Several recent methods used to analyze asymptotic stability of delay-differential equations (DDEs) involve determining the eigenvalues of a matrix, a matrix pencil or a matrix polynomial constructed by Kronecker products. Despite some similarities between the different types of these so-calledmatrix pencil methods, the general ideas used as well as the proofs differ considerably. Moreover, the ...

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...

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

In this paper, we study the bicanonical pencil of a Godeaux surface and of a determinantal Barlow surface. This study gives a simple proof for the unobstructedness of deformations of a determinantal Barlow surface. Then we compute the number of hyperelliptic curves in the bicanonical pencil of a determinantal Barlow surface via classical Prym theory.

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.