[1] Box counting is widely used for characterizing fracture networks as fractals and estimating their fractal dimensions (D). If this analysis yields a power law distribution given by N / r , where N is the number of boxes containing one or more fractures and r is the box size, then the network is considered to be fractal. However, researchers are divided in their opinion about which is the bes...

The fractal tree-like branched network is an effective channel design structure to reduce the hydraulic resistance as compared with the conventional parallel channel network. In order for a laminar flow to achieve minimum hydraulic resistance, it is believed that the optimal fractal tree-like channel network obeys the well-accepted Murray's law of βm = N-1/3 (βm is the optimal diameter ratio be...

Microtubule Affinity-Regulating Kinase 2 (MARK2) protein has a substantial role in regulation of vital cellular processes like induction of polarity, regulation of cell junctions, cytoskeleton structure and cell differentiation. The abnormal function of this protein has been associated with a number of pathological conditions like Alzheimer disease, autism, several carcinomas and development of...

‎let $g$ be a finite group‎. ‎we say that the derived covering number of $g$ is finite if and only if there exists a positive integer $n$ such that $c^n=g'$ for all non-central conjugacy classes $c$ of $g$‎. ‎in this paper we characterize solvable groups $g$ in which the derived covering number is finite‎.‎

Fractal measures of images of continuous maps from the set of p-adic numbers Q p into complex plane C are analyzed. Examples of " anomalous " fractals, i.e. the sets where the D-dimensional Hausdorff measures (HM) are trivial, i.e. either zero, or σ-infinite (D is the Hausdorff dimension (HD) of this set) are presented. Using the Caratheodory construction, the generalized scale-covariant HM (GH...

This paper is an attempt to attain a new and profound model of the nature’s structure using a vortex-fractal theory (VFT). Scientists try to explain some phenomena in Nature that have not been explained so far. The aim of this paper is the vortex-fractal modeling of vortex-ring fractal structure of atoms, molecules, and a creation of elements in the Mendeleev’s periodic table with vortex-ring p...

Aggregation always occurs in industrial processes with fractal-like particles, especially dense systems (the volume fraction, ϕ>1%). However, the classic aggregation theory, established by Smoluchowski 1917, cannot sufficiently simulate particle dynamics systems, particularly those of generat ed particles. In this article, Langevin dynamic was applied to study collision rate aggregations as ...

In this paper we investigate some of the mathematical properties of meiotic recombination. Working within the framework of a genetic model with n loci, where alpha alleles are possible at each locus, we find that the proportion of all possible diploid parental genotypes that can produce a particular haploid gamete is exp[-n log(alpha(2)/[2alpha-1])]. We show that this proportion connects recomb...