4 papers
Spectrum for first-order properties of random hypergraphs
Svetlana Popova
The notion of spectrum of first-order properties introduced by J. Spencer for Erdos-Renyi random graph is considered in relation to random uniform hypergraphs. We study properties…
Existential monadic second order logic of undirected graphs: a disproof of the Le Bars conjecture
Svetlana Popova, Maksim Zhukovskii
In 2001, J.-M. Le Bars disproved the zero-one law (that says that every sentence from a certain logic is either true asymptotically almost surely (a.a.s.), or false a.a.s.) for exi…
On -estimates for probability solutions to Fokker-Planck-Kolmogorov equations
Vladimir I. Bogachev, Svetlana N. Popova, Stanislav V. Shaposhnikov
We prove two new results connected with elliptic Fokker-Planck-Kolmogorov equations with drifts integrable with respect to solutions. The first result answers negatively a long-sta…
A new approach to Nikolskii-Besov classes
Vladimir I. Bogachev, Egor D. Kosov, Svetlana N. Popova
We give a new characterization of Nikolskii-Besov classes of functions of fractional smoothness by means of a nonlinear integration by parts formula in the form of a nonlinear ineq…