This paper is concerned with finite sample approximations to the supremum of a nondegenerate U -process of a general order indexed by a function class. We are primarily interested in situations where the function class as well as the underlying distribution change with the sample size, and the U -process itself is not weakly convergent as a process. Such situations arise in a variety of modern ...

PURPOSE This in vitro study compared the effect of five different techniques on the surface roughness of feldspathic porcelain. MATERIALS AND METHODS 100 feldspathic porcelain disk samples mounted in acrylic resin blocks were divided into five groups (n=20) according to type of surface treatment: I, hydrofluoric acid (HFA); II, Deglazed surface porcelain treated with Neodymium:yttrium- alumin...

In this paper, Kolmogorov-Sinai entropy is studied using mathematical modeling of an observer $ Theta $. The relative entropy of a sub-$ sigma_Theta $-algebra having finite atoms is defined and then   the ergodic properties of relative  semi-dynamical systems are investigated.  Also,  a relative version of Kolmogorov-Sinai theorem  is given. Finally, it is proved  that the relative entropy of a...

A model of laminated wave turbulence is presented. This model consists of two co-existing layers one with continuous waves’ spectra, covered by KAM theory and Kolmogorov-like power spectra, and one with discrete waves’ spectra, covered by discrete classes of waves and Clipping method. Some known laboratory experiments and numerical simulations are explained in the frame of this model. PACS: 47....

The theory of Kolmogorov complexity is based on the discovery, by Alan Turing in 1936, of the universal Turing machine. After proposing the Turing machine as an explanation of the notion of a computing machine, Turing found that there exists one Turing machine which can simulate any other Turing machine. Complexity, according to Kolmogorov, can be measured by the length of the shortest program ...