Equations, inequations and inequalities characterizing the configurations of two real projective conics

Couples of proper, non-empty real projective conics can be classified modulo rigid isotopy and ambient isotopy. We characterize the classes by equations, inequations and inequalities in the coefficients of the quadratic forms defining the conics. The results are well--adapted to the study of the relative position of two conics defined by equations depending on parameters.Comment: 31 pages. See also http://emmanuel.jean.briand.free.fr/publications/twoconics/ Added references to important prior work on the subject. The title changed accordingly. Some typos and imprecisions corrected. To be published in Applicable Algebra in Engineering, Communication and Computin

TO INFORM THEIR DISCRETION: POLICY EDUCATION AND DEMOCRATIC POLITICS

Political Economy,

Marginal Cost Versus Average Cost Pricing with Climatic Shocks in Senegal: A Dynamic Computable General Equilibrium Model Applied to Water

The model simulates on a 20-year horizon, a first phase of increase in the water resource availability taking into account the supply policies by the Senegalese government and a second phase with hydrologic deficits due to demand evolution (demographic growth). The results show that marginal cost water pricing (with a subsidy ensuring the survival of the water production sector) makes it possible in the long term to absorb the shock of the resource shortage, GDP, investment and welfare increase. Unemployment drops and the sectors of rain rice, market gardening and drinking water distribution grow. In contrast, the current policy of average cost pricing of water leads the long-term economy in a recession with an agricultural production decrease, a strong degradation of welfare and a rise of unemployment. This result questions the basic tariff (average cost) on which block water pricing is based in Senegal.Computable General Equilibrium Model, Dynamic, Imperfect Competition, Water, Pricing, Sub Saharan Africa

Crystallization of self-propelled hard-discs : a new scenario

We experimentally study the crystallization of a monolayer of vibrated discs with a built-in polar asymmetry, a model system of active liquids, and contrast it with that of vibrated isotropic discs. Increasing the packing fraction $\phi$, the quasi-continuous crystallization reported for isotropic discs is replaced by a transition, or a crossover towards a "self-melting" crystal. Increasing the packing fraction from the liquid phase, clusters of dense hexagonally-ordered packed discs spontaneously form, melt, split and merge leading to a highly intermittent and heterogeneous dynamics. The resulting steady state cluster size distribution decreases monotonically. For packing fraction larger than $\phi^*$, a few large clusters span the system size and the cluster size distribution becomes non monotonic, the transition being signed by a power-law. The system is however never dynamically arrested. The clusters permanently melt from place to place forming droplets of active liquid which rapidly propagate across the system. This state of affair remains up to the highest possible packing fraction questioning the stability of the crystal for active discs, unless at ordered close packing.Comment: 4 pages, 4 figures, 1 Supp Mat

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

Combinatorial proof for a stability property of plethysm coefficients

Plethysm coefficients are important structural constants in the representation the- ory of the symmetric groups and general linear groups. Remarkably, some sequences of plethysm coefficients stabilize (they are ultimately constants). In this paper we give a new proof of such a stability property, proved by Brion with geometric representation theory techniques. Our new proof is purely combinatorial: we decompose plethysm coefficients as a alternating sum of terms counting integer points in poly- topes, and exhibit bijections between these sets of integer points.Ministerio de Ciencia e Innovación MTM2010–19336Junta de Andalucía FQM–333Junta de Andalucía P12–FQM–269

On the growth of the Kronecker coefficients

We study the rate of growth experienced by the Kronecker coefficients as we add cells to the rows and columns indexing partitions. We do this by moving to the setting of the reduced Kronecker coefficients.Comment: Extended version, Containing 4 appendice