Proof of a conjecture by Gazeau et al. using the Gould Hopper polynomials

We prove the "strong conjecture" expressed by Gazeau et al. in arXiv:1203.3936v1 [math-ph] about the coefficients of the Taylor expansion of the exponential of a polynomial. This implies the "weak conjecture" as a special case. The proof relies mainly about properties of the Gould-Hopper polynomials

The Master Equation for Large Population Equilibriums

We use a simple N-player stochastic game with idiosyncratic and common noises to introduce the concept of Master Equation originally proposed by Lions in his lectures at the Coll\`ege de France. Controlling the limit N tends to the infinity of the explicit solution of the N-player game, we highlight the stochastic nature of the limit distributions of the states of the players due to the fact that the random environment does not average out in the limit, and we recast the Mean Field Game (MFG) paradigm in a set of coupled Stochastic Partial Differential Equations (SPDEs). The first one is a forward stochastic Kolmogorov equation giving the evolution of the conditional distributions of the states of the players given the common noise. The second is a form of stochastic Hamilton Jacobi Bellman (HJB) equation providing the solution of the optimization problem when the flow of conditional distributions is given. Being highly coupled, the system reads as an infinite dimensional Forward Backward Stochastic Differential Equation (FBSDE). Uniqueness of a solution and its Markov property lead to the representation of the solution of the backward equation (i.e. the value function of the stochastic HJB equation) as a deterministic function of the solution of the forward Kolmogorov equation, function which is usually called the decoupling field of the FBSDE. The (infinite dimensional) PDE satisfied by this decoupling field is identified with the \textit{master equation}. We also show that this equation can be derived for other large populations equilibriums like those given by the optimal control of McKean-Vlasov stochastic differential equations. The paper is written more in the style of a review than a technical paper, and we spend more time and energy motivating and explaining the probabilistic interpretation of the Master Equation, than identifying the most general set of assumptions under which our claims are true

Portuguese honey consummer's attitudes and characterization

Este estudo tem como principais objectivos determinar o perfil do consumidor do mel em Portugal e as suas atitudes face ao produto, à produção e ao consumo de mel. Para esse efeito foi elaborado e aplicado um questionário directo online. Este questionário foi aplicado uma amostra representativa de 1037 indivíduos. Foi efectuado um pré-teste do inquérito com cerca de 30 inquiridos. Foram ainda analisadas as atitudes face ao produto, o apoio à apicultura, o foco apícola e as normas subjectivas sobre a produção e ao consumo de mel efectuado de acordo com da Teoria do Comportamento Planeado (TCP) de Ajzen.The aim of this study is to evaluate the honey consumer’s profile in Portugal and their attitudes towards the product, the production and consumption of honey. For this purpose was developed and applied a questionnaire directly online. This questionnaire was completed by a representative sample of 1037 persons. It made a pre-test review with 30 respondents. We also analyzed the attitudes towards the product, supporting beekeeping, beekeeping focus and subjective norms on production and consumption of honey made in accordance with the Theory of Planned Behaviour (TCP) of Ajzen

Heat flux identification using reduced model and the adjoint method. Application to a brake disk rotating at variable velocity

International audienceIn previous works [1], reduced models have been used for solving inverse problems, characterized by a complex geometry requiring a large number of nodes and / or an objective of online identification. The treated application was a brake disc in two-dimensional representation, in rotation at variable speed. The dissipated heat flux at the pad-disk interface had been identified by Beck's method. We present here a similar application using the adjoint method. The modal reduction is done by using special bases (called branch bases) that offer the advantage of dealing with nonlinear problems and / or unsteady parameters. Adjoint method provides particularly accurate results in this configuration

Localization for Random Unitary Operators

We consider unitary analogs of $1-$dimensional Anderson models on $l^2(\Z)$ defined by the product $U_\omega=D_\omega S$ where $S$ is a deterministic unitary and $D_\omega$ is a diagonal matrix of i.i.d. random phases. The operator $S$ is an absolutely continuous band matrix which depends on a parameter controlling the size of its off-diagonal elements. We prove that the spectrum of $U_\omega$ is pure point almost surely for all values of the parameter of $S$. We provide similar results for unitary operators defined on $l^2(\N)$ together with an application to orthogonal polynomials on the unit circle. We get almost sure localization for polynomials characterized by Verblunski coefficients of constant modulus and correlated random phases

Influence of the kind of wood (chestnut and Limousin oak) in the extractives and Klason lignin contents of wood fragments used in the ageing of wine brandies

Só está disponível o resumo da comunicação.Influence of the kind of wood (chestnut and Limousin oak) in the extractives and Klason lignin contents of wood fragments used in the ageing of wine brandie