Intégalités de Sobolev et Temps d'Atteinte

We investigate the links between Sobolev and Nash inequalities, capacity and hitting times estimates and ultracontractive semigroups, in a non-symmetric setting.     

On the structure of weight modules

Given any simple Lie superalgebra , we investigate the structure of an arbitrary simple weight -module. We introduce two invariants of simple weight modules: the shadow and the small Weyl group. Generalizing results of Fernando and Futorny we show that any simple module is obtained by parabolic induction from a cuspidal module of a Levi subsuperalgebra. Then we classify the cuspidal Levi subsuperalgebras of all simple classical Lie superalgebras and of the Lie superalgebra W. Most of them are simply Levi subalgebras of , in which case the classification of all finite cuspidal representations has recently been carried out by one of us (Mathieu). Our results reduce the classification of the finite simple weight modules over all classical simple Lie superalgebras to classifying the finite cuspidal modules over certain Lie superalgebras which we list explicitly.

     

Jagged Partitions

By jagged partitions we refer to an ordered collection of non-negative integers (n₁, n₂,..., n_m) with n_m≥ p for some positive integer p, further subject to some weakly decreasing conditions that prevent them for being genuine partitions. The case analyzed in greater detail here corresponds to p = 1 and the following conditions n_i≥ n_i+1−1 and n_i≥ n_i+2. A number of properties for the corresponding partition function are derived, including rather remarkable congruence relations. An interesting application of jagged partitions concerns the derivation of generating functions for enumerating partitions with special restrictions, a point that is illustrated with various examples. 2000 Mathematics Subject Classification: Primary—05A15, 05A17, 05A19     

Optimizing winter road maintenance operations under real-time information

This paper introduces a real-time optimization model that can be used by maintenance managers to develop and evaluate alternative resources allocation plans for winter road maintenance operations. The model takes into account a wide range of road and weather condition factors such as road network topology, road class, weather forecasts, and contractual service levels, and produces a vehicle dispatch schedule that is optimal with respect to operating costs and quality of service. The model is then used in an analysis on a realistic case to illustrate the potential impact of improved information on winter maintenance operations.     

Filling of a given boundary by p-gons and related problems

We consider here (p,s)-polycycles (3ps) i.e. plane graphs, such that all interior faces are p-gons, all interior vertices are s-valent and any vertex of the boundary (i.e. the exterior face) has valency within [2,s]. The boundary sequence of a (p,s)-polycycle P is the sequence b(P) enumerating, up to a cyclic shift or reversal, the consecutive valencies of vertices of the boundary. We show that the values p=3,4 are the only ones, such that the boundary sequence defines its (p,3)-filling (i.e. a (p,3)-polycycle with given boundary) uniquely.Also we give new results in the enumeration of maps M_n(p,q) (i.e. plane 3-valent maps with only p- and q-gonal faces, such that the q-gons are organized in an n-ring) and two of their generalizations.Both problems are similar (3-valent filling by p-gons of a boundary or of a ring of q-gons) and the same programs were used for both computations.     

Estimating the efficient price from the order flow: A Brownian Cox process approach

At the ultra high frequency level, the notion of price of an asset is very ambiguous. Indeed, many different prices can be defined (last traded price, best bid price, mid price, etc.). Thus, in practice, market participants face the problem of choosing a price when implementing their strategies. In this work, we propose a notion of efficient price which seems relevant in practice. Furthermore, we provide a statistical methodology enabling to estimate this price from the order flow.     

Derivation of Hartreeʼs theory for generic mean-field Bose systems

In this paper we provide a novel strategy to prove the validity of Hartree?s theory for the ground state energy of bosonic quantum systems in the mean-field regime. For the known case of trapped Bose gases, this can be shown using the strong quantum de Finetti theorem, which gives the structure of infinite hierarchies of k-particles density matrices. Here we deal with the case where some particles are allowed to escape to infinity, leading to a lack of compactness. Our approach is based on two ingredients: (1) a weak version of the quantum de Finetti theorem, and (2) geometric techniques for many-body systems. Our strategy does not rely on any special property of the interaction between the particles. In particular, our results cover those of Benguria–Lieb and Lieb–Yau for, respectively, bosonic atoms and boson stars.     

The Lie algebra of type G2 is rational over its quotient by the adjoint action

Let G be a split simple group of type $G_2$ over a field k, and let $\mathfrak{g}$ be its Lie algebra. Answering a question of J.-L. Colliot-Thélène, B. Kunyavski?, V.L. Popov, and Z. Reichstein, we show that the function field $k(\mathfrak{g})$ is generated by algebraically independent elements over the field of adjoint invariants $k{(\mathfrak{g})}^G$.     

A large deviation principle for 2D stochastic Navier–Stokes equation

In this paper one specifies the ergodic behavior of the 2D-stochastic Navier–Stokes equation by giving a Large Deviation Principle for the occupation measure for large time. It describes the exact rate of exponential convergence. The considered random force is non-degenerate and compatible with the strong Feller property.