This article presents two caveats for the analysis of large-scale structure. Within distances for which the fractal structure of the distribution of galaxies obtains, fluctuations may be on the scale of the measurements themselves, as is typical of fractals. Second, within this region it is...

We investigate two important questions about the use of the nonextensive thermostatistics (NETS) formalism in the context of nonlinear galaxy clustering in the Universe. Firstly, we define a quantitative criterion for justifying nonextensivity at different physical scales. Then, we discuss the...

In this paper, we compute the probability that a segment of random position and of constant length intersects a side of a regular lattice with circular sections obstacles. In particular, we obtain the formula of a probability already computed by Caristi and Stoka, as well as the formula of the...

Let ηt be a Poisson point process of intensity t≥1 on some state space Y and let f be a non-negative symmetric function on Yk for some k≥1. Applying f to all k-tuples of distinct points of ηt generates a point process ξt on the positive real half-axis. The scaling limit of ξt as t tends...

We consider laser profiler measured soil profiles and show that the roughness of the cultivated soil can be viewed as an approximately self-affine structure. This conclusion is drawn from the limited range scaling behaviour found in both the variance and the second-order structure function of...

Polar vascular plants native to the Arctic and the Antarctic geobotanical zone have been growing and reproducing effectively under difficult environmental conditions, colonizing frozen ground areas formerly covered by ice.Our macroscopic observations and microscopic studies conducted by means of...

The evolution of compact surface of the 100 nm copper film deposited on the glass-ceramics doped with vanadium coating in the course of the oxidation by the CCl4–L (L = dimethylformamide (DMF), tetrahydrofuran (THF), dimethylsulfoxide (DMSO), CCl4 concentration ≈ 1 mol/L) was studied by...