MATRIX RESOLVING FUNCTIONS IN THE LINEAR GROUP PURSUIT PROBLEM WITH FRACTIONAL DERIVATIVES

In finite-dimensional Euclidean space, we analyze the problem of pursuit of a single evader by a group of pursuers, which is described by a system of differential equations with Caputo fractional derivatives of order $alpha.$ The goal of the group of pursuers is the capture of the evader by at least $m$ different pursuers (the instants of capture may or may not coincide). As a mathematical basis, we use matrix resolving functions that are generalizations of scalar resolving functions. We obtain sufficient conditions for multiple capture of a single evader in the class of quasi-strategies. We give examples illustrating the results obtained

Variety of Aspects of Researches of Graphic Activity as Pedagogical Problem

The paper concerns the works of the educational specialists on the problem of teaching art to children and youth. It analyses the works of A.S. Akhmanov, F.I. Schmidt, A.B. Bakushinsky and others. The article gives the retrospective review of the pedagogical works concerning teaching art to children. It was studied in detail by a great number of educators and methodologists, each of whom revealed one side of it. As a result, the artistic activity has been thoroughly studied and characterized since the 1920s. Almost all of its many aspects were touched and studied. The researchers developed different methods which dealt with space coordination, the peculiarities of the perception of various kinds of art and other aspects of art activity. DOI: 10.5901/mjss.2015.v6n1s2p9

Small-angle neutron scattering and magnetically heterogeneous state in Sr2FeMoO6–δ

Single-phase strontium ferromolybdate (Sr2FeMoO6–δ) samples with different degrees of the superstructural ordering of the Fe/Mo cations were obtained from partially reduced SrFeO3–х, SrMoO4 precursors by the solid-state technology. The study of the temperature dependences of the magnetization measured in the field-cooling and zero-field-cooling regimes indicated an inhomogeneous magnetic state of the samples. The presence of magnetic regions of different nature has also been revealed by the small-angle neutron scattering. For the Sr2FeMoO6–δ samples with different superstructural ordering of the Fe/Mo cations and for all values of the magnetic field induction in the range up to 1.5 T and of the scattering vector in the interval 0.1 >q >0.005 Å–1, the analytical dependence I ~ q–α obeys the Porod law (α ≈ 4), which corresponds to an object with a smooth and well-marked surface and polydisperse grain size. Deviations from the Porod law in the q > 0.1 Å–1 region and a weakening of the neutron scattering in applied magnetic fields may be ascribed to magnetic inhomogeneities with diameters D <6 nm, which are partially destroyed /oriented by magnetic fields В ≥1.5 T.publishe

Terpyridine platinum compounds induce telomere dysfunction and chromosome instability in cancer cells

Telomerase/telomere-targeting therapy is a potentially promising approach for cancer treatment because even transient telomere dysfunction can induce chromosomal instability (CIN) and may be a barrier to tumor growth. We recently developed a dual-HAC (Human Artificial Chromosome) assay that enables identification and ranking of compounds that induce CIN as a result of telomere dysfunction. This assay is based on the use of two isogenic HT1080 cell lines, one carrying a linear HAC (containing telomeres) and the other carrying a circular HAC (lacking telomeres). Disruption of telomeres in response to drug treatment results in specific destabilization of the linear HAC. Results: In this study, we used the dual-HAC assay for the analysis of the platinum-derived G4 ligand Pt-tpy and five of its derivatives: Pt-cpym, Pt-vpym, Pt-ttpy, Pt(PA)-tpy, and Pt-BisQ. Our analysis revealed four compounds, Pt-tpy, Pt-ttpy, Pt-vpym and Pt-cpym, that induce a specific loss of a linear but not a circular HAC. Increased CIN after treatment by these compounds correlates with the induction of double-stranded breaks (DSBs) predominantly localized at telomeres and reflecting telomere-associated DNA damage. Analysis of the mitotic phenotypes induced by these drugs revealed an elevated rate of chromatin bridges (CBs) in late mitosis and cytokinesis. These terpyridine platinum-derived G4 ligands are promising compounds for cancer treatment