Quadratic BSDEs with convex generators and unbounded terminal conditions

In a previous work, we proved an existence result for BSDEs with quadratic generators with respect to the variable z and with unbounded terminal conditions. However, no uniqueness result was stated in that work. The main goal of this paper is to fill this gap. In order to obtain a comparison theorem for this kind of BSDEs, we assume that the generator is convex with respect to the variable z. Under this assumption of convexity, we are also able to prove a stability result in the spirit of the a priori estimates stated in the article of N. El Karoui, S. Peng and M.-C. Quenez. With these tools in hands, we can derive the nonlinear Feynman--Kac formula in this context

On the growth of Kronecker coefficients (extended abstract)

We present a new stability phenomenon for Kronecker coefficients, that we call hook stability: the Kronecker coefficients stabilize if we add cells to the first row and first column of each of the indexing partitions, simultaneously. We also show that when we increase the sizes of the first two rows of their three indexing partitions, in some appropriate way, the Kronecker coefficients grow linearly, and we are able to give asymptotic estimates

Choix d’approvisionnement en eau des ménages de Dakar : une étude économétrique à partir de données d’enquête

International audienc

Influence de la pluviométrie sur la contamination de l'atmosphère et des eaux de pluie par les pesticides

Cette étude a pour objectif d'identifier les facteurs qui influencent la contamination des eaux de pluie par les produits phytosanitaires. Cinq sites contrastés ont été choisis de manière à être représentatifs des zones de productions légumières ou de plein champs et à couvrir les différents modes de contamination des précipitations. Il s'agit des sites de l'Ile de Ouessant, Landivisiau, Plouay, Ploufragan et Rennes. Les évènements pluvieux collectés sont choisis en fonction des caractéristiques de formation de la perturbation et du calendrier des épandages de pesticides.Par ailleurs, les concentrations rencontrées pour le site de Rennes en 2000 (année très humide) ont pu être comparées à celles obtenues lors d'une étude conduite en 1996 sur un site proche mais pour des conditions climatiques plus habituelles (année humide à sèche).Les analyses sont réalisées par extraction en phase solide suivie d'une analyse en chromatographie en phase gazeuse couplée à la spectrométrie de masse, ou par détection azote-phosphore spécifique (NPD) ou détection par capture d'électrons pour les composés halogénés (ECD). Dans ces deux derniers cas, la confirmation de l'identité des produits est réalisée par un système de double colonnes.Sept évènements pluvieux distincts ont été collectés et analysés entre les 15 mars et 15 juillet de l'année 2000. Parmis les produits recherchés six molécules sont régulièrement retrouvées : l'atrazine et son métabolite la déethylatrazine (DEA), l'alachlore, le lindane (gamma HCH) et son isomère le béta HCH ainsi que la desméthryne. Nous avions déjà des observations analogues à l'issu de nos premières investigations de 1996.Les analyses réalisées ont montré l'existence d'une contamination chronique du compartiment atmosphérique par l'atrazine et la DEA pour les zones sous influence agricole. Les niveaux de concentrations rencontrés sont faibles, de l'ordre de 10 ng/L. A ce bruit de fond s'ajoutent en période de traitement, des transferts depuis les parcelles traitées qui conduisent à des valeurs beaucoup plus élevées (de 0,1 à 0,7 µg.L-1). La détection de l'alachlore et de la desmethryne est limitée aux périodes d'application de ces produits.Du lindane, et dans un cas son isomère le béta-HCH, ont pu être mis en évidence sur quelques prélèvements, traduisant une contamination chronique du compartiment aérien due à la rémanence de ce type de composés.Les concentrations dans les pluies, pour un site donné, sont très dépendantes de la pluviométrie. Alors qu'en année de pluviosité normale (1996), les concentrations en période d'application sont élevées, elles restent faibles pour une année humide (2000). Pour s'affranchir de l'effet de dilution, nous avons calculé des retombées massiques (mg.ha-1) pour les deux périodes de collecte de 1996 et 2000. Les résultats de 2000 restent malgré cela très inférieurs à ceux de 1996 (d'un facteur quatre environ). Les surfaces emblavées et les différences d'usage entre les deux années sont trop faibles pour expliquer les écarts obtenus. Ceci nous permet de conclure que c'est l'intensité des transferts sol-air qui détermine les niveaux de contamination de l'atmosphère. L'humidité élevée des sols, pour une année humide, favorise la migration verticale des produits phytosanitaires dans les couches inférieures, réduisant ainsi les concentrations de pesticides susceptibles d'être transférés vers le compartiment aérien.Contamination of rainwater by pesticides was investigated by analyzing samples from 5 locations in Brittany (France). These sites were chosen on the basis of various characteristics including agricultural practices around the site, the direction of prevailing winds (west to east) and the proximity to heavily populated areas. The sites chosen were: Ile de Ouessant (a natural reserve without pesticide application), Landivisiau (a semi-natural zone), Plouay (a rural site with intensive agriculture, mainly cereals and vegetables), Ploufragan (a suburban site) and Rennes (an urban area surrounded by intensive agriculture and orchards). The pesticides to be monitored included the compounds most commonly used in Brittany. New molecules were added to this list to take into account new homologues or uses. Some organochlorines and pesticides with specific application modes were thus included in the list. Analytical techniques involved solid-liquid extraction procedures followed by GC-NPD, GC-ECD or GC-MS after prior derivatisation. Derivatisation was performed with heptafluorobutyric acid to detect urea and sulfonylurea herbicides. Quantification limits were about 5 ng/L for GC-ECD or GC-NPD, and 50 ng/L for molecules detected by GC-MS after derivatisation.Rain episodes were selected according to the prevailing meteorological conditions and the air mass trajectory. Only precipitation events greater than 6 mm were considered, in order to collect sufficient volume for analyses. Thirty-five samples (7 per location) were collected between 15 March and 15 July 2000, corresponding to various weather fronts.Six pesticides were detected: atrazine and its metabolite de-ethylatrazine (DEA), alachlor, desmethryne, lindane and its isomer (beta HCH). Among those detected most concentrations were below 100 ng/L but higher concentrations were occasionally detected during and after spraying in agricultural areas. Lindane was detected at low concentration (<10 ng/L) in several samples collected during different periods and locations. These results demonstrate chronic atmospheric contamination due to the presence of this substance even though its use has been banned in the Economic European Community (EEC) (e.g. in 1999 in France).The most frequently detected compound was atrazine, detected in 60 % of the samples. The presence of atrazine and its metabolite DEA in rainfall indicate chronic contamination of the atmosphere outside of spraying time (mid-March to mid-April). Detection of these compounds was generally limited to agricultural sites, and could also indicate transfer from agricultural areas during soil preparation for maize sowing. These hypotheses will be tested by monitoring atrazine in rainwater during a complete agricultural cycle. Important contamination by atrazine was detected during spraying time at agricultural locations, where concentrations ranged from 10 to 60 ng/L. Detection of alachlor was limited to application periods and rural sites, at levels ranging from 20 to 240 ng/L. However, amounts of alachlor were also detected in Ouessant, even though its use is banned on this isle. This presence was presumably due to the specific conditions of formation of the weather fronts that resulted in rainfall.Concentrations of pesticides in rainwater obtained in 2000 were generally lower than those described in literature or in a previous study done in Brittany. Alachlor and atrazine concentrations were compared to those of a previous study conducted in Brittany in 1996. The two sites chosen were Rennes in 2000 and Le Rheu in 1996. These two locations, separated by 5 km, were not significantly different since Rennes is directly downwind of Le Rheu. Pluviometry was very important in the year 2000, showing a 30 % increase in rainfall compared to the average from 1961-1990. The concentrations of pesticides in both years were also very different. During a year of normal rainfall (e.g., 1996) concentrations of pesticides in application periods were high, but they remained low during wet years (e.g., 2000). These differences could not be explained by a dilution effect - when fall-out was calculated (mg/ha) to correct for the dilution effect, the differences remained important. Maize surfaces (132 000 ha in 1996 compared to 128 000 ha in 2000) and the quantities of pesticides applied (580 tonnes in 1994 in Brittany compared to 350 tonnes for atrazine, and 263 tonnes in 1998 compared to 119 tonnes in 1994 for alachlor) were too similar to explain the differences observed in 1998. Photodegradation processes, which are more important during normal or dry years, should also favour higher concentrations in 2000 than in 1996. Rain concentrations and fallout observed in 2000 remained lower than those obtained in 1996. Thus, it can be concluded that atmospheric contamination is lower for wet years (e.g., 2000) than for normal or dry years (e.g., 1996). Soil humidity, high for wet years, favours the vertical migration of these substances to lower soil layers, reducing pesticide concentrations available to be transferred to the atmosphere

