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Cut locus and optimal synthesis in the sub-Riemannian problem on the group of motions of a plane*

Yuri L. Sachkov (2011)

ESAIM: Control, Optimisation and Calculus of Variations

The left-invariant sub-Riemannian problem on the group of motions (rototranslations) of a plane SE(2) is considered. In the previous works [Moiseev and Sachkov, ESAIM: COCV, DOI: 10.1051/cocv/2009004; Sachkov, ESAIM: COCV, DOI: 10.1051/cocv/2009031], extremal trajectories were defined, their local and global optimality were studied. In this paper the global structure of the exponential mapping is described. On this basis an explicit characterization of the cut locus and Maxwell set is obtained....

Cyclic cohomology of certain nuclear Fréchet algebras and DF algebras

Zinaida Lykova (2008)

Open Mathematics

We give explicit formulae for the continuous Hochschild and cyclic homology and cohomology of certain ⊗ ^ -algebras. We use well-developed homological techniques together with some niceties of the theory of locally convex spaces to generalize the results known in the case of Banach algebras and their inverse limits to wider classes of topological algebras. To this end we show that, for a continuous morphism ϕ: x → y of complexes of complete nuclear DF-spaces, the isomorphism of cohomology groups H...

D sets and IP rich sets in ℤ

Randall McCutcheon, Jee Zhou (2016)

Fundamenta Mathematicae

We give combinatorial characterizations of IP rich sets (IP sets that remain IP upon removal of any set of zero upper Banach density) and D sets (members of idempotent ultrafilters, all of whose members have positive upper Banach density) in ℤ. We then show that the family of IP rich sets strictly contains the family of D sets.

Davenport-Hasse relations and an explicit Langlands correspondence, II : twisting conjectures

Colin J. Bushnell, Guy Henniart (2000)

Journal de théorie des nombres de Bordeaux

Let F / ℚ p be a finite field extension. The Langlands correspondence gives a canonical bijection between the set 𝒢 F 0 ( n ) of equivalence classes of irreducible n -dimensional representations of the Weil group 𝒲 F of F and the set 𝒜 F 0 ( n ) of equivalence classes of irreducible supercuspidal representations of GL n ( F ) . This paper is concerned with the case where n = p m . In earlier work, the authors constructed an explicit bijection π : 𝒢 F 0 ( p m ) → 𝒜 F 0 ( p m ) using a non-Galois tame base change map. If this tame base change satisfies a certain conjectured...

De quelques aspects de la théorie des Q -variétés différentielles et analytiques

Raymond Barre (1973)

Annales de l'institut Fourier

Une Q -variété est le quotient d’une variété par une relation d’équivalence “étale” (feuilletage sans holonomie transversale). Cette catégorie est stable par quotients “étales”, et contient tout quotient d’une Q -variété en groupe par un sous-groupe. Elle forme le meilleur cadre possible pour l’étude des groupes de Lie. Une construction explicite de la cohomologie permettra d’obtenir la suite spectrale de Leray d’un morphisme de Q -variétés, celle des espaces à opérateurs, d’où leur interprétation...

Currently displaying 801 – 820 of 3839