INVERSION OF A MAPPING ASSOCIATED WITH THE AOMOTO–FORRESTER SYSTEM

This article is devoted to the study of a general class of Hamiltonian systems which extends the Calogero systems with external quadratic potential associated to any root system. The interest for such a class comes from a previous article of Aomoto and Forrester. We consider first the one-degree of freedom case and compute the Birkhoff series defined near each of its stationary points. In general, the analysis of the system motivates finding some expression for the inverses of a rational map introduced by Aomoto and Forrester. We derive here some diagrammatic expansion series for these inverses.

On the use of expansion series for stream ciphers

From power series expansions of functions on curves over finite fields, one can obtain sequences with perfect or almost perfect linear complexity profile. It has been suggested by various authors to use such sequences as key streams for stream ciphers. In this work, we show how long parts of such sequences can be computed efficiently from short ones. Such sequences should therefore be considered to be cryptographically weak. Our attack leads in a natural way to a new measure of the complexity of sequences which we call expansion complexity.

Essentially exact asymptotic solutions for Asian derivatives

In this paper, we will show how to obtain asymptotic solutions for the problem of pricing Asian options. Under the assumption that the underlying follows geometric Brownian motion, we will derive Taylor expansion series for the fixed and floating strike Asian options. While there will be no analytical formulae for calculating expansion coefficients, we will provide relatively simple algorithms for calculating them. The methodology is particularly effective for the case of continuously sampled fixed-strike Asian calls where it takes only seconds to obtain constants for the Taylor expansion series that can converge beyond 10 significant digits. It is needless to say that we need to calculate Taylor expansion constants only once and the option price would be an analytical expression constructed from a cumulative normal distribution function, an exponential function and finite sums.

Fatigue Life Prediction Due to Slug Flow in Extra Long Submarine Gas Pipelines Using Fourier Expansion Series

Some offshore gas production fields require transporting of production fluids through very long submarines pipelines, without a previous separation process. In these cases, a slug flow pattern may develop for some production conditions. Condensate slugs traveling in the pipeline, act as moving loads for the piping structure, especially for the unsupported pipe spans which can be of even hundreds of meters long, due to irregular sea bottom, therefore producing a dynamic response of the pipeline that in some cases may significantly reduce its fatigue life. In this work a previously presented model [1], which combines fluid equations for predicting slug characteristics and a structural finite element model of horizontal pipelines transporting slugs, is modified for reducing computational cost and to adapt fatigue life calculations to the case of submarine piping. In order to calculate maximum amplitudes of the dynamic response without a time integration scheme, it is considered that traveling slugs produce periodical loads in time for every spatial point of the pipeline, and consequently these loads may be expressed by means of Fourier expansion series. With these assumptions, a more realistic fatigue calculation for a diversity of pipelines conditions is obtained. Results show that for this improved model computational time is dramatically reduced, without a lost in precision, when compared to the previous model requiring a time integration process.