Nanophotonics and nanometrology with planar X-ray waveguide-resonator

The mechanism of X-ray waveguide-resonance propagation or the radiation superstream model, which can become the ground of X-ray nanophotonics, is discussed briefly. Some attention is devoted to features consideration of the simplest devices characterized by the waveguide-resonance transportation of X-ray beams. The experimental data showing the user possibilities of a simplest waveguide-resonators application for diffractometry are presented. We discuss the main reasons to improve the metrological characteristics for total reflection X-ray fluorescence (TXRF) analytical method in case when the target exciting beam is formed by a waveguide-resonator. Some problems appearing during the waveguide-resonator application are formulated.     

The central limit theorem under the absence of extremal absolute order statistics

One finds conditions for the relation are the absolute order statistics for a repeated sample from a symmetric distribution.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 142, pp. 59–67, 1985.     

Law of the iterated logarithm for the quadratic variation of a wiener process

LetP _a be the class of those partitions of intervals [,T], such that |t _i –t _i–1 |>a, wherea is a constant, . It is proved that for anya lim V(T,P _a )/2Tln ₂T=1 a. s., whereln _i x=ln ln x, ifln x e,ln ₂ x=1, ifln x <e.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 72–80, 1987.