Cycles of linear and semilinear mappings

We give a canonical form of matrices of a cycle of linear or semilinear mapping V_1 --- V_2 --- ... --- V_t --- V_1 in which all V_i are complex vector spaces, each line is an arrow ---> or <---, and each arrow denotes a linear or semilinear mapping.Comment: 18 page

The finite harmonic oscillator and its associated sequences

A system of functions (signals) on the finite line, called the oscillator system, is described and studied. Applications of this system for discrete radar and digital communication theory are explained. Keywords: Weil representation, commutative subgroups, eigenfunctions, random behavior, deterministic constructionComment: Published in the Proceedings of the National Academy of Sciences of the United States of America (Communicated by Joseph Bernstein, Tel Aviv University, Tel Aviv, Israel

Octonionic Mobius Transformations

A vexing problem involving nonassociativity is resolved, allowing a generalization of the usual complex Mobius transformations to the octonions. This is accomplished by relating the octonionic Mobius transformations to the Lorentz group in 10 spacetime dimensions. The result will be of particular interest to physicists working with lightlike objects in 10 dimensions.Comment: Plain TeX, 12 pages, 1 PostScript figure included using eps