Abstract
We study the European river Danube and the South American river Negro daily water levels. We present a fit for the Negro daily water level period and standard deviation. Unexpectedly, we discover that the river Negro and Danube are mirror rivers in the sense that the daily water levels fluctuations histograms are close to the universal non-parametric BHP and reversed BHP, respectively. Hence, the probability of a certain positive fluctuation range in the river Negro is, approximately, equal to the probability of the corresponding symmetric negative fluctuation range in the river Danube.

Abstract
Deegan and Packel (1979) and Holler (1982) proposed two power indices for simple games: the Deegan-Packel index and the Public Good Index. In the definition of these indices, only minimal winning coalitions are taken into account. Using similar arguments, we define two new power indices. These new indices are defined taking into account only those winning coalitions that do not contain null players. The results obtained with the different power indices are compared by means of two real-world examples taken from the political field.

Abstract
We consider the alpha re-scaled Standard & Poor's 100 (SP100) daily index positive returns r(t)(alpha) and negative returns (-r(t))(alpha) that we call, after normalization, the alpha positive fluctuations and alpha negative fluctuations, respectively. We use the Kolmogorov-Smirnov statistical test as a method to find the values of alpha that optimize the data collapse of the histogram of the alpha fluctuations with the truncated Bramwell-Holdsworth-Pinton (BHP) probability density function (pdf) and the truncated generalized log-normal pdf f(LN) that best approximates the truncated BHP pdf. The optimal parameters we found are alpha(+)(BHP) = 0.52, alpha(-)(BHP) = 0.48, alpha(+)(LN) = 0.52 and alpha(-)(LN) = 0.50. Using the optimal alpha's, we compute analytical approximations of the probability distributions of the normalized positive and negative SP100 index daily returns r(t). Since the BHP pdf appears in several other dissimilar phenomena, our result reveals a universal feature of the stock exchange markets.

Abstract
We prove that the speed of convergence of two Markov families determines the smoothness of the conjugacy between them. One of the applications of this result that we give is that the attractors of any two quadratic foldings at the Feigenbaum accumulation point of period doubling are C2+0.11 conjugate. Our main result provides the basis for a complete unification of renormalization and smooth conjugacy results which includes both the classical theorems and more recent results about critical systems.

Abstract
Let f and g be C-r unimodal maps, with r >= 3, topologically conjugated by h and without periodic attractors. If h is strongly differentiable at a point p in the expanding set E(f), with h'(p) not equal 0, then, there is an open renormalization interval J such that h is a C-r diffeomorphism in the basin B(J) of J, and h is not strongly differentiable at any point in I \ B(J). The expanding set E(f) contains all points with positive Lyapunov exponent, and if f has a Milnor's interval cycle attractor A then E(f) has full Lebesgue measure.

Abstract
We prove a one-to-one correspondence between (i) C1+ conjugacy classes of C1+H Cantor exchange systems that are C1+H fixed points of renormalization and (ii) C1+ conjugacy classes of C1+H diffeomorphisms f with a codimension 1 hyperbolic attractor Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. However, we prove that there is no C1+alpha Cantor exchange system, with bounded geometry, that is a C1+alpha fixed point of renormalization with regularity alpha greater than the Hausdorff dimension of its invariant Cantor set. (C) 2007 Published by Elsevier Inc.