We use the fractional integrals to describe fractal solid. We suggest to consider the fractal solid as special (fractional) continuous medium. We replace the fractal solid with fractal mass dimension by some continuous model that is described by fractional integrals. The fractional integrals are considered as approximation of the integrals on fractals. We derive fractional generalization of the...

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...

Today Fractal geometry is completely new area of research in the field of computer science and engineering. It has wide range of applications. Fractals in nature are so complicated and irregular that it is hopeless to model them by simply using classical geometry objects. Benoit Mandelbrot, the father of fractal geometry, from his book The Fractal Geometry of Nature, 1982. This paper explor var...

Model-based diagnostic reasoning often leads to a large number of diagnostic hypotheses. The set of diagnoses can be reduced by taking into account extra observations (passive monitoring), measuring additional variables (probing) or executing additional tests (sequential diagnosis/test sequencing). In this paper we combine the above approaches with techniques from Automated Test Pattern Generat...

Significant advances have been made on our understanding of the fate and transport of engineered nanomaterials. One unexplored aspect of nanoparticle aggregation is how environmental stimuli such as light exposure and temperature variations affect the mobility of engineered nanoparticles. In this study, TiO(2), ZnO, and CeO(2) were chosen as model materials for investigating the mobility of nan...

The fractal interpolation theory was used to the research of road surface roughness, and its simulating method was proposed through the piecewise fractal model. The fractal interpolation model was established for the actual road surface roughness, its influential factors and their laws of influencing were also analyzed, and then the model accuracy was confirmed by the fractal parameters and the...