Borelsommeerbaarheid en een toepassing op een oneindig lineair systeem

Stel dat we eindig veel mieren in het complexe vlak plaatsen, waarbij we de mieren nummeren. Elke mier loopt in de richting van de volgende en de laatste mier beweegt zich in de richting van de eerste. Wanneer de snelheid waarmee de mieren zich verplaatsen evenredig is met de afstand tot hun voorganger, zullen de mieren naar het gemiddelde van...

Topological Extensions of Holomorphic Functional Calculus for Sectorial and Half-plane Type Operators

The theory of functional calculus deals with the idea of 'inserting operators into functions'. The holomorphic (or Dunford-Riesz) functional calculus is based on a class of functions can be represented by the Cauchy-integral formula. A topological extension means that the primary calculus is extended to a wider class of functions and the...

De wiskunde achter Google

The Blum-Hanson Property

The Blum-Hanson property was identified in the 1960's as a property closely related to that of strong mixing. This property is interesting in the field of ergodic theory. It can be shown that if the orbits of all points have the Blum-Hanson property, then the operator is strongly mixing. The converse is not always true and much research has been...

Towards the construction of a normal Lüroth series

In this thesis we present a Lüroth series A that we conjecture to be normal. The series A is constructed by concatenating elements from a probability tree that enumerates all finite Lüroth series. We give an outline for a proof of the normality of A in four steps, of which we will prove three. Regarding the fourth step, which we cannot prove yet...

De Dekpuntstelling van Brouwer (Brouwer's Fixed Point Theorem)