The paper concerns the image, level and sojourn time sets associated with sample paths of Rosenblatt process. We obtain results regarding Hausdorff (both classical macroscopic), packing intermediate dimensions, logarithmic pixel densities. As a preliminary step we also establish inversion property process, as well some technical points distribution Z.

Let $S \subset \Bbb R^n$ be a smooth compact hypersurface with strictly positive second fundamental form, $E$ the Fourier extension operator on $S$, and $X$ Lebesgue measurable subset of $\Bbb R^n$. If contains ball each radius, then problem determining range exponents $(p,q)$ for which estimate $\| Ef \|_{L^q(X)} \leq C \| f \|_{L^p(S)}$ holds is equivalent to restriction conjecture. In this p...

In this paper, the fractal characteristics of goose down assembly are described by determining the pore area fractal dimension and the tortuosity fractal dimension. The goose down assembly, filled with mass of down fibers and pores, is loose and ductile. The pores are varying shapes and sizes, and distribute unevenly. Firstly, micro computed tomography is used to observe the internal microstruc...

We determined the changes in fractal dimensions and spatial correlations of regional pulmonary blood flow with increasing exercise in race horses (n = 4) by using 15-microm fluorescent microspheres. Fluorescence was measured to quantitate regional blood to 1.3-cm(3) samples (n = 1,621-2,503). Perfusion distributions were characterized with fractal dimensions (a measure of spatial variability) a...

We show that when the standard techniques for calculating fractal dimensions in empirical data (such as the box counting) are applied on uniformly random structures, apparent fractal behavior is observed in a range between physically relevant cutoffs. This range, spanning between one and two decades for densities of 0.1 and lower, is in good agreement with the typical range observed in experime...