1,051 research outputs found
Allocution à l'occasion du décès de M. Enrico Cerulli, associé étranger de l'Académie
No full textPouilloux Jean. Allocution à l'occasion du décès de M. Enrico Cerulli, associé étranger de l'Académie. In: Comptes rendus des séances de l'Académie des Inscriptions et Belles-Lettres, 132ᵉ année, N. 3, 1988. pp. 540-542
Aircraft Conflict Resolution: A Benchmark Generator
No full textAircraft conflict resolution is one of the major tasks of computer-aided air traffic management and represents a challenging optimization problem. Many models and methods have been proposed to assist trajectory regulation to avoid conflicts. However, the question of testing the different mathematical optimization approaches against each other is still open. Standard benchmarks include unrealistic scenarios in which all the flights move toward a common point or completely random generated instances. There is a lack of a common set of test instances that allows comparison of the available methods under a variety of heterogeneous and representative scenarios. We present a flight deconfliction benchmark generator that allows the user to choose between (i) different predefined scenario inspired by existing benchmarks in the literature; (ii) pseudo-random traffic meeting certain congestion measurements; (iii) and randomly generated traffic. The proposed setting can account for different levels of difficulty in the deconfliction of the aircraft and allows to explore and compare the real limitations of optimization approaches for aircraft conflict resolution
Linear degenerations of flag varieties: partial flags, defining equations, and group actions
No full textWe continue, generalize and expand our study of linear degenerations of flag varieties from Cerulli Irelli et al. (Math Z 287(1–2):615–654, 2017). We realize partial flag varieties as quiver Grassmannians for equi-oriented type A quivers and construct linear degenerations by varying the corresponding quiver representation. We prove that there exists the deepest flat degeneration and the deepest flat irreducible degeneration: the former is the partial analogue of the mf-degenerate flag variety and the latter coincides with the partial PBW-degenerate flag variety. We compute the generating function of the number of orbits in the flat irreducible locus and study the natural family of line bundles on the degenerations from the flat irreducible locus. We also describe explicitly the reduced scheme structure on these degenerations and conjecture that similar results hold for the whole flat locus. Finally, we prove an analogue of the Borel–Weil theorem for the flat irreducible locus
Polynomial programming prevents aircraft (and other) conflicts
No full textUsing a known algebraic result, we obtain a finite polynomial programming reformulation of a semi-infinite program modeling the aircraft deconfliction problem via subliminal speed regulation. Solving the reformulation yields better results than the state of the art for most of the tested instances
A homological interpretation of the transverse quiver grassmannians
No full textIn recent articles, the investigation of atomic bases in cluster algebras
associated to affine quivers led the second–named author to introduce a variety
called transverse quiver Grassmannian and the first–named and third–named authors
to consider the smooth loci of quiver Grassmannians. In this paper, we prove that,
for any affine quiver Q, the transverse quiver Grassmannian of an indecomposable
representation M is the set of points N in the quiver Grassmannian of M such that
Ext1(N,M/N) = 0.As a corollary we prove that the transverse quiver Grassmannian
coincides with the smooth locus of the irreducible components of minimal dimension
in the quiver Grassmannian
A homological interpretation of transverse quiver Grassmannians
No full textIn recent articles, the investigation of atomic bases in cluster algebras associated to affine quivers led the second–named author to introduce a variety called transverse quiver Grassmannian and the first–named and third–named authors to consider the smooth loci of quiver Grassmannians. In this paper, we prove that, for any affine quiver Q, the transverse quiver Grassmannian of an indecomposable representation M is the set of points N in the quiver Grassmannian of M such that Ext1(N, M/N) = 0. As a corollary we prove that the transverse quiver Grassmannian coincides with the smooth locus of the irreducible components of minimal dimension in the quiver Grassmannian
Espressioni numeriche ed espressioni letterali: continuità o rottura
No full textAbstract. Si analizza il rapporto tra calcolo letterale e calcolo di espressioni numeriche, evidenziando continuità e rotture . Si riporta poi alcuni risultati tratti da una sperimentazione svolta a livello del primo anno della scuola secondaria superiore
L’algebrista : un micromonde pour l’enseignementet l’apprentissage de l’algèbre de calcul
No full textRESUMÉ. Cet article présente un micromonde qui a été expérimenté en classe. Suite à des recherches que nous avions menées pour étudier le rôle du micromonde Cabri dans l’introduction de la géométrie en tant que domaine théorique, nous avons développé un
nouveau projet de recherche dans le contexte de l’algèbre. Nous présentons les principales caractéristiques du projet et décrivons le micromonde que nous avons conçu et son fonctionnement. Nous décrivons brièvement une expérimentation et nous discutons cette
expérience d’enseignement sur quelques exemples tirés de protocoles d’utilisation par les élève
Degenerate Flag Varieties of Type A and C are Schubert Varieties
No full textWe show that any type A or C degenerate flag variety is, in fact, isomorphic to a Schubert
variety in an appropriate partial flag manifold
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