Three aspects of texture are considered by the fractal geometry: Fractal Dimension (FD), Lacunarity and Succolarity. Fractal Dimension has been well studied; a great number of approaches have been presented to extract it from images. It can be computed from black-white to multi-band image. There are many approaches also, from the simple Box-Dimension to the most complex Hausdorff Dimension. The...

In this paper we present some new properties of the metric dimension defined by Bouligand in 1928 and prove the following new projection theorem: Let dimb(A − A) denote the Bouligand dimension of the set A − A of differences between elements of A. Given any compact set A ⊆ R such that dimb(A−A) < m, then almost every orthogonal projection P of A of rank m is injective on A and P |A has Lipschit...

What is the problem we wish to solve when we try to construct a rational economic order? On certain familiar assumptions the answer is simple enough. If we possess all the relevant information, if we can start out from a given system of preferences, and if we command complete knowledge of available means, the problem which remains is purely one of logic. That is, the answer to the question of w...

The role of population size is investigated within a neutrality induced local optima free search space. Neutrality decouples genotypic variation in evolvability from fitness variation. Population diversity and neutrality work in conjunction to facilitate evolvability exploration whilst restraining its loss to drift, ultimately facilitating the evolution of evolvability. The characterising dynam...

The paper deals with an algorithm for Hausdorff dimension estimation based on box-counting dimension calculation. The main goal of the paper is to propose a new approach to box-counting dimension calculation with less computational demands. Streszczenie. W artykule opisano algorytm estymacji wymiaru Hausdorffa oparty o wyznaczanie wymiaru pudełkowego. Głównym celem pracy jest zaproponowanie now...

The present study addresses optimal design of reinforced concrete (RC) columns based on equivalent equations considering deformability regulations of ACI318-14 under axial force and uniaxial bending moment. This study contrary to common approaches working with trial and error approach in design, at first presents an exact solution for intensity of longitudinal reinforcement in column section by...

LP-type problems are an abstract model of linear programming. For some applications it is useful to have LP-type problems satisfying a special property: nondegeneracy. For any LP-type problem there is a nondegenerate refinement, however the complexity measured by the combinatorial dimension may need to increase. We construct an example of an LP-type problem of dimension 4, for which any nondege...

The present paper generalises results by Lutz and Ryabko. We prove a martingale characterisation of exact Hausdorff dimension. On this base we introduce the notion of exact constructive dimension of (sets of) infinite strings. Furthermore, we generalise Ryabko’s result on the Hausdorff dimension of the set of strings having asymptotic Kolmogorov complexity ≤ α to the case of exact dimension. Th...

this paper evaluates and ranks the temporal dimensions, known as fourth dimension of urban design, of a number of places in a city by topsis method. topsis method is technique for order preference by similarity to ideal solution. topsis is one of the renowned methods for classical multi-criteria decision-making (mcdm) problems that defines the positive ideal solution and negative ideal solution...