Electronic mail is very important in present time. Many researchers work for designing, improving, securing, fasting, goodness and others fields in electronic mail. This paper introduced new algorithm to use Cantor sets and cubic spline interpolating function in the electronic mail design. Cantor sets used as the area (or domain) of the mail, while spline function used for designing formula. Th...

Abstract. In this article we give necessary and sufficient conditions that a complex number must satisfy to be a continuous eigenvalue of a minimal Cantor system. Similarly, for minimal Cantor systems of finite rank, we provide necessary and sufficient conditions for having a measure theoretical eigenvalue. These conditions are established from the combinatorial information of the Bratteli-Vers...

Let T : Λ → Λ be an expanding map on a Cantor set. For each suitably normalized Hölder continuous potential, we construct a spectral triple from which one may recover the associated Gibbs measure as a noncommutative measure.

A Cantor set is a nonempty, compact, totally disconnected, perfect subset of IR. Now, the set being totally disconnected means that it is scattered about like a “dust”. If you shine light on a clump of dust floating in the air, the shadow of this dust will look like a bunch of spots on the wall. You would be very surprised if you saw that the shadow was a filled-in shape (like a rabbit, say!). ...

In this paper we define a new class of metric spaces, called multimodel Cantor sets. We compute the Hausdorff dimension and show that the Hausdorff measure of a multi-model Cantor set is finite and non-zero. We then show that a bilipschitz map from one multi-model Cantor set to another has constant Radon-Nikodym derivative on some clopen. We use this to obtain an invariant up to bilipschitz hom...

We estimate the Hausdorff measure and dimension of Cantor sets in terms of a sequence given by the lengths of the bounded complementary intervals. The results provide the relation between the decay rate of this sequence and the dimension of the associated Cantor set. It is well-known that not every Cantor set on the line is an s-set for some 0 ≤ s ≤ 1. However, if the sequence associated to the...

We extend the results obtained for different cases of the product superposition of periodic functions, and the determination of the scattered fields, for the case of circular symmetry. The characteristics of focalization for such cases are studied. We name Cantor-Fresnel zone plate the structures obtained with this method. Also, in this study can be included the focalization by periodic, Cantor...

We show a homeomorphic equivalent relation among the compact subspaces (Cantor middle-third sets, two-sided shift map of Cantor sets and ternary sets etc.) of the real line. Using such result, we show that there exists a chaotic homeomorphism of a compact subspace of the real line onto itself if and only if it is homeomorphic to the Cantor set.

In recent years, folding of various objects have been generated using different approaches. The classical Cantor set is an interesting mathematical construction with links to several areas of analysis and topology. The purpose of this paper is to represent the folding of Cantor string (compliment of Cantor set) using direct folding and folding by cut methods. Moreover, the results governing the...