Under the action of the general linear group, the ranks of matrices A and B forming a m × n pencil A+ λB can change, but in a restricted manner. Specifically, to every pencil one can associate a pair of minimal ranks, which is unique up to a permutation. This notion can be defined for matrix pencils and, more generally, also for matrix polynomials of arbitrary degree. The natural hierarchy it i...

In this thesis we give a complete description of the syzygies of irreducible, nonsingular, canoncial curves C of genus 9. This includes a collection of all possible Betti tables for C. Moreover a direct correspondence between these Betti tables and the number and types of special linear series on C is given. Especially for Cliff(C) = 3 the curve C is contained in determinantal surface Y on a 4d...

A new and simple approach for calculating the eigenstructure of a regular matrix pencil is presented. This proposed approach transforms the generalized eigenvalues problem into a usual eigenvalues problem, and it also can be used to calculate the Weierstrass form of a regular matrix pencil. Mathematics Subject Classification: 93B55

This paper describes structural properties of solutions to distance problems for rectangular matrix pencils. Properties are given for both the closest non-generic pencil and the smallest perturbation which yields a non-generic pencil. Smoothness results are given which suggest a natural geometric understanding of the problem and allow extension to more general distance problems.

We consider the modeling of light beams propagating in highly forward-peaked turbulent media by fractional Fokker-Planck equations and their approximations Fermi pencil beam models. We obtain an error estimate a 1-Wasserstein distance for latter model showing that spreading is well captured pencil-beam approximation small diffusion limit.

We explore the relation between the positive dimensional irreducible components of the characteristic varieties of rank one local systems on a smooth surface and the associated (rational or irrational) pencils. Our study, which may viewed as a continuation of D. Arapura’s paper [1], yields new geometric insight into the translated components relating them to the multiplicities of curves in the ...