The relation between the upper and lower asymptotic estimates of the density and the fractal dimensions on the sphere of the spectral measure for a multivariate stable distribution is discussed. In particular, the problem and the conjecture on the asymptotic estimates of multivariate stable densities in the work of Pruitt and Taylor in 1969 are solved. The proper asymptotic orders of the stable...

We explore the relation between the local fractal dimension and the development of the built-up area of the Northern Margin of the Metropolitan Area of Lisbon (NMAL), for the period between 1960 and 2004. To this end we make use of a Generalized Local Spatial Entropy (GLSE) function based on which urban areas can be classified into five different types. Our analysis of NMAL shows how some of th...

1 Department of Engineering Mechanics, College of Water-Conservancy and Civil Engineering, Shandong Agricultural University, Taian 271000, China 2 Department of Engineering Mechanics, Hohai University, Nanjing 210098, China 3 Institute of Fluid Flow Machinery, Polish Academy of Sciences, 80-952 Gdańsk, Poland 4 Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom...

Investigation of the fractal behaviour of unvoiced plosive consonants leads to interesting observations towards their classi cation. Experimental evidence of the fractal nature of the speech signals themselves, as well as of their derivatives and cumulative sums prompt the use of the associated fractal dimensions to form a discriminative feature set. The obtained feature set is compact in repre...

In this letter we present an idea which reconciles a homogeneous and isotropic Friedmann universe with a fractal distribution of galaxies. We use two observational facts: The flat rotation curves of galaxies and the (still debated) fractal distribution of galaxies with fractal dimension D = 2. Our idea can also be interpreted as a redefinition of the notion of bias.

A 3D scalar grid is a grid of vertices where each vertex is associated with some scalar value. The grid covers some rectilinear region and partitions that region into cubes. An isosurface for a given isovalue is a triangular mesh which approximates the level set for the isovalue. The size of an isosurface is the number of triangles in the isosurfaces mesh, while the size of a scalar grid is the...

Measuring animal track or other trajectories (for example the track of a flowing particle) by divider method to obtain the fractal dimension without knowing the chronology of the points of the path, one can obtain erroneous results. The importance of time-indexing of the track’s point will be demonstrated by a simply geometrical example. Neglecting these indices, the error can be high enough to...

To better understand the characteristics of seepage-pores (pore radius larger than 100 nanometers) and their influence on the permeability of coals, we have conducted fractal analyses for 34 fresh coal samples (mean maximum vitrinite reflectance Ro,max from 0.43% to 4.21%) from North, Northwest and Northeast China. Mercury porosimetry data indicate that the coals are fractal, with pore radius r...

There exists observational evidence that the interstellar medium has a fractal structure in a wide range of spatial scales. The measurement of the fractal dimension (Df) of interstellar clouds is a simple way to characterize this fractal structure, but several factors, both intrinsic to the clouds and to the observations, may contribute to affect the values obtained. In this work we study the e...