The Maximal Rank of Elliptic Delsarte Surfaces

Shioda described in his article from 1986 a method to compute the Lefschetz number of a Delsarte surface. In one of his examples he uses this method to compute the rank of an elliptic curve over k(t). In this article we find all elliptic curves over k(t) for which his method is applicable. For each of these curves we also compute the Mordell-Weil rank

Enron versus EUSES: A Comparison of Two Spreadsheet Corpora

Spreadsheets are widely used within companies and often form the basis for business decisions. Numerous cases are known where incorrect information in spreadsheets has lead to incorrect decisions. Such cases underline the relevance of research on the professional use of spreadsheets. Recently a new dataset became available for research, containing over 15.000 business spreadsheets that were extracted from the Enron E-mail Archive. With this dataset, we 1) aim to obtain a thorough understanding of the characteristics of spreadsheets used within companies, and 2) compare the characteristics of the Enron spreadsheets with the EUSES corpus which is the existing state of the art set of spreadsheets that is frequently used in spreadsheet studies. Our analysis shows that 1) the majority of spreadsheets are not large in terms of worksheets and formulas, do not have a high degree of coupling, and their formulas are relatively simple; 2) the spreadsheets from the EUSES corpus are, with respect to the measured characteristics, quite similar to the Enron spreadsheets.Comment: In Proceedings of the 2nd Workshop on Software Engineering Methods in Spreadsheet

Convergence to the boundary for random walks on discrete quantum groups and monoidal categories

We study the problem of convergence to the boundary in the setting of random walks on discrete quantum groups. Convergence to the boundary is established for random walks on $\hat{\textrm{SU}_q(2)}$. Furthermore, we will define the Martin boundary for random walks on C$^*$-tensor categories and give a formulation for convergence to the boundary for such random walks. These categorical definitions are shown to be compatible with the definitions in the quantum group case. This implies that convergence to the boundary for random walks on quantum groups is stable under monoidal equivalence.Comment: 67 pages; Shortened sections 2 and 5; Corrected Lemma 5.15; Corrected several typo