Here, we study the topological properties of genetic sequence by viewing the entire sequence as a whole. First, a systematic way of coding the gene-combinations in a genetic sequence is developed. Next, we apply the coding method to real genetic sequences, and find a scale-free power-law distribution for some particular kinds of gene-combinations. Furthermore, we also present a model to reprodu...

We continue to study topological properties of the group Homeo(X) of all homeomorphisms of a Cantor set X with respect to the uniform topology τ , which was started in [B-K 1], [B-D-K 1; 2], [B-D-M], and [M]. We prove that the set of periodic homeomorphisms is τ -dense in Homeo(X) and deduce from this result that the topological group (Homeo(X), τ) has the Rokhlin property, i.e., there exists a...

In cryptography, the Cipher Block Chaining (CBC), one of the most commonly used mode in recent years, is a mode of operation that uses a block cipher to provide confidentiality or authenticity. In our previous research work, we have shown that this mode of operation exhibits, under some conditions, a chaotic behaviour. We have studied this behaviour by evaluating both its level of sensibility a...

We study fixed point theorems for maps which satisfy a property of stretching a suitably oriented topological space Z along the paths connecting two disjoint subsets Z− l and Z− r of Z . Our results reconsider and extend previous theorems in [56, 59, 60] where the case of two-dimensional cells (that is topological spaces homeomorphic to a rectangle of the plane) was analyzed. Applications are g...

One-dimensional topological superconductors host Majorana zero modes (MZMs), the nonlocal property of which could be exploited for quantum computing applications. We use spin-polarized scanning tunneling microscopy to show that MZMs realized in self-assembled Fe chains on the surface of Pb have a spin polarization that exceeds that stemming from the magnetism of these chains. This feature, capt...

Abstract. We propose a topological quantum phase transition for quantum states with different Berry phases in hole-doped III-V semiconductor quantum wells with bulk and structure inversion asymmetry. The Berry phase of the occupied Bloch states can be characteristic of topological metallic states. It is found that the adjustment of thickness of the quantum well may cause a transition of Berry p...

We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the “separation property”: different continuity pieces have disjoint images. The continuity pieces act as stable topological manifolds while the points in the discontinuity lines, separating different conti...

In this paper we discuss what kind of constrains combinatorial covering properties of Menger, Scheepers, and Hurewicz impose on remainders of topological groups. For instance, we show that such a remainder is Hurewicz if and only it is σ-compact. Also, the existence of a Scheepers non-σ-compact remainder of a topological group follows from CH and yields a P -point, and hence is independent of Z...

The two main features of the Aharonov-Bohm effect are the topological dependence of accumulated phase on the winding number around the magnetic fluxon, and nonlocality-local observations at any intermediate point along the trajectories are not affected by the fluxon. The latter property is usually regarded as exclusive to quantum mechanics. Here we show that both the topological and nonlocal fe...

An ideal on a set X is a nonempty collection of subsets of X with heredity property which is also closed finite unions. The concept of Γδ : P(X)→ τ defined as follows for every A ∈ X, Γδ(A) = {x ∈ X : there exists a U ∈ τ δ(x) such that U − A ∈ I}, was introduced by Al-Omari and Hatir [1]. In this paper, we introduce and study δ∗-homeomorphism and Γδ-homeomorphism. Also we give some application...