Perfectly matched layers (PML) are a recent technique for simulating the absorption of waves in open domains. They have been introduced for electromagnetic waves and extended, since then, to other models of wave propagation, including waves in elastic anisotropic media. In this last case, some numerical experiments have shown that the PMLs are not always stable. In this paper, we investigate this question from a theoretical point of view. In the first part, we derive a necessary condition for the stability of the PML model for a general hyperbolic system. This condition can be interpreted in terms of geometrical properties of the slowness diagrams and used for explaining instabilities observed with elastic waves but also with other propagation models (anisotropic MaxwellÕs equations, linearized Euler equations). In the second part, we specialize our analysis to orthotropic elastic waves and obtain separately a necessary stability condition and a sufficient stability condition that can be expressed in terms of inequalities on the elasticity coefficients of the model.

We tested the usefulness of aspirin (325 mg twice daily), heparin (1000 units per hour by intravenous infusion), and a combination of the two in the early management of acute unstable angina pectoris in a double-blind, randomized, placebo-controlled trial involving 479 patients. The patients entered the study as soon as possible after hospital admission (at a mean [+/- SD] of 7.9 +/- 8.0 hours after the last episode of pain), and the study was ended after 6 +/- 3 days, when definitive therapy had been selected. Major end points--refractory angina, myocardial infarction, and death--occurred in 23, 12, and 1.7 percent of the 118 patients receiving placebo, respectively. Heparin was associated with a decrease in the occurrence of refractory angina (P = 0.002). The incidence of myocardial infarction was significantly reduced in the groups receiving aspirin (3 percent; P = 0.01), heparin (0.8 percent; P less than 0.001), and aspirin plus heparin (1.6 percent, P = 0.003), and no deaths occurred in these groups. There were too few deaths overall to permit evaluation of the effect of treatment on this end point. The combination of aspirin and heparin had no greater protective effect than heparin alone but was associated with slightly more serious bleeding (3.3 vs. 1.7 percent). We conclude that in the acute phase of unstable angina, either aspirin or heparin treatment is associated with a reduced incidence of myocardial infarction, and there is a trend favoring heparin over aspirin. Heparin treatment is also associated with a reduced incidence of refractory angina.

Solving the wave equation by a C o finite element method requires to mass-lump the term in time of the variational f6rmulation in order to avoid the inversion of a n-diagonal symmetric matrix at each time-step of the algorithm. One can easily get this mass-lumping on quadrilateral meshes by using a h-version of the spectral elements, based on Gauss-Lobatto quadrature formulae but the equivalent method is not obvious for triangular meshes. In this paper we construct and analyze new families of triangular finite elements which fulfill the same requirements as spectral quadratic and cubic finite elements.

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The FRANCE TAVI registry provided reassuring data regarding trends in TAVR performance in an all-comers population on a national scale. Nonetheless, given that TAVR indications are likely to expand to patients at lower surgical risk, concerns remain regarding potentially life-threatening complications and pacemaker implantation. (Registry of Aortic Valve Bioprostheses Established by Catheter [FRANCE TAVI]; NCT01777828).