Coin-tossing measures and their Fourier transforms

A coin-tossing measure μ on [0,1] is a probability measure satisfying

     

Magnetic properties of C60 polymers

Magnetic properties of various C60 polymers are calculated using tight-binding molecular-dynamics and ab initio methods. Our results suggest a mechanism involving an interplay between structural defects and sp(3) hybridization to be responsible for the origin of this magnetism. The onset of magnetism is found to occur much more readily for the Rh-C60 polymeric phase with defects than for any of the other polymers, in agreement with the recent experiment. Our estimate of the magnetic moment is also in very good agreement with the value observed in experiment.     

Carbon nanotube "T Junctions": formation pathways and conductivity

Using tight-binding molecular dynamics we simulate the formation of single wall carbon nanotube T junctions via the fusing of two nanotubes. We propose energetically efficient pathways for this process in which all atoms maintain their sp(2) arrangements throughout. Recent experimental advances have greatly increased the plausibility of synthesizing T junctions as proposed in the simulations. We further report I-V characteristics of the formed junctions.     

Représentations des algèbres de Jordan,variétés de Stiefel et synthèse spectrale

We study the Stiefel's manifolds which arise in the framework of the representations of the Euclidean Jordan and simple algebras. We prove that most of them are not sets of spectral synthesis by using the generalized Bessel functions associated with these representations. To cite this article: A.G. Kalliterakis, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Strategic customer behavior in a queueing system with delayed observations

We consider the single-server Markovian queue with infinite waiting space and assume that there exists a certain reward-cost structure that reflects the customers’ desire for service and their dislike for waiting. The system is unobservable for the customers at their arrival instants, but the administrator provides them with periodic announcements of their current positions at rate \(\theta \), so that they may renege if it is preferable for them to do so. The customers are strategic, and their decision problem is whether to join or not the system upon arrival and whether to stay or renege later. Their strategies are specified by a join probability q and a reneging threshold n. We determine the equilibrium strategies \((n_e,q_e)\) and study the socially optimal strategies \((n_\mathrm{soc},q_\mathrm{soc})\). Extensive numerical experiments provide interesting qualitative insight about the model. In particular, the equilibrium throughput of the system is a unimodal function of \(\theta \). Moreover, despite the fact that we have an avoid-the-crowd situation, it is possible that \(q_\mathrm{soc}>q_e\), in contrast to the classical unobservable model.     

Synchronized abandonments in a single server unreliable queue

We consider a single server unreliable queue represented by a 2-dimensional continuous-time Markov chain. At failure times, the present customers leave the system. Moreover, customers become impatient and perform synchronized abandonments, as long as the server is down. We analyze this model and derive the main performance measures using results from the basic q-hypergeometric series.     

Micellar spheres in a high frequency oscillatory field

The viscoelasticity of aqueous micellar solutions of two oxyethylene/oxybutylene block copolymers (E(92)B(18) and B(20)E(510)) has been investigated using a torsional resonator operated at 26 kHz. For both systems considered, values of the dynamic viscosity (eta'(infinity)) point to partial draining of the micellar corona induced by the high-frequency oscillatory field. At low effective volume fractions, values of the elastic modulus (G'(infinity)) indicate that the repulsive interactions between micelles can be modeled by a power law function u(r) proportional to 1/r(nu) with exponents close to 13 and 6 for copolymers E(92)B(18) and B(20)E(510) respectively. At a critical copolymer concentration (c*) plots of log(G'(infinity)) against log(c) deviate from the straight lines established at low concentrations, implying that the systems undergo ergodic/nonergodic transitions.