We discuss the prepotential describing the effective field theory of N =2 heterotic superstring models. At the one loop-level the prepotential develops logarithmic sin-gularities due to the appearance of charged massless states at particular surfaces in the moduli space of vector multiplets. These singularities modify the classical duality symmetry group which now becomes a representation of th...

The problems of swinging up an inverted pendulum on a cart and controlling it around the upright position have been traditionally treated as two separate problems. This paper proposes a strategy that is globally asymptotically stabilizing under actuator saturation and, in addition, locally exponentially stabilizing. The proposed methodology performs swing up and control simultaneously and uses ...

This paper analyzes a food web with a predator and two non-competing preys where the predation follows the density gradient of the prey. The longterm dynamics of the food web and short-term population crashes and outbreaks are analyzed using singular perturbation analysis.

There are typically several perturbation methods for approaching the solution of weakly nonlinear vibrations (where terms “small” compared to linear ones): Method Strained Parameters, Naive Singular Perturbation Method, Multiple Scales, Harmonic Balance and Averaging. The Straightforward Expansion (SEPM) applied does not usually yield correct solutions. In this manuscript, we provide mathematic...

In chemical engineering, several processes are represented by singular boundary value problems. In general, classical numerical methods fail to produce good approximations for the singular boundary value problems. In this paper, Chebyshev finite difference (ChFD) method and DTM-Pad´e method, which is a combination of differential transform method (DTM) and Pad´e approximant, are applied for sol...

We consider the diffusive single species growth in a plug flow reactor model with distributed delay. For small delay, existence and uniqueness of such wavefronts are proved when the convolution kernel assumes the strong generic delay kernel. The approaches used in this paper are geometric singular perturbation theory and the center manifold theorem.

Lidskii’s perturbation theory ( → 0) is presented in algorithmic form. This clarifies the role of a singular step. When such a step is first encountered, the quantification becomes incomplete beyond the singularity in a way that is described. An application is made to Homotopic Deviation. In this particular case, the missing information can be provided by direct computation.

This paper extends the concept of decentralized integral controllability to nonlinear process, and presents a steady state sufficient condition by using the singular perturbation theory. A numerical method is provided to facilitate the analysis of the proposed condition and is illustrated using an example of a dual tank level control system. © 2004 Elsevier Ltd. All rights reserved.

We study F-theory duals of six dimensional heterotic vacua in extreme regions of moduli space where the heterotic string is very strongly coupled. We demonstrate how to use orientifold limits of these F-theory duals to regain a perturbative string description. As an example, we reproduce the spectrum of a T /ZZ4 orientifold as an F-theory vacuum with a singular K3 fibration. We relate this vacu...