Measuring ecological efficiency with data envelopment analysis (DEA)

The measurement of ecological efficiency provides some important information for the companies’ environmental management. Ecological efficiency is usually measured by comparing environmental performance indicators. Data envelopment analysis (DEA) shows a high potential to support such comparisons, as no explicit weights are needed to aggregate the indicators. In general, DEA assumes that inputs and outputs are ‘goods’, but from an ecological perspective also ‘bads’ have to be considered. In the literature, ‘bads’ are treated in different and sometimes arbitrarily chosen ways. This article aims at the systematic derivation of ecologically extended DEA models. Starting from the assumptions of DEA in production theory and activity analysis, a generalisation of basic DEA models is derived by incorporating a multi-dimensional value function f. Extended preference structures can be considered by different specifications of f, e.g. specifications for ecologically motivated applications of DEA.     

Generalized Brownian functionals and the Feynman integral

To obtain a sufficiently rich class of nonlinear functionals of white noise, resp. the Wiener process, we study riggings of the L² space with the white noise measure. Particular examples are local functionals such as e.g. the ‘square of white noise’ and its exponential with applications in the theory of Feynman Integral.     

Risk premium and fair option prices under stochastic volatility: the HARA solution

We have solved the problem of finding (HARA) fair option price under a general stochastic volatility model. For a given HARA utility, the ‘risk premium’, i.e., the ‘market price of volatility risk’ is determined via a solution of a certain nonlinear PDE. Equivalently, the fair option price is determined as a solution of an uncoupled system of a non-linear PDE and a Black–Scholes type PDE. To cite this article: S.D. Stojanovic, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Lax monads: Indexed monoidal monads

Motivated by the problem of internalizing Enriched Category Theory in a topos, we investigate the notion of a lax monad T on a bicategory B for which we can construct the bicategory B^T of ‘matrices of T-algebras’ and we prove a factorization theorem to this effect.     

Estimation de la fonction de survie sous biais de longueur pour des risques concurrents et proportionnels

Consider a population of individuals who experience two causes of death. We observe the ones alive at time t₀ and follow them until death. Given this length bias sample, we propose an estimator of the survival function of ‘initial survival times’ (i.e., for the entire population) under the assumption of proportional hazards for the two causes of death. The large sample behaviour of our estimator is also studied. To cite this article: J.-Y. Dauxois et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Relative hyperbolization and Pontrjagin classes

The ‘nonpositive curvature retraction theorem’ has a refined version, a version that respects characteristic classes. To cite this article: B.Z. Hu, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Odd and even hamming spheres also have minimum boundary

Combinatorial problems with a geometric flavor arise if the set of all binary sequences of a fixed length n, is provided with the Hamming distance. The Hamming distance of any two binary sequences is the number of positions in which they differ. The (outer) boundary of a set A of binary sequences is the set of all sequences outside A that are at distance 1 from some sequence in A. Harper [6] proved that among all the sets of a prescribed volume, the ‘sphere’ has minimum boundary.We show that among all the sets in which no pair of sequences have distance 1, the set of all the sequences with an even (odd) number of 1's in a Hamming ‘sphere’ has the same minimizing property. Some related results are obtained. Sets with more general extremal properties of this kind yield good error-correcting codes for multi-terminal channels.     

Effondrement de quotients aléatoires de groupes hyperboliques avec torsion

We show that random quotients of hyperbolic groups with ‘harmful’ torsion collapse at densities smaller than expected. To cite this article: Y. Ollivier, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

On the compactification of hyperconcave ends

We find a class of manifolds whose ‘pseudoconcave holes’ can be filled in, even in dimension two. To cite this article: G. Marinescu, T.-C. Dinh, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Vanishing of H1 for Dedekind rings and applications to loop algebras

We establish a version of Serre's ‘Conjecture I’ for Dedekind domains. As an application, we give a parametrization of twisted loop algebras by means of torsors. To cite this article: A. Pianzola, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Averaging lemmas and the X-ray transform

We introduce a new method to prove averaging lemmas, i.e., prove a regularizing effect on the average in velocity of a solution to a kinetic equation. The method does not require the use of Fourier transform and the whole procedure is performed in the ‘real space’; it leads to estimating an operator very similar to the so-called X-ray transform. We are then able to improve the known results when the integrability in space and velocity are different. To cite this article: P.-E. Jabin, L. Vega, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Numerical analysis of the generalized von Kármán equations

