For more than 60 years, the Anderson–Darling test is most frequently used among all Cramér–von Mises (omega-square) tests. This statistic modifies a classical empirical process defined within the [0, 1] interval by multiplying it by weighting function ψ(t) = (t(1–t))–1/2. The weighting function redistributes the test sensitivity to deviations of the distribution function of the observed stochastic quantity from a hypothetical distribution function in different its segments. However, the tests with other weighting functions may also be of interest in practice. New formulas for the eigenvalues of the Anderson–Darling statistic are proposed. The statistic “inverse” to the Anderson–Darling statistic with weighting function ψ(t) = (t(1–t))1/2 is considered. Tests with other weighting functions may also be of interest when weighted Cramér–von Mises statistics are used. The table of quantiles of statistics with weighting functions ψ(t) = tα(1–t)β, α >–1, β >–1 is presented. The quantiles are given for 36 different combinations of parameters α >–1 and β >–1. The table was calculated using accurate numerical methods and without application of modeling techniques.

A words phonetic decoding method in automatic speech recognition is considered. The properties of Kullback–Leibler divergence are used to synthesize the estimation of the distribution of divergence between minimum speech units (e.g., single phonemes) inside a single class. It is demonstrated that the minimum variance of the intraphonemic divergence is reached when the phonetic database is tuned to the voice of a single speaker. The estimations are proven by experimental results on the recognition of vowel sounds and isolated words of Russian language.

Methods for extension of the rejection band of microwave devices on the basis of planar modified mushroom-shaped metamaterials comprising either two-layered topological structures with frequency-selective surfaces or multilayer bulk structures with intermediate layers containing split-ring resonators are proposed. Computer simulation of such devices, clearly demonstrating a twoto six-fold extension of the rejection band is performed. Experimental results confirming the results of numerical simulation are presented.