Estimation of a Bivariate Extreme Value Distribution

Several threshold methods have been proposed for the purpose of estimating a bivariate extreme value distribution from a sample of data whose distribution is only in its domain of attraction. An integrated view of these methods is presented which leads to the introduction of a new asymptotically consistent estimator of the dependence function characterizing the extreme dependence structure. Through Monte Carlo simulations, the new estimator is also shown to do as well as its competitors and to outperform them in cases of weak dependence. To the authors' knowledge, this is the first time that the small-sample behavior of nonparametric bivariate threshold methods has ever been investigated.     

On the speed of a cookie random walk

We consider the model of the one-dimensional cookie random walk when the initial cookie distribution is spatially uniform and the number of cookies per site is finite. We give a criterion to decide whether the limiting speed of the walk is non-zero. In particular, we show that a positive speed may be obtained for just three cookies per site. We also prove a result on the continuity of the speed with respect to the initial cookie distribution.      

Non-parametric estimation of lifetime and repair time criteria for a semi-Markov process

In this Note, we model an industrial system by a semi-Markov process where failure and repair phenomena are in mutual competition. A non-parametric estimation method for system component lifetime and repair time distributions and for associated hazard rate functions is proposed. The lifetime and repair time empirical distributions are reduced to two Kaplan–Meier estimators. A numerical example from an industrial system with three components and one repair man modeled by a birth and death process is provided to illustrate the previous results. To cite this article: A.-L. Afchain, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Interactions of Type II vectorial spatial solitary waves in materials with quadratic non-linearity

We present analytical, numerical and experimental results of the interactions between Type II vectorial spatial solitary waves (QSSW) in second-order non-linear media. We show that the outcome of the interaction can be changed from beam coalescence to steering, crossing or repulsion through a non-coherent control (i.e. the control does not rely on the relative phase between the interacting QSSW). We also provide experimental evidence that both quasi-elastic and inelastic collision between QSSW are feasible in second order non-linear media, depending on the relative velocity of the interacting QSSW. We determine (analytically, numerically and experimentally) the critical transverse velocity for elastic collision to be observed, when the fundamental frequency component of the two interacting beams are orthogonally polarized at the input face of the non-linear crystal.     

Passive phase locking of an array of four fiber amplifiers by an all-optical feedback loop

We report the passive phase locking of an array of four fiber amplifiers in a unidirectional ring cavity. The feedback loop consists of a single-mode fiber that filters intracavity the far-field pattern of the four emitted beams. The pointing of the laser output can be managed by the intracavity filtering.     

Strain Measurement Within a Single-lap Joint Using Embedded Strain Gages

Experimental Techniques -     

Partition coefficients of organic compounds in new imidazolium based ionic liquids using inverse gas chromatography

Partition coefficients of organic compounds in four ionic liquids: 1-ethanol-3-methylimidazolium tetrafluoroborate, 1-ethanol-3-methylimidazolium hexafluorophosphate, 1,3-dimethylimidazolium dimethylphosphate and 1-ethyl-3-methylimidazolium diethylphosphate were measured using inverse gas chromatography from 303.3 to 332.55 K. The influence of gas–liquid and gas–solid interfacial adsorption of different solutes on ionic liquids was also studied. Most of the polar solutes were retained largely by partition while light hydrocarbons were retained predominantly by interfacial adsorption on the ionic liquids studied in this work. The solvation characteristics of the ionic liquids were evaluated using the Abraham solvation parameter model.     

Arrow's theorem: unusual domains and extended codomains

In this paper we establish Arrow's theorem in a general ordinal case. When some configurations are allowed in the domain and if this domain is included in the codomain, the only social functions satisfying the independence condition and the weak Pareto Principle are the absolute dictatorships or the absolute oligarchies.     

Approaches toward the synthesis of 2,5-disubstituted-1,3-thiazolidines

Synthetic approaches for new 2,5-disubstituted-1,3-thiazolidines are described. Steric and electronic effects of the N-substituent of the thiazolidine ring represent the major parameter in the rearrangement process. The nmr studies demonstrate that N-unsubstituted 2,5-disubstituted-1,3-thiazolidines exist as epimeric mixture, while the corresponding N-acetylated analogues exist as a conformer mixture.