Schreier Graphs for a Self-Similar Action of the Heisenberg Group

We construct a faithful self-similar action of the discrete Heisenberg group with the following properties: This action is self-replicating, finite-state, level-transitive, and noncontracting. Moreover, there exist orbital Schreier graphs of action on the boundary of the tree with different degrees of growth.Побудовано точну самоподiбну дію дискретної групи Гейзенберга з наступними властивостями. Дія є рекурентною, скінченностановою, сферично транзитивною, нестискуючою та існують графи Шрайєра дії групи на межі дерева з різними степенями зростання

Study of Scintillator Strip with Wavelength Shifting Fiber and Silicon Photomultiplier

The performance of the $200\times2.5\times1$ cm$^3$ plastic scintillator strip with wavelength shifting fiber read-out by two novel photodetectors called Silicon PhotoMultipliers (SiPMs) is discussed. The advantages of SiPM relative to the traditional multichannel photomultiplier are shown. Light yield and light attenuation measurements are presented. This technique can be used in muon or calorimeter systems.Comment: 9 pages, 5 figure

Processing of low quality ekibastuz coals ashes and natural diatomites to obtain alumina and foamed glass

Analysis of technological solutions on complex processing Ekibastuz coals ashes displays efficiency of complex alkaline technologies. However their significant drawback is the necessity to utilize big volumes of alkaline-silicic solutions. This research demonstrates possibility of their rational utilization by using natural raw diatomites to obtain formed and pelleted foamed glass widely used in construction industry as a heat-insulating material. Based on the data from scientific literature and their own research the authors suggest an improved scheme of complex processing Ekibastuz coals ashes

Wave function engineering in quantum dot-ring nanostructures

Modern nanotechnology allows producing, depending on application, various quantum nanostructures with the desired properties. These properties are strongly influenced by the confinement potential which can be modified, e.g., by electrical gating. In this paper we analyze a nanostructure composed of a quantum dot surrounded by a quantum ring. We show that depending on the details of the confining potential the electron wave functions can be located in different parts of the structure. Since the properties of such a nanostructure strongly depend on the distribution of the wave functions, varying the applied gate voltage one can easily control them. In particular, we illustrate the high controllability of the nanostructure by demonstrating how its coherent, optical, and conducting properties can be drastically changed by a small modification of the confining potential.Comment: 8 pages, 10 figures, 2 tables, revte

Electrical breakdown of a dielectric for the formation of a superconducting nanocontact

Electrical breakdown of the dielectric nanolayer between film electrodes of niobium and an alloy of 50% indium and 50% tin forms a bridge of this alloy between the electrodes. The bridge resistance depends on the breakdown current. The length of the bridge is equal to the thickness of the dielectric (30 nm), and its diameter is 25 nm. The calculated coherence length of the alloy at 0 K is close to the length of the bridge. The calculated critical current of a bridge with a resistance of 1 {\Omega} at a temperature of 0 K is 2 mA. It is concluded that such a bridge should have the properties of a Josephson contact at a temperature lower than the critical temperature of the alloy (6.5 K).Comment: 11 pages, 7 figure

A characterization of those automata that structurally generate finite groups

Antonenko and Russyev independently have shown that any Mealy automaton with no cycles with exit--that is, where every cycle in the underlying directed graph is a sink component--generates a fi- nite (semi)group, regardless of the choice of the production functions. Antonenko has proved that this constitutes a characterization in the non-invertible case and asked for the invertible case, which is proved in this paper

From self-similar groups to self-similar sets and spectra

The survey presents developments in the theory of self-similar groups leading to applications to the study of fractal sets and graphs, and their associated spectra

Regge Field Theory in zero transverse dimensions: loops versus "net" diagrams

Toy models of interacting Pomerons with triple and quaternary Pomeron vertices in zero transverse dimension are investigated. Numerical solutions for eigenvalues and eigenfunctions of the corresponding Hamiltonians are obtained, providing the quantum solution for the scattering amplitude in both models. The equations of motion for the Lagrangians of the theories are also considered and the classical solutions of the equations are found. Full two-point Green functions ("effective" Pomeron propagator) and amplitude of diffractive dissociation process are calculated in the framework of RFT-0 approach. The importance of the loops contribution in the amplitude at different values of the model parameters is discussed as well as the difference between the models with and without quaternary Pomeron vertex.Comment: 34 pages, 36 figure

On the Finiteness Problem for Automaton (Semi)groups

This paper addresses a decision problem highlighted by Grigorchuk, Nekrashevich, and Sushchanskii, namely the finiteness problem for automaton (semi)groups. For semigroups, we give an effective sufficient but not necessary condition for finiteness and, for groups, an effective necessary but not sufficient condition. The efficiency of the new criteria is demonstrated by testing all Mealy automata with small stateset and alphabet. Finally, for groups, we provide a necessary and sufficient condition that does not directly lead to a decision procedure

Peculiarities of micronutrient metabolism in obese pregnant women (literature review)

Here we summarize uptodate data on the influence of the most significant micro, macroelements, and vitamins, such as magnesium, vitamin D, iron, and folic acid, on the course of pregnancy and childbirth in obese women. The paper considers both domestic and foreign recommendations for correcting nutritional deficiencies to prevent the development of complications from the pregravid stage to the end of lactation. Nowadays, the deficiency of micro-, macroelements and vitamins is an extremely urgent problem, especially in a group of special risk, i.e. overweight and obese women, whose number is steadily growing simultaneously with an increase of the number of pregnant women of 35+ years of age. It is important to consider a woman's body mass index to prescribe the minimum effective dose of the necessary drugs. Timely preventive personalized correction of the micronutrient state can reduce the risks of such major obstetric syndromes as preeclampsia, premature birth, fetal growth retardation, miscarriage, and placental dysfunction