Stochastic gradient descent (SGD) is one of the most popular algorithms in modern machine
learning. The noise encountered in these applications is different from that in many …

Hypocoercivity methods are applied to linear kinetic equations with mass conservation and
without confinement in order to prove that the solutions have an algebraic decay rate in the …

The representation of functions by artificial neural networks depends on a large number of
parameters in a non-linear fashion. Suitable parameters are found by minimizing a 'loss …

We study the Hardy type inequalities in the framework of equalities. We present equalities
which immediately imply Hardy type inequalities by drop** the remainder term …

In this paper we first prove a number of important inequalities with explicit constants in the
setting of the Heisenberg group. This includes the fractional and integer Sobolev, Gagliardo …

We present a unified strategy to derive Hardy–Poincaré inequalities on bounded and
unbounded domains. The approach allows proving a general Hardy–Poincaré inequality …

In this paper, we consider the first order Hardy inequalities using simple equalities. This
basic setting not only permits to derive quickly many well-known Hardy inequalities with …