On Transitive Systems of Subspaces in a Hilbert Space

Methods of *-representations in Hilbert space are applied to study of systems of $n$ subspaces in a linear space. It is proved that the problem of description of $n$-transitive subspaces in a finite-dimensional linear space is *-wild for $n \geq 5$.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

On Transitive Systems of Subspaces in a Hilbert Space

Methods of *-representations in Hilbert space are applied to study of systems of n subspaces in a linear space. It is proved that the problem of description of n-transitive subspaces in a finite-dimensional linear space is *-wild for n ≥ 5

Sensitivity of MCF-7 mammosphere CSCs to neutron radiation

Aim: Cancer stem cells (CSCs) are highly resistant to chemotherapy and γ-irradiation. Neutrons have a high linear energy transfer, which can lead to extensive damage to the DNA of tumor cells and CSCs. The aim of this work was to compare the sensitivity of MCF-7 human breast adenocarcinoma cells and CSCs to γ- and γ,n-irradiation. Methods: To increase the number of CSCs, MCF-7 cells were cultured as mammospheres. γ-irradiation was carried out in a GUT-200M device (60Co source) in the dose range of 1-8 Gy at a dose rate of 0.75 Gy/min. γ,n-irradiation was carried out in an IR-8 reactor in the dose range of 0.05-2 Gy at a dose rate of 0.06 Gy/min. DNA DSB formation was assessed by the level of γH2AX foci using fluorescence microscopy and flow cytometry. CSCs were identified by flow cytometry as CD44+/CD24-/low cells. Results: We showed that γ,n-irradiation induced the formation of γH2AX foci of a larger size than did γ-irradiation and led to more severe DNA damage per 1 Gy. Moreover, γ,n-radiation was found to have a high relative biological effectiveness (RBE) as assessed by the cell survival rate, the number of CSCs in culture, and the ability of CSCs to repopulate. The highest RBE of neutron radiation was observed at low doses, when cell survival rate decreased by only 5%-10%. With an increase in the radiation dose, the RBE value decreased for all studied parameters, but it remained as high as 5.Conclusion: γ,n-radiation is highly effective against CSCs. Our results explain the efficacy of neutron therapy for resistant forms of breast cancer