Stable boundary layers in a diffusion problem with nonlinear reaction at the boundary

We prove the existence of nonconstant stable stationary solutions of an evolution problem with a nonlinear reaction acting on the boundary. These solutions present layers at certain points of the boundary. We also study the behavior of these solutions as the small parameter appearing in the equation approaches zero and show some stability properties of the profiles given by these equilibrium solutions.     

Principes de grandes déviations pour des processus de « coarse graining »

We improve the Large Deviations Principle satisfied by a Coarse Grained process already analyzed by Boucher, Ellis and Turkington [Ann. Probab. 27 (1999) 297–324]. To cite this article: J. Trashorras, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

X-ray evidence for the absence of 90°-domains in polycrystalline PbTiO3 thin films with grains below a critical size

3 thin films is systematically studied by using X-ray diffraction (XRD). The PbTiO₃ thin films with different average grain sizes were prepared on various substrates by a sol-gel process. The films on NaCl and fused glass are randomly grain-oriented, while those on (111)Pt/Ti/SiO₂/Si are highly {100} cubic index grain-oriented . It is found from the XRD patterns of the films on NaCl that with decreasing average grain size from 230 to 80 nm, the intensities of high h index (h>l) peaks (hkl), such as (100), (110), (200), (201), (210), (211), etc., decrease rapidly and ultimately disappear, whereas another set of peaks (lkh), including (001), (002), (102), (112), etc., are still intense. This interesting result suggests that at grain size below a certain critical size an increasing number of grains no longer show 90°-domains, which is confirmed by TEM observations. Meanwhile, X-ray evidence of such a grain-size-related absence of 90°-domains is also found for PbTiO₃ films on Pt(111) and fused-glass substrates. The volume fractions of single-domain grains (without 90°-domains) in the films are estimated from their XRD patterns. By combining SEM and TEM investigations, the critical grain size for the formation of 90°-domains is further determined to be near 200 nm. Received: 19 December 1996/Accepted: 24 March 1997     

Newtonian limits of warp drive spacetimes

We find a class of warp drive spacetimes possessing Newtonian limits, which we then determine. The same method is used to compute Newtonian limits of the Schwarzschild solution and spatially flat Friedmann-Robertson-Walker cosmological models. This work was partially supported by FCT/POCTI/FEDER.     

A functional modulus of continuity for Brownian motion

In this paper, we prove a sharpening of large deviation for increments of Brownian motion in (p,r)-capacity and Hölder norm case. As an application, we obtain a functional modulus of continuity for (p,r)-capacity in the stronger topology.     

A note on the acyclicity of the Koszul complex of a module

We prove the vanishing of the Koszul homology group H _μ(Kos(M)_μ), where μ is the minimal number of generators of M. We give a counterexample that the Koszul complex of a module is not always acyclic and show its relationship with the homology of commutative rings.     

A topological characterization of classical BRST cohomology

The recent identification of classical BRST cohomology with the vertical cohomology of a certain fibration is used to compute it in terms of the classical observables and the topology of the gauge orbits. When the gauge orbits are compact and orientable, a duality theorem is exhibited.     

A confidence interval for the slope of a truncated regression

Summary Bhattacharya, Chernoff and Yang (1983) proposed a nonparametric estimate for the slope of a regression lineY = _o X + V subjected to the truncationYy ₀. The estimate corresponds to the zero-crossing of a random functionS _n (). In this paper an estimate for the asymptotic variance of the estimate of the slope is proposed and the rate of convergence is given. The proofs rest heavily on the local behavior ofS _n () in the neighborhood of the true value _o.