A dynamic model for city size distribution beyond Zipf 's law

We present a growth model for a system of cities. This model recovers not only Zipf's law but also other kinds of city size distributions (CSDs). A new positive exponent α, which yields Zipf's law only when equal to 1, was introduced. We define three classes of CSD depending on the value of α: larger than, smaller than, or equal to 1. The model is based on a random growth of the city population together with the variation of the number of cities in the system. The striking result is the peculiar behavior of the model: it is only statistical deterministic. Moreover, we found that the exponent α may be larger, smaller or equal to 1, just like in real systems of cities, depending on the rate of creation of new cities and the time elapsed during the growth. It is to our knowledge the first time that the influence of the time on the type of the distribution is investigated. The results of the model are in very good agreement with real CSD. The classification and model can be also applied to other entities like countries, incomes, firms, etc     

Analysis of carbohydrates in plants by high-performance anion-exchange chromatography coupled with electrospray mass spectrometry

A mass spectrometer was coupled to high-performance anion-exchange chromatography (HPAEC) with the help of electrochemical neutralization of the eluent and post-column addition of lithium chloride for carbohydrate analysis. Parallel selective channels (single ion monitoring) were used to decrease the detection limits and separate unresolved peaks. The mass specific detection allowed the simultaneous analysis of a wide range of sugar alcohols, mono-, di- and oligosaccharides. Carbohydrates extracted from leaves of poplar submitted to drought stress were analyzed using pulsed amperometric detection (PAD), then mass spectrometry. It allowed the confirmation of peak attribution and the identification of salicin as a major compound in the extracts. Different responses to water deficit and re-hydration were obtained for several carbohydrates, suggesting different roles in osmoprotection processes.     

Hydrostatic pressure-forced phase transition from ferroelectric to antiferroelectric in compositions of the PbZr1−x Ti x O3+0.8% WO3 type

Hydrostatic pressure acting on doped lead titanate-zirconate materials with a considerable proportion of zirconium induces a phase transition between ferroelectric and antiferroelectric states, which causes the previously poled specimens to depolarize. Measurements using a capacitance and those made on short-circuited specimens allow us to draw phase diagrams of the following types: “pressure-electric field” and “pressure-composition”. A thermodynamic investigation of the phenomenon permits us to define new characteristic coefficients for this type of depolarization.     

Separation et dosage de traces de bore dans le silicium : Nouvelle méthode de séparation et de dosage de traces de bore. application au dosage du bore dans le silicium

A new method is described for the separation and determination of traces of boron by extraction of methylene blue fluoroborate by dichlorethane The method has been applied to the determination of traces of boron in silicon and silica     

Dynamics of macromolecular chains. II. Orientation relaxation generated by elementary three-bond motions and notion of an independent kinetic segment

In the preceding paper, general equations were established for the motions of chains confined to a tetrahedral lattice. In the present paper, bond orientation correlation and autocorrelation functions are explicitly calculated for the case where only three-bond elementary motions are considered. Effects due to the chain end are analyzed and the relaxation time distribution function is established. The expressions obtained reflect the influence of the chain structure. Finally, to characterize the dynamic behavior of chains in orientation relaxation experiments, the notion of an independent kinetic segment is proposed.     

A new proof of certain littlewood-paley inequalities

The aim of this article is to give a new proof of the L^p-inequalities for the Littlewood-Paley g_*-function. Our main tool is a pointwise equality, relating a function f, and the associated functional g_*(f), which has the form f²=h(f)+g _* ² (f), where h(f) is an explicit function. We obtain this equality as a particular case of a more general one, which is reminiscent of a well-known identity in the stochastic calculus setting, namely the Itô formula. Once the above equality is proved, L^p-estimates for g_*(f) are obviously equivalent to L^p/2-estimates for h(f). We obtain these last estimates (more precisely, H^p/2-estimates for h(f) by using a slight extension of the Coifman-Meyer-Stein theorem relating the so-called tent-spaces and the Hardy spaces. We observe that our methods clearly show that the restriction p>2n/n+1 is closely related to cancellation and size properties of the gradient of the Poisson kernel.     

Bornitude et continuité de la transformation de Lévy en analyse

In our previous papers (Adv. in Math. 138 (1) (1998) 182; Potential Anal. 12 (2000) 419), we have obtained a decomposition of |f|, where f is a function defined on , that is analogous to the one proved by H. Tanaka for martingales (the so-called “Tanaka formula”). More precisely, the decomposition has the form , where is (a variant of ) the density of the area integral associated with f. This functional (introduced by R.F. Gundy in his 1983 paper (The density of area integral, Conference on Harmonic Analysis in Honor of Antoni Zygmund. Wadsworth, Belmont, CA, 1983, pp. 138-149.)) can be viewed as the counterpart of the local time in Euclidean harmonic analysis. In this paper, we are interested in boundedness and continuity properties of the mapping (which we call the Lévy transform in analysis) on some classical function or distribution spaces. As was shown in [4,5], the above (non-linear) decomposition is bounded in L^p for every p∈[1,+∞[, i.e. one has , where C_p is a constant depending only on p. Nevertheless our methods (roughly speaking, the Calderón-Zygmund theory in [4], stochastic calculus and martingale inequalities in [5]) both gave constants C_p whose order of magnitude near 1 is O(1/(p−1)). The aim of this paper is two-fold: first, we improve the preceding result and we answer a natural question, by proving that the best constants C_p are bounded near 1. Second, we prove that the Lévy transform is continuous on the Hardy spaces H^p with p>n/(n+1).