In a normed linear space X, consider a nonempty closed set K which has the property that for some r > 0 there exists a set of points xo € X\K, d(xoK) > r, which have closest points p(xo) € K and where the set of points xo — r((xo — p(xo))/\\xo — p(zo)||) is dense in X\K. If the norm has sufficiently strong differentiability properties, then the distance function d generated by K has similar dif...

In this paper, we consider a particular class of integral equations of the fourth kind and show that tractability and differentiability index of the given system are 3. Tractability and dierentiability index are introduced based on the-smoothing property of a Volterra integral operator and index reduction procedure, respectively. Using the notion of index, we give sucient conditions for the exi...

We analyze whether a given set of analytic functions is an Extended Chebyshev system. This family of functions appears studying the number of limit cycles bifurcating from some nonlinear vector field in the plane. Our approach is mainly based on the so called Derivation-Division algorithm. We prove that under some natural hypotheses our family is an Extended Chebyshev system and when some of th...

Recently, a new scheme was proposed for deniable authentication. Its main originality lied on applying a chaos-based encryption-hash parallel algorithm and the semi-group property of the Chebyshev chaotic map. Although original and practicable, its insecurity and inefficiency are shown in this paper, thus rendering it inadequate for adoption in e-commerce.

Let K be a number field with algebraic closure K, let S be a finite set of places of K containing the archimedean places, and let φ be a Chebyshev polynomial. We prove that if α ∈ K is not preperiodic, then there are only finitely many preperiodic points β ∈ K which are S-integral with respect to α.