32,118 research outputs found
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 . 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
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