A Borel invariantization

Numerical Invariantization for Morphological PDE Schemes

Based on a new, general formulation of the geometric method of moving frames, invariantization of numerical schemes has been established during the last years as a powerful tool to guarantee symmetries for numerical solutions while simultaneously reducing the numerical errors. In this paper, we make the first step to apply this framework to the differential equations of image processing. We foc...

Borel structures and Borel theories

We show that there is a complete, consistent Borel theory which has no “Borel model” in the following strong sense: There is no structure satisfying the theory for which the elements of the structure are equivalence classes under some Borel equivalence relation and the interpretations of the relations and function symbols are Borel in the natural sense. We also investigate Borel isomorphisms be...

Borel Conjecture and Dual Borel Conjecture

We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.

A Course on Borel Sets

A Modified Borel Summation Technique

We compare and contrast three different perturbative expansions for the quartic anharmonic oscillator wavefunction and apply a modified Borel summation technique to determine the energy eigenvalues. In the first two expansions this provides the energy eigenvalues directly however in the third method we tune the wavefunctions to achieve the correct large x behaviour as first illustrated in [1]. ...