The famous game Towers of Hanoi is related with a family of so–called Hanoi–graphs. We regard these non self–similar graphs as geometrical objects and obtain a sequence of fractals (HGα)α converging to the Sierpiński gasket which is one of the best studied fractals. It is shown that this convergence holds not only with respect to the Hausdorff distance, but that also Hausdorff dimension does co...

In this paper we identify a class of profinite groups (totally torsion free groups) that includes all separable Galois fields containing an algebraically closed subfield, and demonstrate it can be realized as inverse limit virtually finitely generated abelian (tfvfga) groups. We show by examples the condition is quite restrictive. particular, semidirect products are rarely totally free. The res...

This paper considers in general the problem of finding the minimum of a given functional f(u) over a set B by approximately minimizing a sequence of functionals /„(«„) over a "discretized" set B„; theorems are given proving the convergence of the approximating points un in Bn to the desired point u in B. Applications are given to the Rayleigh-Ritz method, regularization, Chebyshev solution of d...

A method is presented for clustering signal space generated by information intensive decentralized systems. By identifying signal space with locally square summable functions, a universal dynamics is designed for successively approximating feature parameters in Fourier images. The approximation sequence is not monotone. However, we can design aggregation scheme for ordering Fourier images gover...

In this paper we propose an enhanced version of the DCSK (Differential Chaos Shift Keying) scheme where the carrier symbolic dynamics are exploited for conveying useful information. This is achieved by means of a pseudo-chaotic encoder which spreads the input sequence approximating the dynamics of the Bernoulli shift. The information encoded in the pseudo-chaotic carrier is retrieved by using s...

We consider a particular class of hybrid systems, defined by a piecewise affine dynamic over non-overlapping regions of the state space. We want to control their behaviors so that it reaches a target by minimizing a given cost. We provide a new numerical algorithm under-approximating the controllable domain under the given hybrid dynamic. Given an optimal sequence of states of the hybrid automa...