Nonlinear observer for synchronization of chaotic systems with application to secure data transmission

The main issue of this work is related with the design of a class of nonlinear observer in order to synchronize chaotic dynamical systems in a master-slave scheme, considering different initial conditions. The oscillator of Chen is proposed as a benchmark model and a bounded-type observer is proposed to reach synchronicity between both two chaotic systems. The proposed observer contains a proportional and sigmoid form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Some numerical simulations were carrying out in order to show the operation of the proposed methodology, with possible applications to secure data communications issues.     

Stable Manifolds for Impulsive Equations Under Nonuniform Hyperbolicity

For impulsive differential equations, we establish the existence of invariant stable manifolds under sufficiently small perturbations of a linear equation. We consider the general case of nonautonomous equations for which the linear part has a nonuniform exponential dichotomy. One of the main advantages of our work is that our results are optimal, in the sense that for vector fields of class C ¹ outside the jumping times, we show that the invariant manifolds are also of class C ¹ outside these times. The novelty of our proof is the use of the fiber contraction principle to establish the smoothness of the invariant manifolds. In addition, using the same approach we can also consider linear perturbations.     

OnE-compact modules over SISI rings

Summary We extend to the case of SISI rings, studied by Vamos in [8], the duality for noetherian rings studied by Orsatti in [7]. We prove that some properties of this duality can be generalized, while others hold only in the noetherian case.

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Riassunto Si estende al caso dei SISI anelli, studiati da Vamos in [8], la dualità studiata da Orsatti in [7] per gli anelli noetheriani. Si dimostra che alcune proprietà di questa dualità si possono generalizzare, mentre altre sono caratteristiche del caso noetheriano.

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Lavoro eseguito nell’ambito dell’attività dei gruppi di ricerca matematici del C.N.R.     

Canonical localizers and nonmaximal orders in the Witt setting

Let d(n) denote the number of positive integers dividing the positive integer n. We show that as x approaches ∞, $\text{\#{n ≤ x: d(n)}\text{divides}\text{n} = (}\text{x}\text{√}\text{log}\text{x)(}\text{log log}\text{x)}{}^{\mathrm{?1\; +\; 0(1)}}$.