Algèbres de Maurer-Cartan et Holonomie
Algèbres différentielles en théorie des champs
Les algèbres différentielles sont apparues comme des outils commodes ou même inévitables pour exprimer les symétries continues, exactes ou brisées, suivant la situation physique envisagée, dans le cadre de l’algorithme de Feynman de la théorie quantique des champs perturbative. Les algèbres de courants, les théories de Yang-Mills, la première quantification de la corde, sont proposées comme exemples classiques.
Algorithmic computations of Lie algebras cohomologies
From the text: The aim of this work is to advertise an algorithmic treatment of the computation of the cohomologies of semisimple Lie algebras. The base is Kostant’s result which describes the representation of the proper reductive subalgebra on the cohomologies space. We show how to (algorithmically) compute the highest weights of irreducible components of this representation using the Dynkin diagrams. The software package offers the data structures and corresponding procedures for computing...
Algorithmic construction of hyperfunction solutions to invariant differential equations on the space of real symmetric matrices.
All linear and bilinear natural concomitants of vector valued differential forms
Almost classical solutions of Hamilton-Jacobi equations.
Almost global solutions for non hamiltonian semi-linear Klein-Gordon equations on compact revolution hypersurfaces
This paper is devoted to the proof of almost global existence results for Klein-Gordon equations on compact revolution hypersurfaces with non-Hamiltonian nonlinearities, when the data are smooth, small and radial. The method combines normal forms with the fact that the eigenvalues associated to radial eigenfunctions of the Laplacian on such manifolds are simple and satisfy convenient asymptotic expansions.
Almost homoclinic solutions for a certain class of mixed type functional differential equations
We shall be concerned with the existence of almost homoclinic solutions for a class of second order functional differential equations of mixed type: , where t ∈ ℝ, q ∈ ℝⁿ and T>0 is a fixed positive number. By an almost homoclinic solution (to 0) we mean one that joins 0 to itself and q ≡ 0 may not be a stationary point. We assume that V and u are T-periodic with respect to the time variable, V is C¹-smooth and u is continuous. Moreover, f is non-zero, bounded, continuous and square-integrable....
Almost product structures and Monge-Ampère equations.
Almost sure Weyl asymptotics for non-self-adjoint elliptic operators on compact manifolds
In this paper, we consider elliptic differential operators on compact manifolds with a random perturbation in the 0th order term and show under fairly weak additional assumptions that the large eigenvalues almost surely distribute according to the Weyl law, well-known in the self-adjoint case.
Almost symplectic structures and harmonic morphisms
In this paper, we introduce the notion of symplectic harmonic maps between tamed manifolds and establish some properties. In the case where the manifolds are almost Hermitian manifolds, we obtain a new method to contruct harmonic maps with minimal fibres. We finally present examples of such applications between projectives spaces.
Almost symplectic structures on the linear frame bundle from linear connection
We describe all M fm-natural operators S: Q ↝ Symp P1 transforming classical linear connections ∇ on m-dimensional manifolds M into almost symplectic structures S(∇) on the linear frame bundle P1M over M.
Amenability and coamenability of algebraic quantum groups.
An abstract characterization of the jet spaces
An abstract differential equation and the potential bifurcation theorems by Krasnosel'skij
An abstract differential inequality and eigenvalues of variational inequalities
An accuracy improvement in Egorov's theorem.
We prove that the theorem of Egorov, on the canonical transformation of symbols of pseudodifferential operators conjugated by Fourier integral operators, can be sharpened. The main result is that the statement of Egorov's theorem remains true if, instead of just considering the principal symbols in Sm/Sm-1 for the pseudodifferential operators, one uses refined principal symbols in Sm/Sm-2, which for classical operators correspond simply to the principal plus the subprincipal symbol, and can generally...
An acyclic extension of the braid group.
An addition theorem for the manifolds with the Laplacian having discrete spectrum.
An admissible synthesis for control systems on differentiable manifolds