University of Marne-la-Vallée

About: University of Marne-la-Vallée is a based out in . It is known for research contribution in the topics: Estimator & Context (language use). The organization has 831 authors who have published 1855 publications receiving 55316 citations.

Nonconventional ergodic averages and nilmanifolds

Abstract: We study the L2-convergence of two types of ergodic averages. The first is the average of a product of functions evaluated at return times along arithmetic progressions, such as the expressions appearing in Furstenberg?fs proof of Szemer?Ledi?fs theorem. The second average is taken along cubes whose sizes tend to +??. For each average, we show that it is sufficient to prove the convergence for special systems, the characteristic factors. We build these factors in a general way, independent of the type of the average. To each of these factors we associate a natural group of transformations and give them the structure of a nilmanifold. From the second convergence result we derive a combinatorial interpretation for the arithmetic structure inside a set of integers of positive upper density.

Complete Destruction of p-Nitrophenol in Aqueous Medium by Electro-Fenton Method

Abstract: An indirect electrochemical method, which is very efficient for the degradation of organic pollutants in water, is described. The method, named electro-Fenton, is based on electrocatalytical generation of Fenton's reagent to produce hydroxyl radicals, which are very active toward organic compounds. An industrial pollutant, p-nitrophenol (PNP), was chosen for this study and was eventually mineralized. The major intermediary degradation products such as hydroquinone, benzoquinone, 4-nitrocatechol, 1,2,4-trihydroxybenzene and 3,4,5-trihydroxy- nitrobenzene were unequivocally identified by HPLC and GC-MS methods. The rate constants of the hydroxylation reactions were determined. The mineralization of the initial pollutant and the intermediates formed during electro-Fenton treatment was followed by total organic carbon (TOC) analyses. Dependence of mineralization on the amount of electrical energy consumed is shown by the relative decrease of TOC values. A mineralization reaction mechanism is proposed.

Gaussian multiplicative chaos and applications: A review

Abstract: In this article, we review the theory of Gaussian multiplicative chaos initially introduced by Kahane’s seminal work in 1985. Though this beautiful paper faded from memory until recently, it already contains ideas and results that are nowadays under active investigation, like the construction of the Liouville measure in $2d$-Liouville quantum gravity or thick points of the Gaussian Free Field. Also, we mention important extensions and generalizations of this theory that have emerged ever since and discuss a whole family of applications, ranging from finance, through the Kolmogorov-Obukhov model of turbulence to $2d$-Liouville quantum gravity. This review also includes new results like the convergence of discretized Liouville measures on isoradial graphs (thus including the triangle and square lattices) towards the continuous Liouville measures (in the subcritical and critical case) or multifractal analysis of the measures in all dimensions.

Strong consistency of estimators for multivariate arch models

Abstract: This paper deals with the asymptotic properties of quasi-maximum likelihood estimators for multivariate heteroskedastic models. For a general model, we give conditions under which strong consistency can be obtained; unlike in the current literature, the assumptions on the existence of moments of the error term are weak, and no study of the various derivatives of the likelihood is required. Then, for a particular model, the multivariate GARCH model with constant correlation, we describe the set of parameters where these conditions hold.

Continuous-time predictive-maintenance scheduling for a deteriorating system

Abstract: A predictive-maintenance structure for a gradually deteriorating single-unit system (continuous time/continuous state) is presented in this paper. The proposed decision model enables optimal inspection and replacement decision in order to balance the cost engaged by failure and unavailability on an infinite horizon. Two maintenance decision variables are considered: the preventive replacement threshold and the inspection schedule based on the system state. In order to assess the performance of the proposed maintenance structure, a mathematical model for the maintained system cost is developed using regenerative and semi-regenerative processes theory. Numerical experiments show that the s-expected maintenance cost rate on an infinite horizon can be minimized by a joint optimization of the replacement threshold and the a periodic inspection times. The proposed maintenance structure performs better than classical preventive maintenance policies which can be treated as particular cases. Using the proposed maintenance structure, a well-adapted strategy can automatically be selected for the maintenance decision-maker depending on the characteristics of the wear process and on the different unit costs. Even limit cases can be reached: for example, in the case of expensive inspection and costly preventive replacement, the optimal policy becomes close to a systematic periodic replacement policy. Most of the classical maintenance strategies (periodic inspection/replacement policy, systematic periodic replacement, corrective policy) can be emulated by adopting some specific inspection scheduling rules and replacement thresholds. In a more general way, the proposed maintenance structure shows its adaptability to different possible characteristics of the maintained single-unit system.