The ‘generalized von Kármán equations’ constitute a mathematical model for a nonlinearly elastic plate subjected to boundary conditions ‘of von Kármán type’ only on a portion of its lateral face, the remaining portion being free. We establish here the convergence of a conforming finite element approximation to these equations. The proof relies in particular on a compactness method due to J.-L. Lions and on Brouwer's fixed point theorem. To cite this article: P.G. Ciarlet et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Weights computation for simplicial Whitney forms of degree one

We investigate some simple techniques of computation of the weights (‘moments’) of simplicial Whitney p-forms of first polynomial degree. The classical metric-dependent computation of weights is shown to be equivalent to an affine one, more suitable in the context of differential forms. To cite this article: F. Rapetti, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Large deviations and estimation in infinite-dimensional models

Consider a random sample from a statistical model with an unknown, and possibly infinite-dimensional, parameter - e.g., a nonparametric or semiparametric model - and a real-valued functional T of this parameter which is to be estimated. The objective is to develop bounds on the (negative) exponential rate at which consistent estimates converge in probability to T, or, equivalently, lower bounds for the asymptotic effective standard deviation of such estimates - that is, to extend work of R.R. Bahadur from parametric models to more general (semiparametric and nonparametric) models. The approach is to define a finite-dimensional submodel, determine Bahadur's bounds for a finite-dimensional model, and then ‘sup’ or ‘inf’ the bounds with respect to ways of defining the submodels; this can be construed as a ‘directional approach’, the submodels being in a specified ‘direction’ from a specific model. Extension is made to the estimation of vector-valued and infinite-dimensional functionals T, by expressing consistency in terms of a distance, or, alternatively, by treating classes of real functionals of T. Several examples are presented.     

The weak null condition for Einstein's equations

We show that Einstein's equations of General Relativity expressed in wave coordinates satisfy a ‘weak null condition’. In a forthcoming article we will use this to prove a global existence result for Einstein's equations in wave coordinates with small initial data. To cite this article: H. Lindblad, I. Rodnianski, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Cognitive trajectory of proof by contradiction for transition-to-proof students

History and research on proof by contradiction suggests proof by contradiction is difficult for students in a number of ways. Students’ comprehension of already-written proofs by contradiction is one such aspect that has received relatively little attention. Applying the cognitive lens of Action-Process-Object-Schema (APOS) Theory to proof by contradiction, we constructed and tested a cognitive model that describes how a student might construct the concept ‘proof by contradiction’ in an introduction to proof course. Data for this study was collected from students in a series of five teaching interventions focused on proof by contradiction. This paper will report on two participants as case studies to illustrate that our cognitive trajectory for proof by contradiction is a useful model for describing how students may come to understand the proof method.     

Formes fermées et feuilletages 2-isotropes

In this Note we introduce, for a closed form of any degree, the notion of 2-isotropic foliation, which plays the same role as that of the Lagrangian foliation in the symplectic case. After constructing an affine structure on its leaves we describe the tubular neighborhood of a ‘Lagrangian’ transverse section. To cite this article: F.-J. Turiel, C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Jeux à champ moyen. I – Le cas stationnaire

We introduce here a general approach to model games with a large number of players. More precisely, we consider N players Nash equilibria for long term stochastic problems and establish rigorously the ‘mean field’ type equations as N goes to infinity. We also prove general uniqueness results and determine the deterministic limit. To cite this article: J.-M. Lasry, P.-L. Lions, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Contrôlabilité à zéro avec contraintes sur le contrôle

We study a problem of null-controllability for the parabolic heat equation with linear constraints on the control. The main tool used to solve the problem of existence and convergence is an observability inequality of Carleman type, which is ‘adapted’ to the constraints. We then apply the obtained results to the sentinels theory of Lions. To cite this article: O. Nakoulima, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

A twisted theorem of Chebotarev

The classical function field version of Chebotarev's Theorem follows from the Lang–Weil estimate and an ‘untwisting’ trick. We obtain an analogue in the framework of difference schemes, using Hrushovski's twisted Lang–Weil estimate. To cite this article: I. Toma?i?, C. R. Acad. Sci. Paris, Ser. I 347 (2009).