A new method for calculating fractal dimension is developed in this paper. The method is based on the box dimension concept; however, it involves direct estimation of a suboptimal covering of the data set of interest. By finding a suboptimal cover, this method is better able to estimate the required number of covering elements for a given cover size than is the standard box counting algorithm. ...

A theory of resource-bounded dimension is developed using gales, which are natural generalizations of martingales. When the resource bound ∆ (a parameter of the theory) is unrestricted, the resulting dimension is precisely the classical Hausdorff dimension (sometimes called “fractal dimension”). Other choices of the parameter ∆ yield internal dimension theories in E, E2, ESPACE, and other compl...

‎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.‎ 

In this paper, we investigate the singular points of suitable weak solutions co-rotational Beris-Edwards $ {\bf{Q}} $-tensor system modeling hydrodynamic motion nematic liquid crystals. More precisely, on one hand, give an upper bound for number at any fixed time; other obtain a parabolic fractal dimension possible set, which is bounded by \frac{455}{321}(\approx1.417) $.

The statistical properties of intra-chromosome maps obtained by a genome-wide chromosome conformation capture method (Hi-C) are described in the framework of the hierarchical crumpling model of heteropolymer chain with quenched disorder in the primary sequence. We conjecture that the observed Hi-C maps are statistical averages over many different ways of hierarchical genome folding, and show th...

In this study, a fractal, Y-shaped dual-mode resonator bandpass filter (BPF) with input-output cross-coupling is introduced. A parallel-coupling feed structure with a cross coupling has been used to generate two transmission zeroes (TZs) near the lower and upper cutoff frequency that can effectively improve the passband edge selectivity. Also, a fractal shaped based on conventional diamond and ...

Background: In food industry, carotenoids are used as food colorants conferring yellow to red color. This research was designed to study on lipid and β-carotene production by Rhodosporidium diobovatum cultured with different Carbon to Nitrogen (C/N) ratios. Methods: R. diobovatum was cultured in a medium containing 40 g/l glucose (as the carbon source) and different C/N ratios (20, 50, and 80)...

We solve exactly the 6-vertex model on a dynamical random lattice, using its representation as a large N matrix model. The model describes a gas of dense nonintersecting oriented loops coupled to the local curvature defects on the lattice. The model can be mapped to the c = 1 string theory, compactified at some length depending on the vertex coupling. We give explicit expression for the disk am...

Abstract In this paper, we discuss a connection between geometric measure theory and number theory. This method brings new point of view for some number-theoretic problems concerning digit expansions. Among other results, show that each integer k , there is $M>0$ such if $b_{1},\ldots ,b_{k}$ are multiplicatively independent integers greater than M infinitely many whose base $b_{1},b_{2},\ld...