The superdiffusion equation with a fractional Laplacian Δα/2 in N-dimensional space describes the asymptotic (t→∞) behavior of a generalized Poisson process with the range (discontinuity) distribution

The probability density functions (PDFs) of the increments of fluctuating particle fluxes are investigated. It is found that the PDFs have heavy power-law tails decreasing as x ^{−α − 1} at x → ∞. This makes it possible to describe these PDFs in terms of fractionally stable distributions (FSDs) q(x; α, β, θ, λ). The parameters α, β, γ, and λ were estimated statistically using as an example the time samples of fluctuating particle fluxes measured in the edge plasma of the L-2M stellarator. Two series of fluctuating fluxes measured before and after boronization of the vacuum chamber were processed. It is shown that the increments of fluctuating fluxes are well described by DSDs. The effect of boronization on the parameters of FSDs is analyzed. An algorithm for statistically estimating the FSD parameters and a procedure for processing experimental data are described.

The problem of calculating the Mittag-Leffler function $E_{\rho ,\mu }(z)$ is considered in the paper. To solve this problem integral representations for the function $E_{\rho ,\mu }(z)$ are transformed in such a way that they could not contain complex variables and parameters. Integral representations written in this form allow one to use standard methods of numerical integration to calculate integrals contained in them. To verify the correctness of the integral representations obtained the function $E_{\rho ,\mu }(z)$ was calculated both with the use of obtained formulas and with the use of known representations of the Mittag-Leffler function. The calculation results demonstrate their exact matching. This fact is indicative of the correctness of new integral representations of the function $E_{\rho ,\mu }(z)$ that were obtained.

In our study, we estimate an effect from chromosome aberrations and genome mutations on changes in microRNA expression profiles in cancer cell lines demonstrating different radiosensitivity. Here, cell viability and microRNA spectrum have been estimated 1, 4, and 24 h after irradiation. MiSeq high-throughput sequencing system (Illumina, San Diego, CA, USA) is employed to perform microRNA spectrum estimation. In the K562 cell line, the number of expressed microRNAs in chromosomes demonstrates a more pronounced variation. An analysis of microRNA effects on signaling pathway activity demonstrates differences in post-transcriptional regulation of the expression of genes included into 40 signaling pathways. In the K562 cell line, microRNA dynamics analyzed for their dependence on chromosome localization show a wider scattering of microRNA expression values for a pair of chromosomes compared to the HL-60 cell line. An analysis of microRNAs expression in the K562 and HL-60 cell lines after irradiation has shown that chromosome abnormalities can affect microRNA expression changes. A study of radiation-induced changes of microRNA expression profiles in the K562 and HL-60 cell lines has revealed a dependence of microRNA expression changes on the number of chromosome aberrations and genome mutations.

Results are presented from experimental studies of variations in the plasma parameters during the excitation of a multiaxis magnetic configuration by the induction current (up to 17 kA) in the basic...