Subexponential estimations in Shirshov's height theorem (in English)

In 1993 E. I. Zelmanov asked the following question in Dniester Notebook: "Suppose that F_{2, m} is a 2-generated associative ring with the identity x^m=0. Is it true, that the nilpotency degree of F_{2, m} has exponential growth?" We show that the nilpotency degree of l-generated associative algebra with the identity x^d=0 is smaller than Psi(d,d,l), where Psi(n,d,l)=2^{18} l (nd)^{3 log_3 (nd)+13}d^2. We give the definitive answer to E. I. Zelmanov by this result. It is the consequence of one fact, which is based on combinatorics of words. Let l, n and d>n be positive integers. Then all the words over alphabet of cardinality l which length is greater than Psi(n,d,l) are either n-divided or contain d-th power of subword, where a word W is n-divided, if it can be represented in the following form W=W_0 W_1...W_n such that W_1 >' W_2>'...>'W_n. The symbol >' means lexicographical order here. A. I. Shirshov proved that the set of non n-divided words over alphabet of cardinality l has bounded height h over the set Y consisting of all the words of degree <n. Original Shirshov's estimation was just recursive, in 1982 double exponent was obtained by A.G.Kolotov and in 1993 A.Ya.Belov obtained exponential estimation. We show, that h<Phi(n,l), where Phi(n,l) = 2^{87} n^{12 log_3 n + 48} l. Our proof uses Latyshev idea of Dilworth theorem application.Comment: 21 pages, Russian version of the article is located at the link arXiv:1101.4909; Sbornik: Mathematics, 203:4 (2012), 534 -- 55

Neutron lifetime measurements using gravitationally trapped ultracold neutrons

Our experiment using gravitationally trapped ultracold neutrons (UCN) to measure the neutron lifetime is reviewed. Ultracold neutrons were trapped in a material bottle covered with perfluoropolyether. The neutron lifetime was deduced from comparison of UCN losses in the traps with different surface-to-volume ratios. The precise value of the neutron lifetime is of fundamental importance to particle physics and cosmology. In this experiment, the UCN storage time is brought closer to the neutron lifetime than in any experiments before:the probability of UCN losses from the trap was only 1% of that for neutron beta decay. The neutron lifetime obtained,878.5+/-0.7stat+/-0.3sys s, is the most accurate experimental measurement to date.Comment: 38 pages, 19 figures,changed conten

АВТОНОМНАЯ СИСТЕМА ЭЛЕКТРОСНАБЖЕНИЯ НА БАЗЕ АСИНХРОННОГО ГЕНЕРАТОРА И ТОКОВОГО КОМПЕНСАТОРА

The possibility of building an aircraft power supply system based on an asynchronous generator investigated. One of the key features of this system is usage of a current source inverter (CSI) for induction machine self-excitation. Besides, induction machine output voltage stabilization is achieved at variable shaft speed operating conditions. Moreover, generator output voltage distortion is compensated in case of non-linear or unbalanced loads. As the power converter a current source inverter is used. This allows one not to use dc-link capacitor which has well known limitations. A mathematical model of the system is proposed. In order to obtain power quality indices the algebraization of the differential equations method (ADE) is used. The results of analytical calculations are presented.Исследуются возможности построения системы электроснабжения самолета на базе асинхронного генератора. Инновациями в такой системе будет использование полупроводникового преобразователя типа инвертора тока для самовозбуждения асинхронной машины, с параллельным решением задачи стабилизации напряжения при переменной скорости вращения вала машины и, при необходимости, компенсацией искажений напряжения генератора, вызванное нелинейностью или несимметрией нагрузки. В качестве преобразователя используется автономный инвертор тока, в отличие от инвертора напряжения, не содержащий электролитического конденсатора, имеющего известные ограничения. Построена математическая модель системы. Для анализа энергетических соотношений применяются прямые методы расчета АДУ. Результаты аналитических расчетов представлены.Досліджуються можливості побудови системи електропостачання літака на базі асинхронного генератора. Інноваціями у такій системі буде використання напівпровідникового перетворювача типу інвертора струму для самозбудження асинхронної машини, з паралельним вирішенням задачі стабілізації напруги при змінній швидкості обертання валу машини та, при необхідності, компенсацією викривлення напруги генератора, спричиненого нелінійністю або несиметрією навантаження. У якості перетворювача використовується автономний інвертор струму, який, на відміну від інвертора напруги, не містить електролітичного конденсатора, що має відомі обмеження Збудовано математичну модель системи. Для аналізу енергетичних співвідношень застосовуються методи розрахунку АДУ. Результати аналітичних розрахунків наведено

