(a) Find Galois points and the Galois groups for singular plane curves. – for smooth curves, the number of Galois points is at most three (resp. four) if they are outer (resp. inner). The Galois groups are cyclic. [46, 62] – (i) How is the structure of Galois group and how many Galois points do there exist? Is it true that the maximal number of outer (resp. inner) Galois points is three (resp. ...

We give the classification of the configurations of the elliptic curves on the Fano surface of a smooth cubic threefold. That means that we give the number of such curves, their intersections and a plane model. This classification is linked to the classification of the automorphism groups of theses surfaces. The Fano surface of the Fermat cubic of P is the only one to contain 30 elliptic curves...

Physiological and pharmacological studies of hormones, drugs, and neurotransmitters often generate families of sigmoidal dose-response curves. Optimally efficient data analysis should involve simultaneous description of all curves, rather than fitting each one individually. We have developed a general computerized method to describe the dose-response curves in terms of basal and maximal respons...

Abstract Let S be a compact complex surface in class VII 0 + containing cycle of rational curves C = ∑ D j . A the maximal connected divisor If there is another component ′ then curves, and Inoue-Hirzebruch surface. only one each i chain which intersects curve for at most meets In other words, we do not prove existence those , but if some exist looks like Kato with perhaps missing curves. The p...

ACKNOWLEDGEMENTS I would like to thank my adviser Michael Zieve for teaching me to fish. I would like to thank Jeffrey Lagarias for helpful feedback in writing this thesis. I would like to thank my family (Peter, Susan, and Holly), my beautiful girlfriend Becky, and the community of Michigan graduate students for keeping me sane.