Osteoporosis is a condition of decreased bone mass. This leads to fragile bones which are at an increased risk for fractures, more often, it affects postmenopausal women. In this paper we propose a study of osteoporosis with the fractal dimension. After an introduction to the theory and fractal dimension, we use the box counting method for the segmentation of radiographic images, the study of t...

. In this paper the principle of fractal theory and fractal brownion motion(FBM) are analyzed in detail. And it also analyses the physical meaning of FBM’s two parameters H and σ . The improved Diamond-Square algorithm is discussed in light of fractal interpolation and use it to simulate cloud, two-dimension texture terrain surface and three-dimension terrain. There are many kinds of effect whe...

The fractal distribution is the best statistical model for the size-frequency distributions that result from some lithic reduction processes. Fractals are a large class of complex, self-similar sets that can be described using power-law relations. Fractal statistical distributions are characterized by an exponent, D, called the fractal dimension. I show how to determine whether the size-frequen...

We study geometrical representation of oscillatory integrals with an analytic phase function and a smooth amplitude compact support. Geometrical properties the curves defined by integral depend on type critical point phase. give explicit formulas for box dimension Minkowski content these curves. Methods include Newton diagrams resolution singularities.

In this work we derive lower bounds for the Hausdorff and fractal dimensions of the global attractor of the Sabra shell model of turbulence in different regimes of parameters. We show that for a particular choice of the forcing term and for sufficiently small viscosity term ν, the Sabra shell model has a global attractor of large Hausdorff and fractal dimensions proportional to logν−1 for all v...

We introduce a fractal dimension for a metric space based on the persistent homology of subsets of that space. We exhibit hypotheses under which this dimension is comparable to the upper box dimension; in particular, the dimensions coincide for subsets of R whose upper box dimension exceeds 1.5.