We show that if E is a real Banach space such that E has the approximation property and such that 1 → n,s, E, then the set of extreme points of the unit ball of PI (nE) is equal to {±φn : φ ∈ E , φ = 1}. Under the ...

We characterise the real extreme points of the unit ball of mΨ0, the complex extreme points of the unit ball of mΨ and the real extreme and exposed points of the unit ball of (mΨ0)′. Using these characterisations we show ...

Let S be a set of 2n points on a circle such that for each point p∈S also its antipodal (mirrored with respect to the circle center) point p′ belongs to S. A polygon P of size n is called antipodal if it consists of precisely ...

Forecasting the risk of extreme losses is an important issue in the management of financial risk. There has been a great deal of research examining how option implied volatilities (IV) can be used to forecast asset return ...

Many classical univalence criteria depending on the Schwarzian derivative are special cases of a result, proved in [18], involving both conformal mappings and conformal metrics. The classical theorems for analytic functions ...

In this work we are interested in the Demyanov-Ryabova conjecture for a finite family of polytopes. The conjecture asserts that after a finite number of iterations (successive dualizations), either a 1-cycle or a 2-cycle ...