No abstract

The aim of this paper is to study the dynamics of the real cubic polynomials that have a fixed point of multiplicity two. Such polynomials are conjugate to f a (x) = ax 2 (x − 1) + x, a ̸ = 0. We will show that when a > 0 and x ̸ = 1, then | f n a (x)| converges to 0 or ∞ and, if a < 0 and a belongs to a special subset of the parameter space, then there is a closed invariant subset Λ a of R on which f a is chaotic.

As far as marketing is concerned, brands have received much attention and become a key player in modern society. In fact, they are everywhere and they have penetrated all spheres of our life including economic, social, cultural, sporting, even religious aspects of our life.In spite of their pervasiveness and widespread use, brands have been also the subject of growing criticism (Klein, 1999). Brands are intangible assets that produce added benefits for the business. This issue pertains to the domain of strategic brand management whose focal concern is how to create value with proper brand management. Branding is crucial in B2B marketing and has attracted much attention. Business sectors have to differentiate themselves from the competitors, not only on the basis of their product but also on the basis of aspects such as management competencies, technologies, services and infrastructure.Industrial product marketers, whether large or small, should formulate their branding strategies effectively so that they can compete with the global competitors. The purpose of the current paper is to briefly discuss branding process. Moreover, it also examines the issues involved in the branding of B2B organizations. Finally, the paper concludes by introducing the strategies for business branding in the contemporary global environment. Paper is based on secondary information sources, ranging from print to electronic media.

Abstract. A recursive family {Fn} of holomorphic functions on the Riemann sphere is defined and some elementary properties of this family is described. Then the Julia set of Fn is computed. Finally this family as a real recursive family is studied and it is shown that Fn is chaotic on a specific subset of R.

The aim of this paper is to compute the topological entropy of the real cubic polynomials [Formula: see text], where [Formula: see text], in certain cases. To accomplish this, some algorithms for counting the number of laps of [Formula: see text], the [Formula: see text]th iteration of [Formula: see text], are presented.