Soft spin wave near nu=1: evidence for a magnetic instability in Skyrmion systems

The ground state of the two-dimensional electron gas near nu=1 is investigated by inelastic light scattering measurements carried down to very low temperatures. Away from nu=1, the ferromagnetic spin wave collapses and a new low-energy spin wave emerges below the Zeeman gap. The emergent spin wave shows soft behavior as its energy increases with temperature and reaches the Zeeman energy for temperatures above 2 K. The observed softening indicates an instability of the two-dimensional electron gas towards a magnetic order that breaks spin rotational symmetry. We discuss our findings in light of the possible existence of a Skyrme crystal.     

Porous materials with two populations of voids under internal pressure: II. Growth and coalescence of voids

This study is devoted to the mechanical behaviour of polycrystalline materials with two populations of voids, small spherical voids located inside the grains and larger spheroidal voids located at the grain boundaries. In part I of the work, instantaneous effective stress–strain relations were derived for fixed microstructure. In this second part, the evolution of the microstructure is addressed. Differential equations governing the evolution of the microstructural parameters in terms of the applied loading are derived and their integration in time is discussed. Void growth results in a global softening of the stress–strain response of the material. A simple model for the prediction of void coalescence is proposed which can serve to predict the overall ductility of polycrystalline porous materials under the combined action of thermal dilatation and internal pressure in the voids.     

Post-processing in masking-based β-order MMSE speech enhancement

A post-processing technique for improving the performance of the masking-based β-order MMSE method in speech enhancement is proposed in this letter. After the enhancement process, weak spectral components in the high-frequency band are usually over-attenuated. A non-linear high-frequency regeneration technique is used to re-synthesize the upper-band signal based on the lower-band speech.     

Sur quelques limites de la physique des particules chargées vers la (magnéto)hydrodynamiqueOn some limits in charged particle physics towards (magneto)hydrodynamic equations

We discuss the connection between different scalings limits of the quantum-relativistic Dirac–Maxwell system. In particular we give rigorous results for the quasi-neutral/non-relativistic limit of the Vlasov–Maxwell system: we obtain a magneto-hydro-dynamic system when we consider the magnetic field as a non-relativistic effect and we obtain the Euler equation when we see it as a relativistic effect. A mathematical key is the modulated energy method. To cite this article: Y. Brenier et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 239–244.     

Rate of convergence of crossover operators

We study the convergence of mating operators on {0, 1}ⁿ. In particular, we answer questions of Rabani, Rabinovich, and Sinclair (1998) by giving tight estimates on the divergence between the finite‐ and infinite‐population processes, thus solving positively the problem of the simulability of such quadratic dynamical systems. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 23: 58–72, 2003     

On binomial Thue-Mahler equations

We give a rather sharp upper bound for the degree of a binomial Thue--Mahler equation in terms of the coefficients and the primes involved. Further, we establish explicit lower bounds for the greatest prime factor of a binomial binary form at integral points. Our estimates considerably generalize and improve the earlier results obtained in this direction.     

Polar factorization and monotone rearrangement of vector-valued functions

Given a probability space (X, μ) and a bounded domain Ω in ?^d equipped with the Lebesgue measure |·| (normalized so that |Ω| = 1), it is shown (under additional technical assumptions on X and Ω) that for every vector-valued function u ∈ L^p (X, μ; ?^d) there is a unique “polar factorization” u = ?Ψs, where Ψ is a convex function defined on Ω and s is a measure-preserving mapping from (X, μ) into (Ω, |·|), provided that u is nondegenerate, in the sense that μ(u^?1(E)) = 0 for each Lebesgue negligible subset E of ?^d. Through this result, the concepts of polar factorization of real matrices, Helmholtz decomposition of vector fields, and nondecreasing rearrangements of real-valued functions are unified. The Monge-Ampère equation is involved in the polar factorization and the proof relies on the study of an appropriate “Monge-Kantorovich” problem.     

Rigidité d'Einstein du plan hyperbolique complexeEinstein rigidity of the complex hyperbolic plane

We prove that every Einstein metric on $\text{B}{}^4\text{?}\text{C}{}^2$ asymptotic to the Bergmann metric is equal to it up to a diffeomorphism. The proof relies on the construction of a solution of Seiberg–Witten equations in this infinite volume setting. Therefore, and more generally, if M⁴ is a manifold with a CR-boundary at infinity, an adapted spin^c-structure which has a nonzero Kronheimer–Mrowka invariant and an asymptotically complex hyperbolic Einstein metric, we produce a solution of Seiberg–Witten equations with an strong exponential decay property. To cite this article: Y. Rollin, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 671–676.     

Biosensor for determination of glucose and sucrose in fruit juices by flow injection analysis

Glucose and sucrose were measured with an amperometric method by using the flow injection analysis technique. A carbon paste electrode with a renewable surface containing glucose oxidase, horseradish peroxidase, and ferrocene was used in combination with the soluble enzymes invertase and mutarotase. The effect of invertase, mutarotase, and ascorbic acid on the electrode response was examined. Glucose and sucrose concentrations were determined with <3% errors. The proposed method for glucose and sucrose measurements was validated in real samples of fruitjuices. The results were also compared with those obtained with the ultraviolet method.