Homotopy groups of EChG24∧A1E_{C}^{hG_{24}}\wedge A_1

Let $A_1$ be any spectrum in a class of finite spectra whose mod $2$ cohomology is isomorphic to a free module of rank one over the subalgebra $\mathcal{A}(1)$ of the Steenrod algebra. Let $E_{C}$ be the second Morava-$E$ theory associated to a universal deformation of the formal completion of the supersingular elliptic curve $(C) : y^{2}+y = x^{3}$ defined over $\mathbb{F}_{4}$ and $G_{24}$ a maximal finite subgroup of automorphism group $\mathbb{S}_{C}$ of the formal completion of $C$. In this paper, we compute the homotopy groups of $E_{C}^{hG_{24}}\wedge A_1$ by means of the homotopy fixed point spectral sequence.Comment: 82 pages, 29 figure

Traçage de l'empreinte lithogénique en mers de Corail et des Salomon : apport des terres rares et de la composition isotopique du neodyme

Le but de cette thèse était de mieux contraindre les flux continent-océan à l'aide de traceurs géochimiques, les terres rares (REE) et la composition isotopique du néodyme (Nd-IC), en se focalisant sur les mers de Corail et des Salomon, région de l'Océan Pacifique Sud-Ouest (OPS) où circulent les eaux alimentant le Pacifique Equatorial et qui est le siège d'importantes modifications hydrologiques et géochimiques des masses d'eau. Un nouveau protocole analytique des terres rares dissoutes (dREE)a été développé. Ce système 'seaSLOW' permet la préconcentration simultanée de 8 échantillons d'eau de mer, réduisant considérablement le temps d'analyse, avec un excellent blanc de chimie -moins de 0,5% du signal de dREE-, des limites de détection ~1/40 de la concentration moyenne d'eau de mer et des rendements > 90%. Mais surtout, le seaSLOW est peu coûteux, facile à fabriquer, ce qui le rend accessible pour d'autres utilisateurs, en particulier des pays en développement. Les profils verticaux de dREE ont été réalisés pour 143 échantillons prélevés en mers de Corail et des Salomon (campagne PANDORA; été 2012). Les concentrations de dREE - à l'exception du Ce insoluble - montrent des profils de type nutriment soit de faibles valeur en surface et plus riches en profondeur (ex: les concentrations de Nd varient de ~ 5 à 25 pmol / kg entre surface et fond) Des enrichissements locaux en dREE sont observés le long des côtes et dans les trois détroits, sorties de la mer Salomon. Des modèles en boite révèlent un enrichissement net significatif de REE dans la thermocline inférieure (soit: 145 ± 46 tNd / an). L'empreinte basaltique a été mise en évidence par des anomalies positives Eu et Ce, en particulier dans la couche de surface. La très bonne corrélation entre les Terres Rares lourdes et le silicium dissous est confirmée. Ces résultats sont publiés dans Pham et al (2019). Le Nd-IC dissous a également été mesuré sur les mêmes échantillons. Les distributions des deux paramètres Nd (concentration Nd et Nd-IC) entre la mer de Corail, l'entrée et la sortie de la mer Salomon ont été établies sous forme de profils verticaux et de cartes représentant les couches transportant les différentes masses d'eau. Les profils verticaux montrent tous plus de Nd-IC radiogénique dans la couche de surface (jusqu'à εNd = +3), des valeurs minimales de eNd à des profondeurs intermédiaires (~ 1100m) avant d'augmenter à nouveau en profondeur. À l'échelle régionale, des signaux de Nd-IC très positifs sont observés aux sorties nord de la mer Salomon, reflétant probablement la libération de matières radiogèniques dans les masses d'eau au cours de leur parcours à travers la mer Salomon. L'occurrence de processus d'échange aux frontières (BE) a été suggérée à de nombreux endroits, soit à l'échelle locale (ex: les eaux de surface traversant Indispensable Strait) ou à l'échelle régionale (ex: les eaux profondes à travers la mer Salomon). La quantification du BE via des modèles en boîtes a pu être réalisée pour la partie inférieure de la thermocline inférieure (LLTW) et la couche supérieure des couches d'eau profonde (UCDW). À titre d'illustration, l'apport externe de Nd nécessaire pour équilibrer à la fois les variations de Nd-IC et les concentrations de Nd de la couche profonde supérieure (UCDW) entre l'entrée sud et les sorties nord de la Mer des Salomon est de 105 ± 50 TNd / an. L'application des deux paramètres Nd a permis de mieux identifier les sources de matière et de réduire les incertitudes affectant les processus. Les études futures de ces distributions de paramètres sur les particules en suspension collectées aux mêmes stations permettront d'obtenir une image complète des processus régissant les échanges entre particules et dissous.The aim of this thesis was to better constrain the land-ocean fluxes using geochemical tracers, Rare Earth Element (REE) and Neodymium Isotopic Composition (Nd-IC). The studied area was the Coral and Solomon Seas, a part of the Southwest Pacific Ocean (SPO) where the waters feeding the Equatorial Pacific Ocean are circulating which confers an important role in the climate regulation to this area. The SPO is also a place where important hydrological and chemical modifications of the water masses occur. A new dREE analytical protocol was developed to replace the one used for years in my research team. This "seaSLOW" manifold allows the simultaneous treatment of 8 seawater samples, dramatically reducing the analytical time, with a low matrix blank signal - less than 0.5% for dREE signal. Affordable detection limits (equal ~1/40 of the average seawater concentration) and high quantitative recoveries (>90%) were obtained during the blank and performance tests, respectively. The strong points of seaSLOW are that it is low-cost (equal one fifteenth of the commercial product seaFAST) and easy to fabricate, making it accessible for other users, including developing countries. Vertical profiles of dissolved REE (dREE) concentrations for 143 samples collected in the Coral and Solomon Seas as part of the PANDORA cruise in summer 2012 were analyzed. dREE concentration -except the insoluble Ce- indicates the nutrient like profiles, i.e. low values at the surface increasing at depth (e.g. Nd concentrations range from ~5 pmol/kg at the surface to ~ 25 pmol/kg in the deepest layers). Local dREE enrichments are observed along the coast and in the three northern exiting straits of the Solomon Sea (a.k.a: Indispensable, Solomon and Vitiaz Straits). dREE variations in the different water layers were quantified using box models, pointing out a net enrichment of 145 ± 46 tNd/year in the lower thermocline. The basaltic material imprint was brought to light by positive Eu and Ce anomalies, especially in surface layer. The better correlation between heavy REE (HREE) and Si cycle than that observed for the LREE in the oceanic water was also confirmed. These results are published in Chemical Geology (Pham et al, 2019). Dissolved Nd-IC were also measured on the same samples. The distributions of both Nd parameters (Nd concentration and Nd-IC) between the the Coral Sea, the entrance and the exit of the Solomon Sea were established as vertical profiles and as maps representing the layers transporting the different water bodies. All the vertical profiles show similar patterns with more radiogenic Nd-IC in the surface layer (up to εNd = +3), minimal e_Nd values at Intermediate depths (~1100m) before increasing again toward the bottom. On a regional scale, higher Nd-IC signals are observed at the northern exits than at the southern entrance of the Solomon Sea, likely reflecting the release of radiogenic material to the water masses during their pathways across the Solomon Sea. The occurrence of boundary exchange (BE) processes were suggested at many place within the sea, either at a local scale (e.g: surface water passing through Indispensable strait) or at the regional scale (e.g: deep water across the Solomon Sea). Quantification of BE via box models was conducted for the lower part of the Lower thermocline (LLTW) and the upper layer of the deep water layers (UCDW). As an illustration, the external input of Nd required to balance both the Nd-IC and Nd concentrations of the upper deep layer (UCDW) between the southern entrance and the northern exits is of 105±50 TNd/y. Applying Nd both parameters helped to better identify the sources of material and to reduce the uncertainties affecting the processes. Future studies of these parameter distributions on the suspended particles collected at the same stations will help to get a full picture of the processes governing the dissolved-particulate exchanges

