Multicriteria Semi-Obnoxious Network Location Problems (MSNLP) with Sum and Center Objectives

Locating a facility is often modeled as either the maxisum or the minisum problem, reflecting whether the facility is undesirable (obnoxious) or desirable. But many facilities are both desirable and undesirable at the same time, e.g., an airport. This can be modeled as a multicriteria network location problem, where some of the sum-objectives are maximized (push effect) and some of the sum-objectives are minimized (pull effect).We present a polynomial time algorithm for this model along with some basic theoretical results, and generalize the results also to incorporate maximin and minimax objectives. In fact, the method works for any piecewise linear objective functions. Finally, we present some computational results.     

Atomistic phenomena in dense fluid shock waves

The shock structure problem is one of the classical problems of fluid mechanics and at least for non-reacting dilute gases it has been considered essentially solved. Here we present a few recent findings, to show that this is not the case. There are still new physical effects to be discovered provided that the numerical technique is general enough to not rule them out a priori. While the results have been obtained for dense fluids, some of the effects might also be observable for shocks in dilute gases.     

Stable model categories are categories of modules

A stable model category is a setting for homotopy theory where the suspension functor is invertible. The prototypical examples are the category of spectra in the sense of stable homotopy theory and the category of unbounded chain complexes of modules over a ring. In this paper we develop methods for deciding when two stable model categories represent ‘the same homotopy theory’. We show that stable model categories with a single compact generator are equivalent to modules over a ring spectrum. More generally stable model categories with a set of generators are characterized as modules over a ‘ring spectrum with several objects’, i.e., as spectrum valued diagram categories. We also prove a Morita theorem which shows how equivalences between module categories over ring spectra can be realized by smashing with a pair of bimodules. Finally, we characterize stable model categories which represent the derived category of a ring. This is a slight generalization of Rickard's work on derived equivalent rings. We also include a proof of the model category equivalence of modules over the Eilenberg-Mac Lane spectrum HR and (unbounded) chain complexes of R-modules for a ring R.     

Asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors

We derive results on the asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors. They appear in particular in delta–gamma models in financial risk management approximating portfolio returns. Quantile estimation corresponds to the estimation of the Value-at-Risk, which is a serious problem in high dimension.     

Profinite groups of finite cohomological dimension

Let 1→N→G→G/N→1 be a short exact sequence of profinite groups, and let p be a prime number. We prove that if G is of finite cohomological p-dimension n:=cd_p(G)<∞ and if the order of $\text{H}{}^{\mathrm{k}}\text{(N,}\text{F}{}_{\mathrm{p}}\text{)}$ is finite for k:=cd_p(N), the virtual cohomological p-dimension of G/N equals n?k. To cite this article: T. Weigel, P. Zalesskii, C. R. Acad. Sci. Paris, Ser. I 338 (2004).