A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems

期刊： EXPOSITIONES MATHEMATICAE, 2021; 39 (1)

In the qualitative theory of differential equations in the plane one of the most difficult objects to study is the existence of limit cycles. There ar......

A note on commutators in algebras of unbounded operators

期刊： EXPOSITIONES MATHEMATICAE, 2020; 38 (2)

We show that the identity is the sum of two commutators in the algebra of all operators affiliated with a von Neumann algebra of type Hi, settling a q......

A fully stochastic approach to limit theorems for iterates of Bernstein operators

期刊： EXPOSITIONES MATHEMATICAE, 2018; 36 (2)

This paper presents a stochastic approach to theorems concerning the behavior of iterations of the Bernstein operator B-n taking a continuous function......

JIF：0.49

Limit cycles of the classical Lienard differential systems: A survey on the Lins Neto, de Melo and Pugh's conjecture

期刊： EXPOSITIONES MATHEMATICAE, 2017; 35 (3)

In 1977 Lins Neto et al. (1977) conjectured that the classical Lienard system (x) over bar = y - F(x), (y) over bar = -x, with F (x) a real polynomial......

JIF：0.74

Convex bodies via gravitational potentials

期刊： EXPOSITIONES MATHEMATICAE, 2017; 35 (4)

This note geometrically generalizes the main theorem in Shahgholian's 1992 paper [2], from R-3 to R-n >= 2 via the Minkowski functional of a convex......

JIF：0.74