On the structure and representations of the insertion-elimination Lie algebra

We examine the structure of the insertion-elimination Lie algebra on rooted trees introduced in \cite{CK}. It possesses a triangular structure \g = \n_+ \oplus \mathbb{C}.d \oplus \n_-, like the Heisenberg, Virasoro, and affine algebras. We show in particular that it is simple, which in turn implies that it has no finite-dimensional representations. We consider a category of lowest-weight representations, and show that irreducible representations are uniquely determined by a "lowest weight" $\lambda \in \mathbb{C}$. We show that each irreducible representation is a quotient of a Verma-type object, which is generically irreducible

Assessing the agro-environmental sustainability of organic mixed-crop dairy systems on the basis of a multivariate approach

Sustainable development calls upon the farming sector to commit itself to the transmission of natural resources to future generations. The INRA research team of Mirecourt studies the design of environmentally-friendly farming systems. The design of these systems is based on a multitude of objectives, and their evaluation is determined by a wide range of criteria. This work aims at determining the practical conditions for implementing agricultural systems considered to be sustainable from an environmental point of view. Two organic dairy systems considered to be environmentally friendly ex ante have been designed in partnership with the staff of the INRA research team of Mirecourt. A grazing dairy system and a mixed-crop dairy system are being experimentally tested at the system scale. The two systems have environmental and agricultural objectives. They are managed using multi-objective decision rules and are assessed on their biotechnical and practical properties, using a structured multiyear experimental design, completed by a model-based assessment. Assessment is oriented towards progressive and permanent re-designing of the systems in order to increase their environmental sustainability and feasibility at the practical level. Knowledge acquired from the two prototypes will then have to be validated on commercial farms

Backward error analysis and the substitution law for Lie group integrators

Butcher series are combinatorial devices used in the study of numerical methods for differential equations evolving on vector spaces. More precisely, they are formal series developments of differential operators indexed over rooted trees, and can be used to represent a large class of numerical methods. The theory of backward error analysis for differential equations has a particularly nice description when applied to methods represented by Butcher series. For the study of differential equations evolving on more general manifolds, a generalization of Butcher series has been introduced, called Lie--Butcher series. This paper presents the theory of backward error analysis for methods based on Lie--Butcher series.Comment: Minor corrections and additions. Final versio

Combinatorial Hopf algebras in quantum field theory I

This manuscript stands at the interface between combinatorial Hopf algebra theory and renormalization theory. Its plan is as follows: Section 1 is the introduction, and contains as well an elementary invitation to the subject. The rest of part I, comprising Sections 2-6, is devoted to the basics of Hopf algebra theory and examples, in ascending level of complexity. Part II turns around the all-important Faa di Bruno Hopf algebra. Section 7 contains a first, direct approach to it. Section 8 gives applications of the Faa di Bruno algebra to quantum field theory and Lagrange reversion. Section 9 rederives the related Connes-Moscovici algebras. In Part III we turn to the Connes-Kreimer Hopf algebras of Feynman graphs and, more generally, to incidence bialgebras. In Section10 we describe the first. Then in Section11 we give a simple derivation of (the properly combinatorial part of) Zimmermann's cancellation-free method, in its original diagrammatic form. In Section 12 general incidence algebras are introduced, and the Faa di Bruno bialgebras are described as incidence bialgebras. In Section 13, deeper lore on Rota's incidence algebras allows us to reinterpret Connes-Kreimer algebras in terms of distributive lattices. Next, the general algebraic-combinatorial proof of the cancellation-free formula for antipodes is ascertained; this is the heart of the paper. The structure results for commutative Hopf algebras are found in Sections 14 and 15. An outlook section very briefly reviews the coalgebraic aspects of quantization and the Rota-Baxter map in renormalization.Comment: 94 pages, LaTeX figures, precisions made, typos corrected, more references adde

From Polymer Adsorption to Encapsulation of Particles

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From Polymer Adsorption to Encapsulation of Particles

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Additifs modificateurs de croissance de particules de silice

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Evaluation of the adsorption trends of a low molecular-weight polyelectrolyte with a site-binding model

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Contribution of Polymer and Surfactant on the Electrodeposition of Particles

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Contribution of Polymer and Surfactant on the Electrodeposition of Particles

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