Traité de l'existence et des attributs de Dieu (Nouvelle édition, accompagnée de notes et précédée d'une introduction et d'une analyse des chapitres, par M. Alph. Aulard,...) / par Fénelon

[Traité de l'existence de Dieu (français). 1878]

Traité de l'existence et des attributs de Dieu ; suivi de Lettres sur divers sujets de métaphysique et de religion / par Fénelon,...

[Traité de l'existence de Dieu (français). 1878]

Existence of sparsely supported correlated equilibria

We show that every finite N-player normal form game possesses a correlated equilibrium with a precise lower bound on the number of outcomes to which it assigns zero probability. In particular, the largest games with a unique fully supported correlated equilibrium are two-player games; moreover, the lower bound grows exponentially in the number of players N.

Constraints and non-existence of rational expectations equilibria

In this article we show that in the presence of trading constraints, such as short sale constraints, the standard definition of a Rational Expectations Equilibrium allows for equilibrium prices that reveal information unknown to any active trader in the market. We propose a new definition of the Rational Expectations Equilibrium that incorporates a stronger measurability condition than measurability with respect to the join of the information sets of the agents and give an example of non-existence of equilibrium. The example is robust to perturbations on the data of the economy and the introduction of new assets.

On the existence of doubling measures with certain regularity properties

Given a compact pseudo-metric space, we associate to it upper and lower dimensions, depending only on the pseudo-metric. Then we construct a doubling measure for which the measure of a dilated ball is closely related to these dimensions.

On the existence of bi-pyramidal central configurations of the n + 2-body problem with an n-gon base

Abstract. In this paper we prove the existence of central con gurations of the n + 2{body problem where n equal masses are located at the vertices of a regular n{gon and the remaining 2 masses, which are not necessarily equal, are located on the straight line orthogonal to the plane containing the n{gon passing through its center. Here this kind of central con gurations is called bi{pyramidal central con gurations. In particular, we prove that if the masses mn+1 and mn+2 and their positions satisfy convenient relations, then the con guration is central. We give explicitly those relations.

Direct evidence for the existence of dairying farms in prehistoric Central Europe (4th millennium BC)

The molecular and isotopic chemistry of organic residues from archaeological potsherds was used to obtain further insight into the dietary trends and economies at the Constance lake-shore Neolithic settlements. The archaeological organic residues from the Early Late Neolithic (3922-3902 BC) site Hornstaad-Hornle IA/Germany are, at present, the oldest archaeological samples analysed at the Institute of Mineralogy and Geochemistry of the University of Lausanne. The approach includes 13C/12C and 15N/14N ratios of the bulk organic residues, fatty acids distribution and 13C/12C ratios of individual fatty acids. The results are compared with those obtained from the over 500 years younger Neolithic (3384-3370 BC) settlement of Arbon Bleiche 3/Switzerland and with samples of modern vegetable oils and fat of animals that have been fed exclusively on C3 forage grasses. The overall fatty acid composition (C9 to C24 range, maximizing at C14 and C16), the bulk 13C/12C and 15N/14N ratios (delta13C, delta15N) and the 13C/12C ratios of palmitic (C16:0), stearic (C18:0) and oleic acids (C18:1) of the organic residues indicate that most of the studied samples (25 from 47 samples and 5 from 41 in the delta13C18:0 vs. delta13C16:0 and delta13C18:0 vs. delta13C18:1 diagrams, respectively) from Hornstaad-Hornle IA and Arbon Bleiche 3 sherds contain fat residues of pre-industrial ruminant milk, and young suckling calf/lamb adipose. These data provide direct proof of milk and meat (mainly from young suckling calves) consumption and farming practices for a sustainable dairying in Neolithic villages in central Europe around 4000 BC.dagger