recent studies on wavelet transform and fractal modeling applied on mammograms for the detection of cancerous tissues indicate that microcalcifications and masses can be utilized for the study of the morphology and diagnosis of cancerous cases. it is shown that the use of fractal modeling, as applied to a given image, can clearly discern cancerous zones from noncancerous areas. in this paper, f...

The size effect on structural strength is an important phenomenon with a very old history. Unfortunately, despite abundant experimental evidence, this phenomenon is still not taken into account in most specifications of the design codes for concrete structures, as well as the design practices for polymer composites, rock masses and timber. The main reason appears to be a controversy between two...

The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of t...

Analyses and investigations on river flow behavior are major issues in design, operation and studies related to water engineering. Thus, recently the application of chaos theory and new techniques, such as chaos theory, has been considered in hydrology and water resources due to relevant innovations and ability. This paper compares the performance of chaos theory with Anfis model and discusses ...

This study aims to evaluate the efficiency of the concentration-number (C-N) fractal model for discrimination of soil horizon regarding the depth distribution profile. In this regard, soil parameters such as pH, organic carbon content, calcareous mineral content, electrical conductivity and available phosphorus of Ziarat forestland in Golestan Province, north of Iran, has been investigated. The...

Fluctuational transitions between two co-existing chaotic attractors, separated by a fractal basin boundary, are studied in a discrete dynamical system. It is shown that the mechanism for such transitions is determined by a hierarchy of homoclinic points. The most probable escape path from the chaotic attractor to the fractal boundary is found using both statistical analyses of fluctuational tr...

Studies over the past decade have reported power-law distributions for the areas of terrestrial lakes and Arctic melt ponds, as well as fractal relationships between their areas and coastlines. Here we report similar fractal structure of ponds in a tidal flat, thereby extending the spatial and temporal scales on which such phenomena have been observed in geophysical systems. Images taken during...

According to the theory of deterministic fractal geometry, images can be modeled by deterministic fractal objects which are attractors of sets of two dimensional affine transformations. In this paper, a fractal modeling approach is developed to analyze and model mammographic breast tissue background. We show that general mammographic parenchymal and ductal patterns can be well modeled by a set ...

The notion of fractality, in the context of positive-valued probability distributions, is conventionally associated with the class of Paretian probability laws. In this research we show that the Paretian class is merely one out of six classes of probability laws – all equally entitled to be ordained fractal, all possessing a characteristic power-law structure, and all being the unique fixed poi...

Long term power load has a big impact on the development of industry of power. The forecasting models of linear systems even a single forecasting model of the nonlinear systems can not forecast the long term power load greatly. In the study, the combined forecasting model of nonlinear systems including chaos and fractal was established to improve the accuracy of the forecast. First, the charact...