Real and imaginary Kirkwood gaps

Working in the real and the imaginary

The science we practice is shaped by our interactions with people; the enthusiastic teachers, the fascinating mentors, the inspiring colleagues, and the inquisitive students. The science we enjoy takes us into areas we couldn't have anticipated. From time to time, we come back to reality and try to find ways to share our new explorations with our friends and relatives and to convert our insight...

Tom Kirkwood

Tom Kirkwood is Professor of Medicine and Director of the Institute for Ageing and Health at Newcastle University, UK. After training in mathematics and biology at the Universities of Cambridge and Oxford he first worked on the measurement of blood clotting and fibrinolytic factors. Early in his career he began an interest in the biology of ageing which he has followed since 1975. In 1977 he pu...

Imaginary automorphisms on real hyperelliptic curves

A real hyperelliptic curve X is said to be Gaussian if there is an automorphism α : XC → XC such that α = [−1]C ◦ α, where [−1] denotes the hyperelliptic involution on X. Gaussian curves arise naturally in several contexts, for example when one studies real Jacobians. In the present paper we study the properties of Gaussian curves and we describe their moduli spaces. MSC 2000: 14H15, 14H37, 14P...

[Bird flu: a real or imaginary threat?].

A real explanation for imaginary eigenvalues

Abstract This paper first reviews how anti-symmetric matrices in two dimensions yield imaginary eigenvalues and complex eigenvectors. It is shown how this carries on to rotations by means of the Cayley transformation. Then the necessary tools from real geometric algebra are introduced and a real geometric interpretation is given to the eigenvalues and eigenvectors. The latter are seen to be two...