Let H(λ) = A0 + λA1 be a square singular matrix pencil, and let λ0 ∈ C be an eventually multiple eigenvalue of H(λ). It is known that arbitrarily small perturbations of H(λ) can move the eigenvalues of H(λ) anywhere in the complex plane, i.e., the eigenvalues are discontinuous functions of the entries of A0 and A1. Therefore, it is not possible to develop an eigenvalue perturbation theory for a...

We discuss some aspects of perturbative (0, 2) Calabi-Yau moduli space. In particular, we show how models with different (0, 2) data can meet along various sub-loci in their moduli space. In the simplest examples, the models differ by the choice of desingularization of a holomorphic V-bundle over the same resolved Calabi-Yau base while in more complicated examples, even the smooth Calabi-Yau ba...

We illustrate how to extend the concept of structural stability through applying it to the front propagation speed selection problem. This consideration leads us to a renormalization group study of the problem. The study illustrates two very general conclusions: (1) singular perturbations in applied mathematics are best understood as renormalized perturbation methods, and (2) amplitude equation...

We consider a singularly perturbed system of second-order differential equations describing steady state of a chemical process that involves three species, two reactions (one of which is fast), and diffusion. Formal asymptotic expansion of the solution is constructed. The theorem on estimation of the remainder is proved.

iv v Summary The thesis was conducted during a period of six months at the University of Cali-In this thesis we revisit the classic slow coherency and area aggregation approach to model reduction in power networks. The slow coherency approach is based on identifying sparsely and densely connected areas of a network, within which all generators swing coherently. A timescale separation and singul...

I present a class of functions unifying all singular limits for the emission of soft or collinear gluons in gauge-theory amplitudes at any order in perturbation theory. Each function is a generalization of the antenna functions of previous works. The helicity-summed interferences of these functions are thereby also generalizations to higher orders of the Catani-Seymour dipole factorization func...

In this paper are studied the nets of principal curvature lines on surfaces embedded in Euclidean 3−space near their end points, at which the surfaces tend to infinity. This is a natural complement and extension to smooth surfaces of the work of Garcia and Sotomayor (1996), devoted to the study of principal curvature nets which are structurally stable –do not change topologically– under small p...