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)

Вплив поліпропіленової фібри на властивості цементно-піщаних ремонтних розчинів

It is given the results of studies of physical and mechanical properties of the cement-sand mortar, modified polypropylene fibers for concrete repair and restoration of waterworks Water Management and reclamation complexНаведено результати досліджень фізико-механічних властивостей цементно-піщаних розчинів, модифікованих поліпропіленовою фіброю для ремонту та відновлення залізобетонних гідротехнічних споруд водогосподарсько-меліоративного комплекс

Influence of the focused ion beam parameters on the etching of planar nanosized multigraphene/SiC field emitters

The equipment of the Collective Usage Center “Nanotechnologies” and the Research and Educational Center "Nanotechnologies" of Southern Federal University was used for this study. This work was funded by Internal grant of Southern Federal University No. VnGr-07/2017-26

Investigation of the effect of upper electrode material on the memristor properties of strained carbon nanotubes

The reported study was funded by RFBR according to the research project No. 16-29-14023 ofi_m

Effect of thickness on the piezoelectric properties of LiNbO3 films

The results were obtained using the equipment of Research and Education Center and the Center of collective use “Nanotechnology” of Southern Federal University