Notes sur la fonction ζ de Riemann, 4

Opération fondamentale de l'arithmétique, familière depuis des millénaires, la division euclidienne n'a pas livré tous ses secrets. Ainsi, notons pour k et a entiers positifs, le reste de la division euclidienne de k par a, et imaginons un instant que, par un choix convenable d'un entier n et de réels c₂,…,c_n, nous sachions rendre arbitrairement petite la quantité

     

The dispersive effect of cross-aging with archimedean copulas

In this work, we compare conditional distributions derived from bivariate archimedean copulas in terms of their respective variabilities using the dispersive stochastic order. Specifically, we fix the underlying copula and we consider the effect of increasing the second component on the variability of the conditional distribution of the first component. Characterizations are provided in terms of the generator and of the marginal distributions. Several examples involving standard parametric copulas such as Clayton and Frank ones are discussed.     

Silver ionic conductivity enhancement by network former mixed in oxide-based glasses

Glasses in the binary system xAg₂P₂O₆ − (1 − x)Ag₂Te₂O₅ have been prepared for 0 x 1. For each composition only one glass transition temperature is observed in the temperature range of 180–220 °C. All glasses appear homogeneous considering their optical and electrical properties. Nevertheless, in SEM observations, some glass compositions appear to be heterogeneous after decoration following short nitric acid etching. For each composition, conductivity data obtained in the temperature range of 25–200 °C using impedance techniques obey an Arrhenius relationship with a composition independent pre-exponential term. Variation of the conductivity activation energy with x induces correlative variations of isothermal conductivity curves leading to an increase of the ionic conductivity of about one order of magnitude compared with linearity at 25 °C. This behaviour is discussed with respect to the thermodynamic properties of the glassy solutions.     

Long-Time Bath Correlations in the Pollak–Grabert–Hänggi Theory

We analyze some cases for which the Pollak–Grabert–Hänggi theory on the activated rate processes for generalized Langevin dynamics exhibits unexplained disagreements with numerical results. First we analyze carefully the PGH theory and we show that a kind of Markovian hypothesis implicitly made in the reasoning is sometimes violated. Then we propose modifications of the original theory in order to take into account the possible effects caused by this violation, and we compare the corrected results with simulations.     

Weak invariance of the multidimensional rank statistic for nonstationary absolutely regular processes

In this paper, we study the weak invariance of the multidimensional rank statistic when the underlying random variables are nonstationary absolutely regular.     

基于耦合道Gamow壳模型计算17O和17F的能谱以及16O(p,p)反应的微分散射截面

利用耦合道Gamow壳模型计算了17O和17F的低激发能谱以及16O(p,p)反应的低能弹性散射截面。结果表明,17O和17F中非束缚共振态能级的核子发射宽度的计算需要合理地考虑连续态耦合效应。计算得到的17O和17F的低激发能谱以及16O(p,p)反应的低能弹性散射激发函数都与实验数据吻合较好。这说明基于现实核力的计算可更好地描述16O(p,p)反应的低能弹性散射截面。     

A tabu search procedure for multicommodity location/allocation with balancing requirements

We propose a tabu search heuristic for the location/allocation problem with balancing requirements. This problem typically arises in the context of the medium term management of a fleet of containers of multiple types, where container depots have to be selected, the assignment of customers to depots has to be established for each type of container, and the interdepot container traffic has to be planned to account for differences in supplies and demands in various zones of the geographical territory served by a container shipping company. It is modeled as a mixed integer program, which combines zero-one location variables and a multicommodity network flow structure. Extensive computational results on a set of benchmark problems and comparisons with an efficient dual ascent procedure are reported. These show that tabu search is a competitive approach for this class of problems.     

The cut cone III: On the role of triangle facets

The cut polytopeP _n is the convex hull of the incidence vectors of the cuts (i.e. complete bipartite subgraphs) of the complete graph onn nodes. A well known class of facets ofP _n arises from the triangle inequalities:x _ij +x _ik +x _jk ≤ 2 andx _ij -x _ik -x _jk ≤ 0 for 1 ≤i,j, k ≤n. Hence, the metric polytope M_n, defined as the solution set of the triangle inequalities, is a relaxation ofP _n . We consider several properties of geometric type for P_n, in particular, concerning its position withinM _n . Strengthening the known fact ([3]) thatP _n has diameter 1, we show that any set ofk cuts,k ≤ log₂ n, satisfying some additional assumption, determines a simplicial face ofM _n and thus, also, ofP _n . In particular, the collection of low dimension faces ofP _n is contained in that ofM _n . Among a large subclass of the facets ofP _n , the triangle facets are the closest ones to the barycentrum of P_n and we conjecture that this result holds in general. The lattice generated by all even cuts (corresponding to bipartitions of the nodes into sets of even cardinality) is characterized and some additional questions on the links between general facets ofP _n and its triangle facets are mentioned.     

Stochastic production frontiers and panel data: A latent variable framework

This paper deals with the issue of estimating production frontier and measuring efficiency from a panel data set. First, it proposes an alternate method for the estimation of a production frontier on a short panel data set. The method is based on the so-called mean-and-covariance structure analysis which is closely related to the generalized method of moments. One advantage of the method is that it allows us to investigate the presence of correlations between individual effects and exogenous variables without the requirement of some available instruments uncorrelated with the individual effects as in instrumental variable estimation. Another advantage is that the method is well suited to a panel data set with a short number of periods. Second, the paper considers the question of recovering individual efficiency levels from the estimates obtained from the mean-and-covariance structure analysis. Since individual effects are here viewed as latent variables, they can be estimated as factor scores, i.e., weighted sums of the observed variables. We illustrate the proposed methods with the estimation of a stochastic production frontier on a short panel data of French fruit growers.     

Concretely Locally Presentable and Locally Generated Categories

We give concrete versions of the characterizations of locally -presentable (resp. -generated) categories as categories of models of (resp. weakly) -ary limit-theories and of (resp. weakly) -ary essentially algebraic theories. By concrete we mean that starting with a category of -structures, the theories obtained are extensions of the original ones, and the equivalences of categories are concrete isomorphisms. -presentable and -generated objects are also investigated from this viewpoint.