Hamilton Jacobi Bellman equations in infinite dimensions with quadratic and superquadratic Hamiltonian

We consider Hamilton Jacobi Bellman equations in an inifinite dimensional Hilbert space, with quadratic (respectively superquadratic) hamiltonian and with continuous (respectively lipschitz continuous) final conditions. This allows to study stochastic optimal control problems for suitable controlled Ornstein Uhlenbeck process with unbounded control processes

A study of the effectiveness of a phonetic and activity approach to the teaching of spelling in grade four,

Includes appendices. Thesis (M.A.)--Boston Universit

Quadratic BSDEs driven by a continuous martingale and application to utility maximization problem

In this paper, we study a class of quadratic Backward Stochastic Differential Equations (BSDEs) which arises naturally when studying the problem of utility maximization with portfolio constraints. We first establish existence and uniqueness results for such BSDEs and then, we give an application to the utility maximization problem. Three cases of utility functions will be discussed: the exponential, power and logarithmic ones

Differentiability of backward stochastic differential equations in Hilbert spaces with monotone generators

The aim of the present paper is to study the regularity properties of the solution of a backward stochastic differential equation with a monotone generator in infinite dimension. We show some applications to the nonlinear Kolmogorov equation and to stochastic optimal control

Surface intermediate species of the 4-isobutylacetophenone adsorption-reaction over fosfotungstic Wells-Dawson heteropoly acid

Surface adsorbed species of isobutybenzene and 4-isobutylacetophenone on bulk fosfotungstic Wells-Dawson acid H6P2W18O62.xH2O (HPA) have been screened in the present investigation. The evolution of chemisorbed species towards products was followed through infrared spectroscopy of systems containing liquid reactants and the solid acid kept at various temperatures. 4-Isobutylacetophenone adsorbs on Brønsted acid sites of the heteropoly acid and further reacts towards a condensation product similarly to the reaction of acetophenone over other acid materials such as, mordenite, niobic acid and sulfated zirconia. The condensation product possesses well defined infrared signals at 1654 cm-1 and 1597 cm-1 that resemble the carbonyl stretching vibration and the double bond of dypnone C6H5COHC=C(CH3)C6H5. Additional signals at 1221 cm-1 and a shoulder at 1284 cm-1 ascribed to the vibration of the C6H5 species in the C6H5COHC= group, give more evidences of the formation of a chalcone type compound. A reaction mechanism of the Aldol condensation of 4-isobutylacetophenone through an enol reactive intermediate is proposed.Centro de Investigación y Desarrollo en Ciencias Aplicada