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Acid-base reactions --- Acid-base equilibria

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Absolute zero. --- Electrochemistry. --- Energy. --- Enthalpy. --- Equilibria. --- Heat engines. --- Thermochemistry. --- Thermodynamic equilibrium.

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Biological aspects. --- Catalysis. --- Coordination complex. --- Dissymmetry. --- Electron-transfer. --- Equilibria. --- Ligand. --- Metal-ligand bond. --- Substitution.

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Spaces of infinite dimension have played an increasing role in the last four decades concerning their applications in models both for economics and for finance. The intertemporal allocation of resources, commodity differentiation, uncertainty, dynamics of the fundamental variables of financial markets, are some of the issues that can be properly captured by means of the mathematical techniques that are typical in such spaces. This collection contains some recent contributions in this area. Achille Basile, Editor’s Preface Ciro Tarantino, Coalitional fairness with many agents and commodities Anna Canale - Ciro Tarantino, Embedding and compactness results for multiplication operators in Sobolev spaces

Asymmetric information --- embeddings --- ex-post core --- compact operators --- c-fair allocations --- expectations equilibria --- Fefferman inequalities --- rational

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After 99 % of the LMO crystallization, a residual liquid enriched in K, REE and P known as the urKREEP remained. In its latest stages, the urKREEP might have undergone silicate liquid immiscibility producing a ferrobasaltic melt forming the REEP-fraction (enriched in REE, Fe, Ca and Ti) and a granitic melt forming the K-fraction (enriched in Si, Na, K and Al). This liquid separation might be a significant process in the granite formation and phosphates by metasomatism of the ferrobasaltic melt during its ascent. This study aimed at understanding the residual liquid evolution of the magma ocean and had a special interest on the formation of large immiscible droplets. The mineral phases, textures and the influence of parameters (starting temperature, equilibrium time) were also studied. We used Pt-loops in the controlled-atmosphere furnace over 1140-980 °C under reducing conditions (Iron-Wustïte buffer) to produce melt compositions reproducing an evolution by fractional crystallization. First, the Pt-loops were saturated in iron to remove any iron loss from the powders. These powders were stuck on a Pt-loop and placed into the controlled-atmosphere furnace at the starting temperature. A cooling rate of 1 °C/h were used and once the target temperature was reached, maintained for 72h before quenching. Mineral phases were analysed by using the electron microprobe at the university of Aachen. Added to these results, data of isothermal experiments were used to compare immiscible droplets and better constraint the liquid evolution until the onset of immiscibility.
Most experimental products contain olivine, pyroxene, plagioclase, a silica phase (trydimite) and ilmenite. Some show Fe metal, whitlockite, ulvöspinel and two melts. The two-liquid field was reached at 1000 °C where Si-rich granitic melt droplets are formed. Cooling experiments resulted in small size immiscible droplets, while those from isothermal experiments were larger.
During cooling of the LMO residuum, the residual liquid evolved towards a Fenner trend by being enriched in Fe, K, P, Ca and a depletion in Al, Ti enriched until ilmenite saturation and then get depleted. At 1000 °C, the residual liquid entered the two-liquid field producing a granitic melt. Phosphate saturation was only reached in bulk Moon composition enriched in phosphorous. This lack of phosphates prior to immiscibility suggested that they might be formed by the ferrobasaltic melt. As cooling proceeds, ilmenite and fayalite crystallized from the ferrobasaltic melt promoting the rise of this one by metasomatism. However, when metasomatism occurs, a mineral phase is formed beneath the melt: a phosphate. The ferrobasaltic melt being Fe-rich, the first crystallizing phosphate might be a whitlockite and in the late stages of the ferrobasaltic melt, apatite as the melt becomes enriched in halogens.
Almost all experimental products showed a porphyritic texture prior to silicate liquid immiscibility (with only one intergranular texture) and immiscible texture once immiscibility is reached. The little diversity of these textures suggested that using a sufficiently slow cooling rate and decreasing the starting temperature lead to similar textures. Moreover, the equilibrium time seemed to have an impact on the size of immiscible droplets: long equilibrium time produced large immiscible droplets and a mature immiscible texture while shorter ones produced small droplets and an immature texture. 
The origin of lunar granite has two main origins: 1) Production of small volume of granite by silicate liquid immiscibility in depth (their low viscosity preventing them from migrating). 2) Basaltic underplating producing large volume of silicic magma and possibly the cause of silicic volcanism.

Experimental petrology, --- Liquid immiscibility --- urKREEP --- Phase equilibria --- Physique, chimie, mathématiques & sciences de la terre > Sciences de la terre & géographie physique