Silicon-carbide semiconductors as base for active rectifier

В докладе представлена концепция построения преобразователя частоты по типу активного выпрямителя на сверхмалые массо-габаритные показатели (до 0,4 кг/кВт) с использованием карбид-кремниевых транзисторов. В основе концепции заложены принципы наращивания мощности преобразователей за счет параллельного соединения преобразователей меньшей мощности (модулей). Алгоритм управления всем преобразователем реализован на базе микроконтроллера и программируемой логической интегральной схемы (ПЛИС). Совокупность достоинств микросхем, а также ряд технических решений обеспечили независимое централизованное управление 36 транзисторами на постоянной частоте коммутации 75 кГц. Эквивалентная пульсность тока для рассматриваемого трехфазного преобразователя составляет 450 кГц. В работе представлены промежуточные результаты испытаний образца на номинальную мощность 25 кВт.The report introduces the concept of building the inverter-type active rectifier on ultra-small weight and size parameters (up to 0.4 kg / kW). The concept based on the principles of increasing converters power due to the parallel connection of lower power converters (modules). The control algorithm is implemented on microcontroller and programmable logic integrated circuits (FPGAs) co-working. Set of advantages applied digital circuits, as well as a number of technical solutions that organize synchronous and discontinuous operation of two chips in a single computational cycle, ensure the independence of the centralized management of 36 transistors on a constant switching frequency of 75 kHz. Equivalent frequencyof ripples in current for the considered three-phase inverter is 450 kHz. The paper presents the interim results of the test sample to the nominal power of 25 kW

INDICATIVE ROLE OF VEGETATION IN THE RECLAMATION OF PRECASPIAN ARID LANDSCAPES (THE REPUBLIC OF KALMYKIA)

Aim. The paper studies the influence of water reclamation on vegetation in the central part of the Caspian depression. Findings are necessary for the monitoring studies of natural ecosystems in their modern usage.Methods. The use of key site method and eco-dynamic profiling makes it possible to trace changes in the horizontal structure of vegetation in the coastal and canal areas of the salt lakes. Results. The findings of field research allowed identifying the environmental levels: low, medium, high. Xerophilous species fall out of the phytocenosis composition, while the typical salt-loving plants become widespread, forming endogenous succession of progressive type in a Precaspian desert zone. It aims to desalinize the upper layers of the soil, lower the groundwater and salinity levels. Conclusions. Fluctuation and succession processes can be observed in the central part of the Precaspian depression, the indicator of which is vegetation, its species composition

Synthis and Phisical And Chemical; Properties of SiO[2]-B[2]O[3] and SiO[2]-P[2]O[5] Thin Film Systems and Powders

The SiO[2]-B[2]O[3] and SiO[2]-P[2]O[5] films were synthesized by using film forming solutions having a P[2]O[5] content of up to 30% and B[2]O[3] up to 40%. Properties of the filmforming solutions and binary oxides were examined. The physical and chemical processes occurring in the solution during the heat treatment of films were examined. The conditions for producing films of different thicknesses were determined. The kinetic parameters were calculated

BLR kinematics and Black Hole Mass in Markarian 6

We present results of the optical spectral and photometric observations of the nucleus of Markarian 6 made with the 2.6-m Shajn telescope at the Crimean Astrophysical Observatory. The continuum and emission Balmer line intensities varied more than by a factor of two during 1992-2008. The lag between the continuum and Hbeta emission line flux variations is 21.1+-1.9 days. For the Halpha line the lag is about 27 days but its uncertainty is much larger. We use Monte-Carlo simulation of the random time series to check the effect of our data sampling on the lag uncertainties and we compare our simulation results with those obtained by random subset selection (RSS) method of Peterson et al. (1998). The lag in the high-velocity wings are shorter than in the line core in accordance with the virial motions. However, the lag is slightly larger in the blue wing than in the red wing. This is a signature of the infall gas motion. Probably the BLR kinematic in the Mrk 6 nucleus is a combination of the Keplerian and infall motions. The velocity-delay dependence is similar for individual observational seasons. The measurements of the Hbeta line width in combination with the reverberation lag permits us to determine the black hole mass, M_BH=(1.8+-0.2)x10^8 M_sun. This result is consistent with the AGN scaling relationships between the BLR radius and the optical continuum luminosity (R_BLR is proportional to L^0.5) as well as with the black-hole mass-luminosity relationship (M_BH-L) under the Eddington luminosity ratio for Mrk 6 to be L_bol/L_Edd ~ 0.01.Comment: 17 pages, 10 figures, accepted for publication in MNRA