The fractal dimension (FD) is a widely used magnitude having a basic formulation in terms of the Hausdorff measure. However, there are a lot of practical definitions mostly used to compute the FD of a given system not yet having a mathematically rigorous approach. In this paper, we analyze these...

In this paper we present an algorithm to estimate the Hausdorff fractal dimension. The algorithm uses a recursive formula with a fast enough convergence. The accuracy of results is independent on the size, i.e., degree of definition of the fractal set. This fact is particularly useful when...

We describe a symbolic-numerical method for the Fourier stability analyses of difference initial-value problems approximating the initial-value problems for hyperbolic or parabolic PDEs. The Fourier method is reduced to the algebra of the resultants. We further use the REDUCE computer algebra...

A problem posed by O. L. Deutsch (Deutsch, O. L. 1988. Artificial intelligence design challenge---Background, analysis, and relative performance of algorithms. J. Guidance, Control, and Dynamics 11 386--393.) as the Artificial Intelligence Design Challenge for the 1987 American Institute of...