Spectral multiplicity for powers of weakly mixing automorphisms

We study the behavior of maximal multiplicities $mm (R^n)$ for the powers of a weakly mixing automorphism $R$. For some special infinite set $A$ we show the existence of a weakly mixing rank-one automorphism $R$ such that $mm (R^n)=n$ and $mm(R^{n+1}) =1$ for all $n\in A$. Moreover, the cardinality $cardm(R^n)$ of the set of spectral multiplicities for $R^n$ is not bounded. We have $cardm(R^{n+1})=1$ and $cardm(R^n)=2^{m(n)}$, $m(n)\to\infty$, $n\in A$. We also construct another weakly mixing automorphism $R$ with the following properties: $mm(R^{n}) =n$ for $n=1,2,3,..., 2009, 2010$ but $mm(T^{2011}) =1$, all powers $(R^{n})$ have homogeneous spectrum, and the set of limit points of the sequence $\{\frac{mm (R^n)}{n} : n\in \N \}$ is infinite

Study of the dependence of Young's modulus of vertically aligned carbon nanotubes on their aspect ratio

The reported study was funded by RFBR according to the research projects No.16-29-14023 ofi_m, No.18-32-00652 and by grant of the Southern Federal University (project No. VnGr-07/2017-26)

Vertically Aligned Carbon Nanotubes Production by PECVD

This chapter presents the results of experimental studies of the PECVD technological mode parameters’ influence on the formation of catalytic centers and carbon nanotubes’ (CNTs’) growth processes. This chapter also presents the ability to regulate the growth parameter for the controlled production of CNTs with the required geometric parameters, properties, and growth mechanisms. The results of experimental studies of the heating temperature and activation time effects on the catalytic center formation will be presented. This chapter also shows the effects of growth temperature, heating rate, and the activation time on the geometric and structural parameters of the carbon nanotubes. Experimental studies were carried out with the use of AFM, SEM, TEM, and EXAFS techniques. The results can be used in the development of technological processes for creating ultrafast energy-efficient electronic component base with carbon nanostructures, particularly nanoelectromechanical switches, flexo- and piezoelectric generators, gas sensors, and high-performance emitters

Vector Meson Production in Ultraperipheral Heavy Ion Collisions

The ultraperipheral heavy ion collisions (UPC's) are an important alternative to study the QCD dynamics until the next generation of $e^+e^-/ ep / eA$ colliders become reality. Due to the coherent action of all the protons in the nucleus, the electromagnetic field is very strong and the resulting flux of equivalent photons is large, which allows to study two-photon as well as photonuclear interactions at high energies. In this paper we present a brief review of the vector meson production in UPC's at high energies using the QCD color dipole approach to describe their photonuclear production and the perturbative QCD Pomeron (BFKL dynamics) to describe the double meson production in photon-photon process. Predictions for rates and integrated cross sections are presented for energies of RHIC and LHC.Comment: 16 pages, 1 figure. Version to be published in Journal of Physics G: Nuclear and Particle Physic

Dynamics of СО2 evolution bу plants at low pressure

Dynamics of СО2 evolut:ion at low pressure was studied in barley, maize, реа, wheat and pine seedlings using the gas exchange system with laser photoacoust:ic spectrometer. The СО2 evolut:ion from plant surfaces to environment increased with decreasing air pressure. Simultaneously the changes in act:ivities of phosphoenolpyruvat

The Assessment of Light Environment with the First Generation Leds

The article describes experimental studies on the effectiveness of lighting installations (LI) with light-emitting diodes (LEDs). It is established that LED-based lighting does not cause a negative impact on the organ of vision and the human body as a whole. The changes in the functional parameters of the organ of sight, which occur during the visual performance has the corresponding limits of physiological fluctuations and are reversible. The integral indicators of the efficiency of LED-based lighting were estimated. The practical significance of the results was shown