We obtain an explicit expression relating the writhing number, W [C], of the quantum path, C, with any value of spin, s, of the particle which sweeps out that closed curve. We consider a fractal approach to the fractional spin particles and , in this way, we make clear a deeper connection between the Gauss-Bonnet theorem with the spin-statistics relation via the concept of Hausdorff dimension, ...

we introduce a model for prediction the behavior of electrodes which modified withcarbon nanotubes in a polymer medium. these kinds of polymer composites aredeveloped in recent years, and experimental data for its percolation threshold isavailable. we construct a model based on percolation theory and fractal dimensionsand using experimental percolation threshold for calculating the moments of c...

Fractal image coding is a novel technique for still ima ge c ompression. I n t his paper, a low b it rate r egion-based fractal image compression algorithm i s pr oposed, sev eral techniques ar e i ncluded as follows. First, we improve the performance of quadtree segmentation by adaptive threshold. T hen, a me rging s cheme is e mployed t o t he r esulting quadtree segm entation t hat co mbines...

It is well known that the permeability and density of an aggregate decreases with its size, affecting its settling velocity and coagulation rate (rate of particle capture) with other particles. This change in aggregate density with size can be described by fractal scaling relationships. Two distinctly different fractal scaling approaches, however, have been used to describe aggregate permeabili...

A minor-closed class of matroids is (strongly) fractal if the number n-element in dominated by excluded minors. We conjecture that when K an infinite field, K-representable strongly fractal. prove sparse paving with at most k circuit-hyperplanes a least three. The minor-closure spikes (with k≥5) satisfies strictly weaker condition: 2t-element However, there are only finitely many minors ground ...

Purpose – Fractal geometry can be used to model natural objects which cannot be easily represented by the euclidean geometry. However, contemporary computer-aided design (CAD) and computer-aided manufacturing (CAM) systems cannot be used to model a fractal object efficiently. In a general layer manufacturing (LM) workflow, a model described by the euclidean geometry is required in order to gene...

Fluctuations in light scattering from a finite ensemble of fractal clusters are studied numerically and theoretically. It is shown that, for a wide range of wavelengths and angles, relative fluctuations in the scattered intensity are very close to 1 and do not depend on the number of monomers N in fractal clusters (whereas they are proportional to 1/AN for trivial clusters). The relations descr...

We consider a map called a double rotation, which is composed of two rotations on a circle. Specifically, a double rotation is a map on the interval [0, 1) that maps x ∈ [0, c) to {x + α}, and x ∈ [c, 1) to {x + β}. Although double rotations are discontinuous and non-invertible in general, we show that almost every double rotation can be reduced to a simple rotation, and the set of parameters s...