On extending actions of groups

Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications

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

Quantum quenches in fractonic field theories

We study out-of-equilibrium dynamics caused by global quantum quenches in fractonic scalar field theories. We consider several types of quenches, in particular, the mass quench in theories with different types of discrete rotational symmetries ($\mathbb{Z}_4$ and $\mathbb{Z}_8$), as well as an instantaneous quench via the transition between them. We also investigate fractonic boundary quenches, where the initial state is prepared on a finite-width slab in Euclidean time. We find that perturbing a fractonic system in finite volume especially highlights the restricted mobility via the formation and subsequent evolution of specific $\mathbb{Z}_4$-symmetric spatial structures. We discuss a generalization to $\mathbb{Z}_n$-symmetric field theories, and introduce a proper regularization, which allows us to explicitly deal with divergences inherent to fractonic field theories.Comment: v1: 21 pages, 8 figures; v2: 20 pages, 8 figures, minor correction

Entanglement entropy in de Sitter: no pure states for conformal matter

In this paper, we consider the entanglement entropy of conformal matter for finite and semi-infinite entangling regions, as well as the formation of entanglement islands in four-dimensional de Sitter spacetime partially reduced to two dimensions. We analyze complementarity and pure state condition of the entanglement entropy of pure states and show that they never hold in the given setup. We consider two different types of Cauchy surfaces in the extended static patch and flat coordinates, correspondingly. For former, we found that entanglement entropy of a pure state is always bounded from below by a constant and never becomes zero, as required by quantum mechanics. In turn, the difference between the entropies for some region and its complement, which should be zero for a pure state, in direct calculations essentially depends on how the boundaries of these regions evolve with time. Regarding the flat coordinates, it is impossible to regularize spacelike infinity in a way that would be compatible with complementarity and pure state condition, as opposed, for instance, to two-sided Schwarzschild black hole. Finally, we discuss the information paradox in de Sitter and show that the island formula does not resolve it. Namely, we give examples of a region with a time-limited growth of entanglement entropy, for which there is no island solution, and the region, for which entanglement entropy does not grow, but the island solution exists.Comment: v1: 25 pages, 10 figures; v2: 25 pages, 10 figures, references added, notation clarifie

Entanglement Islands and Infrared Anomalies in Schwarzschild Black Hole

In this paper, island formation for entangling regions of finite size in the asymptotically flat eternal Schwarzschild black hole is considered. We check the complementarity property of entanglement entropy which was implicitly assumed in previous studies for semi-infinite regions. This check reveals the emergence of infrared anomalies after regularization of a Cauchy surface. A naive infrared regularization based on ``mirror symmetry'' is considered and its failure is shown. We introduce an improved regularization that gives a correct limit agreed with the semi-infinite results from previous studies. As the time evolution goes, the endpoints of a finite region compatible with the improved regularization become separated by a timelike interval. We call this phenomenon the ``Cauchy surface breaking''. Shortly before the Cauchy surface breaking, finite size configurations generate asymmetric entanglement islands in contrast to the semi-infinite case. Depending on the size of the finite regions, qualitatively new behaviour arises, such as discontinuous evolution of the entanglement entropy and the absence of island formation. Finally, we show that the island prescription does not help us to solve the information paradox for certain finite size regions.Comment: v1: 55 pages, 19 figures; v2: 57 pages, 19 figures, references added, Sec. 5 presentation improve

Nucleon Resonances and Quark Structure

A pedagogical review of the past 50 years of study of resonances, leading to our understanding of the quark content of baryons and mesons. The level of this review is intended for undergraduates or first-year graduate students. Topics covered include: the quark structure of the proton as revealed through deep inelastic scattering; structure functions and what they reveal about proton structure; and prospects for further studies with new and upgraded facilities, particularly a proposed electron-ion collider.Comment: 21 pages, 15 figure

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

Local quenches in fracton field theory: non-causal dynamics and fractal excitation patterns

We study the out-of-equilibrium dynamics induced by a local perturbation in fracton field theory. For the ${\mathbb Z}_4$ and ${\mathbb Z}_8$-symmetric free fractonic theories, we compute the time dynamics of several observables such as the two-point Green function, $\langle \phi^2\rangle$ condensate, energy density, and the dipole momentum. The time-dependent considerations highlight that the free fractonic theory breaks causality and exhibits instantaneous signal propagation, even if an additional relativistic term is included to enforce a speed limit in the system. For the theory in finite volume, we show that the fracton wave front acquires fractal shape with non-trivial Hausdorff dimension, and argue that this phenomenon cannot be explained by a simple self-interference effect.Comment: v1: 25 pages, 7 figures; v2: 25 pages, 7 figures, references added, minor correction

SURGICAL CORRECTION OF INSUFFICIENCY OF CEREBRAL BLOOD FLOW AT THE ATHEROSCLEROSIS OF EXTRACEREBRAL ARTERIES

There is more than 1 million people who have had a stroke in Russia; the third part of these people are of working age, and only every fourth patient returned to job. This article discusses one of the most effective methods of stroke prevention - the procedure of carotid endarterectomy. We performed 468 reconstructive operations in 448 patients. 65 % (305) of surgeries were open carotid endarterectomies. In other cases, operations of prosthetics or blood flow switching between extracerebral arteries (ECA) (163) were carried out. Short-term results of reconstructive operations showed that 96 % of outcomes were positive. Perioperative mortality at operations made 1.06 %. The general complications made 4.5 %, minor complications were observed in 21 patients (4.4 %). The five years survival rate of patients operated on ECA made 86 %, the main cause of death in recent follow-up period was a cardiac pathology (58 %), brain disorders made 15 %. Among dominating risk factors are coronary heart disease, previous transient ischemic attacks and residual neurologic impairment