133 research outputs found
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" . 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
Evaluation of the adsorption trends of a low molecular-weight polyelectrolyte with a site-binding model
International audienc
Contribution of Polymer and Surfactant on the Electrodeposition of Particles
International audienc
Contribution of Polymer and Surfactant on the Electrodeposition of Particles
International audienc
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