A global optimization approach to pooling problems in refineries

The pooling problem is an important optimization problem that is encountered in operation and scheduling of important industrial processes within petroleum refineries. The key objective of pooling is to mix various intermediate products to achieve desired properties and quantities of products. First, intermediate streams from various processing units are mixed and stored in intermediate tanks referred to as pools. The stored streams in pools are subsequently allowed to mix to meet varying market demands. While these pools enhance the operational flexibility of the process, they complicate the decisionmaking process needed for optimization. The problem to find the least costly mixing recipe from intermediate streams to pools and then from pools to sale products is referred to as the pooling problem. The research objective is to contribute an approach to solve this problem. The pooling problem can be formulated as an optimization program whose objective is to minimize cost or maximize profit while determining the optimal allocation of intermediate streams to pools and the blending of pools to final products. Because of the presence of bilinear terms, the resulting formulation is nonconvex which makes it very difficult to attain the global solution. Consequently, there is a need to develop computationally-efficient and easy-to-implement global-optimization techniques to solve the pooling problem. In this work, a new approach is introduced for the global optimization of pooling problems. The approach is based on three concepts: linearization by discretizing nonlinear variables, pre-processing using implicit enumeration of the discretization to form a convex-hull which limits the size of the search space, and application of integer cuts to ensure compatibility between the original problem and the discretized formulation. The continuous quality variables contributing to bilinear terms are first discretized. The discretized problem is a mixed integer linear program (MILP) and can be globally solved in a computationally effective manner using branch and bound method. The merits of the proposed approach are illustrated by solving test case studies from literature and comparison with published results