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

Quantitative estimates and extrapolation for multilinear weight classes

In this paper we prove a quantitative multilinear limited range extrapolation theorem which allows us to extrapolate from weighted estimates that include the cases where some of the exponents are infinite. This extends the recent extrapolation result of Li, Martell, and Ombrosi. We also obtain vector-valued estimates including $\ell^\infty$ spaces and, in particular, we are able to reprove all the vector-valued bounds for the bilinear Hilbert transform obtained through the helicoidal method of Benea and Muscalu. Moreover, our result is quantitative and, in particular, allows us to extend quantitative estimates obtained from sparse domination in the Banach space setting to the quasi-Banach space setting. Our proof does not rely on any off-diagonal extrapolation results and we develop a multilinear version of the Rubio de Francia algorithm adapted to the multisublinear Hardy-Littlewood maximal operator. As a corollary, we obtain multilinear extrapolation results for some upper and lower endpoints estimates in weak-type and BMO spaces.Comment: 44 pages. Minor improvements. To appear in Mathematische Annale