This paper introduces a complete Gn-Menger space and defines the Hausdorff–Pompeiu distance in space. Furthermore, we show novel fixed-point theorem for Gn-Menger-θ-contractions fractal spaces.

Background:Leukemia is cancer of blood and bone marrow cells. In general, there are four types of leukemia: chronic myelogenous leukemia (CML), acute myeloid leukemia (AML), B-cell chronic lymphocytic leukemia (CLL) and acute lymphoblastic leukemia (ALL).  Fractal geometry can be introduced as one of the effective ways to detect this type of cancer. In this study, with introduc...

Fractal analysis of earthquakes, lineages and waterways are considered as one of the practical tools to evaluate tectonic activity. With the help of fractal analysis, structural maturity and tectonic dynamics can be evaluated. In this research, using fractal analysis and box counting method and fild studies, the measured fractal dimensions for the designed network of Alborz province were studie...

In this report we present experimental results using Haussdorf-Besicovich fractal dimension for performing morphological galaxy classification. The fractal dimension is a topological, structural and spatial property that give us information about the space were an object lives. We have calculated the fractal dimension value of the main types of galaxies: ellipticals, spirals and irregulars; and...

The notion of fractality, in the context of positive-valued probability distributions, is conventionally associated with the class of Paretian probability laws. In this research we show that the Paretian class is merely one out of six classes of probability laws – all equally entitled to be ordained fractal, all possessing a characteristic power-law structure, and all being the unique fixed poi...

recent studies on wavelet transform and fractal modeling applied on mammograms for the detection of cancerous tissues indicate that microcalcifications and masses can be utilized for the study of the morphology and diagnosis of cancerous cases. it is shown that the use of fractal modeling, as applied to a given image, can clearly discern cancerous zones from noncancerous areas. in this paper, f...

nique for estimating the potential similarity of protein 3D shape is proposed. It is found tures of proteins are of self-similarity, such a phenomenon can be well described by imensions. We then adopt the size and the volume fractal dimensionality of proteins to the spatial complexity of the protein shape. Such quantitative measurement is helpful to earch space when we retrieve protein structur...

phenomena in two dimensions. I spent most of the academic years 2013-2015 in Bonn, Germany (at the Max-Planck Institut and then the Hausdorff Center). In general, the Hausdorff dimension of a product is at least the sum of the dimensions of the two spaces. Does equality hold if one space is Euclidian? So let be. I find this discussion in Wikipedia very good: Fractal dimension Imagine a particul...

We study the problem of adsorption and collapse transition of a linear polymer chain situated in a fractal container represented by a 4-simplex lattice and interacting with a surface adsorbed linear polymer chain. The adsorbed chain monomers act as pinning sites for the polymer chain. This problem has been solved exactly using real space renormalization group transformation. The resulting phase...