Chaotic attractors in the two-dimensional border-collision normal form (a piecewise-linear map) can persist throughout open regions of parameter space. Such robust chaos has been established rigorously some regimes. Here we provide formal results for original regime [S. Banerjee, J.A. Yorke, C. Grebogi, Robust Chaos, Phys. Rev. Lett. 80(14):3049-3052, 1998]. We first construct a trapping region...

We consider uncertain fractional-order linear time invariant (FO-LTI) systems with interval coefficients. Our focus is on the robust controllability issue for interval FO-LTI systems in statespace form. We re-visited the controllability problem for the case when there is no interval uncertainty. It turns out that the stability check for FO-LTI systems amounts to checking the conventional intege...

A novel invariant pattern recognition approach is proposed based on a special gradient-type recurrent analog associative memory. The system exhibits stable equilibrium points in predefined positions specified by feature vectors extracted from the training set, while invariance to geometrical transformations is inferred by using the tangent distance. Experimental results for handwritten characte...

The original aim of this paper is to construct a graph associated to a vector space. By inspiration of the classical definition for the Cayley graph related to a group we define Cayley graph of a vector space. The vector space Cayley graph ${rm Cay(mathcal{V},S)}$ is a graph with the vertex set the whole vectors of the vector space $mathcal{V}$ and two vectors $v_1,v_2$ join by an edge whenever...

Abstract In the present paper, we consider a special class of third-order polynomial evolutionary equations. These equations, via Lie theory admit same one-parameter point transformations which leave equations invariant. Reductions with these invariant functions lead to highly nonlinear ordinary differential We use power series establish interesting solutions reduced whereby recurrence relation...

It is commonly known that wavelet expansions are very sensitive to translation of an input signal due to their dyadic structure. Without proper time alignment of the signal to the decomposition basis vectors, a compact expansion may be unattainable. Recently, work has been done to combat translation sensitivity by determining the best translation-invariant expansion of a signal with respect to ...

We consider a generalized class of relay controllers where the system input may take values in a finite set of constant vectors. A simple continuous-time design method is proposed for linear time invariant (LTI) systems. Furthermore, it is used in the sampled-data case in order to guarantee (locally) the practical stabilization to a bounded ellipsoid containing the origin. The sampling interval...

In this paper we present a set of 3D-rigid motion invariant texture features. We experimentally establish that when they are combined with mean attenuation intensity differences the new augmented features are capable of discriminating normal from abnormal liver tissue in arterial phase contrast enhanced X-ray CT–scans with high sensitivity and specificity. To extract these features CT-scans are...

Let be weighted Bergman space on a bounded symmetric domain . It has analytic continuation in the weight and for in the so-called Wallach set still forms unitary irreducible (projective) representations of . We give the irreducible decomposition of the tensor product of the representation for any two unitary weights and we find the highest weight vectors of the irreducible components. We find a...