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

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

Study of growth temperature effect on wetting layer during In/GaAs droplet epitaxy

This work was supported by the Russian Science Foundation Grant No. 15-19-10006. The results were obtained using the equipment of the Research and Education Center and Center for Collective Use "Nanotechnologies" of Southern Federal University

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

Improving outpatient care in chronic heart failure

Despite advances in pharma and high-technology medicine, the rate of burdensome hospital admissions and mortality in patients with chronic heart failure (CHF) remains high. Over half of all admission-entailing decompensations have been repeatedly shown to emerge from non-compliance with outpatient prescriptions. Poor adherence to medication and non-medication treatment can only be broken by improving the patient’s awareness of the disease and his closer monitoring by healthcare professionals. The power of clinical and laboratory illness monitoring in line with the recommended quality criteria of medical aid in heart failure (HF) is strongly limited today by time resources available in outpatient and midwifery clinics. Meanwhile, an international and certain domestic experience has been built up to run CHF outpatient centres with involvement of specially-trained nursing and senior medical staff. Analytic evidence on such centres suggests a reduction in mortality and hospitalisation rate among the visiting patients. To combat existing drawbacks of CHF outpatient care, the National Medical Research Center of Cardiology in alliance with the Specialist Society of Heart Failure have developed the nurses’ guidelines for CHF rooms and are launching a medical staff training programme to manage CHF rooms, registry and data analysis. Furthermore, a procedure has been developed for patient routing to regional CHF outpatient cabinets that is being actively deployed in the Tyumen Region

Generic representations of abelian groups and extreme amenability

If $G$ is a Polish group and $\Gamma$ is a countable group, denote by \Hom(\Gamma, G) the space of all homomorphisms $\Gamma \to G$. We study properties of the group \cl{\pi(\Gamma)} for the generic \pi \in \Hom(\Gamma, G), when $\Gamma$ is abelian and $G$ is one of the following three groups: the unitary group of an infinite-dimensional Hilbert space, the automorphism group of a standard probability space, and the isometry group of the Urysohn metric space. Under mild assumptions on $\Gamma$, we prove that in the first case, there is (up to isomorphism of topological groups) a unique generic \cl{\pi(\Gamma)}; in the other two, we show that the generic \cl{\pi(\Gamma)} is extremely amenable. We also show that if $\Gamma$ is torsion-free, the centralizer of the generic $\pi$ is as small as possible, extending a result of King from ergodic theory.Comment: Version

Role of portocaval shunts in development of complications after liver transplantation

Rationale. Portal blood flow is a key component in the viability of the liver transplant. Portocaval shunts formed on the background of the liver cirrhosis before transplantation can cause portal vein steal syndrome, with subsequent development of ischemic necrosis of the graft. To date, the tactics of treating patients with portal vein steal syndrome during liver transplantation has not been sufficiently developed. This paper presents a literature review and our own experience on this important, but little-studied issue. Purpose. The purpose of this research is to study the role of portocaval shunts in the development of complications after liver transplantation, based on a retrospective analysis of clinical cases. Conclusions. In liver transplantation, portocaval shunts can cause the development of portal vein steal syndrome with subsequent development of liver failure. For the diagnosis of portal vein steal syndrome, it is important to use the data obtained at all stages of liver transplantation. Surgical correction of portal vein steal syndrome can be performed during liver transplantation and in the early postoperative period. © 2022 by the authors

A new measurement of the Collins and Sivers asymmetries on a transversely polarised deuteron target

New high precision measurements of the Collins and Sivers asymmetries of charged hadrons produced in deep-inelastic scattering of muons on a transversely polarised 6LiD target are presented. The data were taken in 2003 and 2004 with the COMPASS spectrometer using the muon beam of the CERN SPS at 160 GeV/c. Both the Collins and Sivers asymmetries turn out to be compatible with zero, within the present statistical errors, which are more than a factor of 2 smaller than those of the published COMPASS results from the 2002 data. The final results from the 2002, 2003 and 2004 runs are compared with naive expectations and with existing model calculations.Comment: 40 pages, 28 figure