Institute of Theoretical Physics, U. of Tübingen, D-72070 Tübingen, Germany (Dated: February 2, 2008) Abstract A semi-perturbative calculation of the ghost-gluon vertex in Landau gauge Yang-Mills theory in four and three Euclidean space-time dimensions is presented. Non-perturbative gluon and ghost propagators are employed, which have previously been calculated from a truncated set of Dyson– Sc...

In this paper, a homotopy perturbation method (HPM) and modified homotopy perturbation (MHPM) are proposed to solve singular integral equation with generalized Abel's kernel.

Exchange lemmas are used in geometric singular perturbation theory to track flows near normally hyperbolic invariant manifolds. We prove a General Exchange Lemma, and show that it implies versions of existing exchange lemmas for rectifiable slow flows and loss-of-stability turning points. © 2007 Elsevier Inc. All rights reserved. MSC: 34E15; 34C30

We introduce a framework for the analysis of extremum seeking systems for dynamic maps based on Lie bracket approximations and singular perturbation theory. Using the introduced framework, we provide an extremum seeking regulator for a unicycle and prove its stability properties. © 2017 Elsevier Ltd. All rights reserved.

After reviewing a number of results from geometric singular perturbation theory, we discuss several approaches to obtain periodic solutions in a slow manifold. Regarding nonhyperbolic transitions we consider relaxation oscillations and canard-like solutions. The results are illustrated by prey-predator systems.

We study a singular perturbation problem for a nonlocal evolution operator. The problem appears in the analysis of the propagation of flames in the high activation energy limit, when admitting nonlocal effects. We obtain uniform estimates and we show that, under suitable assumptions, limits are solutions to a free boundary problem in a viscosity sense and in a pointwise sense at regular free bo...

In general, for higher order elliptic equations and boundary value problems like the biharmonic equation and the linear clamped plate boundary value problem neither a maximum principle nor a comparison principle or – equivalently – a positivity preserving property is available. The problem is rather involved since the clamped boundary conditions prevent the boundary value problem from being rea...

Let A denote a square complex matrix and let E be a perturbation matrix. The purpose of this paper is to investigate the perturbation of the Drazin inverse when B = A + E satisfies the rank conditions rankA = rankB = rankAB, where r and s denote the indices of A and B, respectively. We will derive an explicit representation of B as a function of A and B −A , for certain positive integers j, k. ...

We consider the approximation of a weakly coupled system of two singularly perturbed reaction-diffusion equations, with the finite element method. The first differential equation contains a small parameter multiplying the highest derivative, while the second does not. As a result, the first component of the solution to the system will contain boundary layers and our goal is to construct and ana...

The Beverton-Holt and Ricker functions are two distinct ecological descriptions of the link between a parental population size and subsequent offspring that may survive to become part of the fish stock. This report presents a model consisting of a system of ordinary differential equations (ODEs), which couples a pre-recruit stage with several adult stages. Elements of slow-fast dynamics capture...