Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

An approximation scheme for cake division with a linear number of cuts

In the cake cutting problem, n = 2 players want to cut a cake into n pieces so that every player gets a ‘fair’ share of the cake by his own measure. We prove the following result: For every ¿>0, there exists a cake division scheme for n players that uses at most c ¿n cuts, and in which each player can enforce to get a share of at least (1-¿)/nof the cake according to his own private measur

An approximation scheme for cake division with a linear number of cuts

In the cake cutting problem, n=2 players want to cut a cake into n pieces so that every player gets a ‘fair’ share of the cake by his own measure. We prove the following result: For every e>0, there exists a cake division scheme for n players that uses at most cen cuts, and in which each player can enforce to get a share of at least (1-e)/n of the cake according to his own private measure