In this report, we focus on the synthetic challenges for nanoscale 3D fractal architectures, namely the multi-generation growth with control in both size uniformity and colloidal stability; by directing the simultaneous growth of Au and polyaniline on Au seeds, fractal nanoparticles can be achieved with a topology distinctively different from those of spheres, cubes or rods.

Despite half a century of fuzzy sets and fuzzy logic progress, as fuzzy sets address complex and uncertain information through the lens of human knowledge and subjectivity, more progress is needed in the semantics of fuzzy sets and in exploring the multi-modal aspect of fuzzy logic due to the different cognitive, emotional and behavioral angles of assessing truth. We lay here the foundations of...

We have pursued in the literature a fractal-like structure for the fractional quantum Halll effect-FQHE which consider the Hausdorff dimension associated with the quantum mechanics paths and the spin of the particles or quasiparticles termed fractons. These objects carry rational or irrational values of spin and satisfy a fractal distribution function associated with a fractal von Neumann entro...

Fractal geometry provides a powerful tool for scale-free spatial analysis of cities, but the fractal dimension calculation results always depend on methods and scopes of study area. This phenomenon has been puzzling many researchers. This paper is devoted to discussing the problem of uncertainty of fractal dimension estimation and the potential solutions to it. Using regular fractals as archety...

A novel printed octagonal fractal microstrip antenna with semi-elliptical ground plane is presented for ultra wide band applications. The proposed antenna has a compact size of 20×20×1 mm³. The measured result of the antenna exhibits the ultra wide band characteristics from 2/9 to 14/2 GHz. In this paper, reducing antenna’s size by 35%, the same results were achieved, while small dimension frac...

In this paper, a new compact multiband patch microstrip antenna design is presented as a candidate for use in modern multi-functions communication systems. The proposed antenna design is fractally generated using Koch fractal curve geometry applied to the conventional square microstrip patch antenna. Antenna structures resulting from the successive iterations in the proposed fractal generation ...

Dimensionality reduction is an important issue in data mining and machine learning. Traina[1] proposed a feature selection algorithm to select the most important attributes for a given set of n-dimensional vectors based on correlation fractal dimension. The author used a kind of multi-dimensional “quad-tree” structure to compute the fractal dimension. Inspired by his work, we propose a new and ...

We describe two dimensional DNA walks, and analyze their fractal properties. We show results for the complete genome of S. cerevisiae. We find that the mean square deviation of the walks is superdifussive, corresponding to a fractal structure of dimension lower than two. Furthermore, the coding part of the genome seems to have smaller fractal dimension, and longer correlations, than noncoding p...

BACKGROUND The purpose of this study was to quantify the heterogeneous distribution of echodensities in the pericardial fluid of patients with tuberculous pericarditis using echocardiography and fractal analysis, and to determine whether there were differences in the fractal dimensions of effusive-constrictive and effusive non-constrictive disease. METHODS We used fractal geometry to quantify...