating, such as the neural control of body heat and the servo-control of the heart rate.     

Large scale behavior of wavelet coefficients of non-linear subordinated processes with long memory

We study the asymptotic behavior of wavelet coefficients of random processes with long memory. These processes may be stationary or not and are obtained as the output of non-linear filter with Gaussian input. The wavelet coefficients that appear in the limit are random, typically non-Gaussian and belong to a Wiener chaos. They can be interpreted as wavelet coefficients of a generalized self-similar process.     

FP-injective semirings,semigroup rings and Leavitt path algebras

In this paper we give characterisations of FP-injective semirings (previously termed “exact” semirings in work of the first author). We provide a basic connection between FP-injective semirings and P-injective semirings, and establish that FP-injectivity of semirings is a Morita invariant property. We show that the analogue of the Faith-Menal conjecture (relating FP-injectivity and self-injectivity for rings satisfying certain chain conditions) does not hold for semirings. We prove that the semigroup ring of a locally finite inverse monoid over an FP-injective ring is FP-injective and give a criterion for the Leavitt path algebra of a finite graph to be FP-injective.     

Invertibility of functional Galois connectionsInversibilité des correspondances de Galois fonctionnelles

We consider equations of the form Bf=g, where B is a Galois connection between lattices of functions. This includes the case where B is the Fenchel transform, or more generally a Moreau conjugacy. We characterize the existence and uniqueness of a solution f in terms of generalized subdifferentials, which extends K. Zimmermann's covering theorem for max-plus linear equations. To cite this article: M. Akian et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 883–888.     

Perturbation of eigenvalues of matrix pencils and the optimal assignment problem

We extend the perturbation theory of Vi?ik, Ljusternik and Lidski?? to the case of eigenvalues of matrix pencils. This extension allows us to solve certain degenerate cases of this theory. We show that the first order asymptotics of the eigenvalues of a perturbed matrix pencil can be computed generically by methods of min-plus algebra and optimal assignment algorithms. We illustrate this result by discussing a singular perturbation problem considered by Najman. To cite this article: M. Akian et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).