In this paper, using a power series methodology we describe a design procedure applicable to analytic nonlinear plants. Our technique is a generalization of the linear H theory. In contrast to previous work on this topic ([3], [14], [15]), we now are able to explicitly incorporate a causality constraint into the theory. In fact, we show that it is possible to reduce a causal optimal design prob...

In transportation and telecommunication systems, the performance of the underlying network can often be improved by upgrading some of the arcs in the network. If an arc is upgraded, the travel time along this arc is reduced by a discount factor α, 0 ≤ α < 1. With respect to different minimax network objectives, we define a series of problems that involve finding the best q arcs in a network to ...

We present a numerical method, based on exact series expansions, that distinguishes between lattice-based models both in combinatorics and statistical mechanics that are likely to be solvable in terms of simple functions of mathematical physics, and those that possess a natural boundary in a suitably de ned complex plane. This latter class cannot therefore be algebraic, nor di erentiably nite n...

The interaction between an atom and a one mode external driving field is an ubiquitous problem in many branches of physics and is often modeled using the Rabi Hamiltonian. In this paper we present a series of analytically solvable Hamiltonians that approximate the Rabi Hamiltonian and compare our results to the Jaynes-Cummings model which neglects the so-called counter-rotating term in the Rabi...

Recently, Gómez-Ullate et al. [1] have studied a particular N -particle quantum problem with an elliptic function potential supplemented by an external field. They have shown that the Hamiltonian operator preserves a finite dimensional space of functions and as such is quasi exactly solvable (QES). In this paper we show that other types of invariant function spaces exist, which are in close rel...

A high temperature expansion is employed to map some complex anisotropic nonhermitian three dimensional Ising models with algebraic long range interactions into a solvable two dimensional variant. Some solutions are presented. This framework further allows for some very simple general observations. It will be seen that the absence of a “phase interference” effect plays an important role in high...