A note about rappels and uniform discounts

A Note on Uniform Operators

An operator is uniform if its restriction to any infinite-dimensional invariant subspace is unitarily equivalent to itself. We show that a uniform operator having a proper infinite-dimensional invariant subspace resembles an analytic Toeplitz operator in the way that the weakly closed algebra generated by it and the identity operator is isomorphic to a subalgebra of the Calkin algebra; furtherm...

A Note about the Critical Bandwidth for a Kernel Density Estimator with the Uniform Kernel

Among available bandwidths for kernel density estimators, the critical bandwidth is a data-driven one, which satisfies a constraint on the number of modes of the estimated density. When using a random bandwidth, it is of particular interest to show that it goes toward 0 in probability when the sample size goes to infinity. Such a property is important to prove satisfying asymptotic results abou...

A Theorem About Uniform Distribution

A Note on Uniform HDT0L Systems

A note about Painlevé equations

In this short paper we present a recent work concerning the equivalence with the first Painlevé equation y = 6y+x (resp. the second Painlevé equation y = 2y + yx+ α) under the action of fiber-preserving transformations. More specifically, we explicitly compute the change of coordinates that maps the generic second order differential equation to the Painlevé first equation (resp. the Painlevé se...