We prove an infinite-dimensional version of Sard’s theorem for Fréchet manifolds. Let M (respectively, N) be a bounded Fréchet manifold with compatible metric d M (respectively, d N ) modeled on Fréchet spaces E (respectively, ...

We construct a faithful self-similar action of the discrete Heisenberg group with the following properties: This action is self-replicating, finite-state, level-transitive, and noncontracting. Moreover, there exist orbital ...

It is known since Galois that an algebraic equation can be solved using suitable n-th roots whenever the corresponding Galois group is soluble. The object of this note is to construct real numbers with the use of the n-th ...

The paper is devoted to solution of a problem of separation of variables in the wave equation utt−uxx+V(x)u=0. We give a complete classification of potentials V(x) for which this equation admits a nontrivial separation of ...

Let P:X → V be a projection from a real Banach space X onto a subspace V and let S ⊂ X. In this setting, one can ask if S is left invariant under P, i.e., if PS ⊂ S. If V is finite-dimensional and S is a cone with particular ...

Finite volume grand canonical correlation functions of nonequilibrium systems of d-dimensional Brownian particles, interacting through a regular (long-range) pair potential with integrable first partial derivatives, are ...

Problems of singular perturbation of reducible invertible operators are classified and their applications to the analysis of stochastic Markov systems represented by random evolutions are considered. The phase merging, ...

We consider a smoothing problem for stochastic processes satisfying stochastic differential equations with Wiener processes that may not have a semimartingale property with respect to the joint filtration.