Estimates in Beurling--Helson type theorems. Multidimensional case

We consider the spaces $A_p(\mathbb T^m)$ of functions $f$ on the $m$ -dimensional torus $\mathbb T^m$ such that the sequence of the Fourier coefficients $\hat{f}=\{\hat{f}(k), ~k \in \mathbb Z^m\}$ belongs to $l^p(\mathbb Z^m), ~1\leq p<2$. The norm on $A_p(\mathbb T^m)$ is defined by $\|f\|_{A_p(\mathbb T^m)}=\|\hat{f}\|_{l^p(\mathbb Z^m)}$. We study the rate of growth of the norms $\|e^{i\lambda\varphi}\|_{A_p(\mathbb T^m)}$ as $|\lambda|\rightarrow \infty, ~\lambda\in\mathbb R,$ for $C^1$ -smooth real functions $\varphi$ on $\mathbb T^m$ (the one-dimensional case was investigated by the author earlier). The lower estimates that we obtain have direct analogues for the spaces $A_p(\mathbb R^m)$

Propagation of Light in the Field of Stationary and Radiative Gravitational Multipoles

Extremely high precision of near-future radio/optical interferometric observatories like SKA, Gaia, SIM and the unparalleled sensitivity of LIGO/LISA gravitational-wave detectors demands more deep theoretical treatment of relativistic effects in the propagation of electromagnetic signals through variable gravitational fields of the solar system, oscillating and precessing neutron stars, coalescing binary systems, exploding supernova, and colliding galaxies. Especially important for future gravitational-wave observatories is the problem of propagation of light rays in the field of multipolar gravitational waves emitted by a localized source of gravitational radiation. Present paper suggests physically-adequate and consistent mathematical solution of this problem in the first post-Minkowskian approximation of General Relativity which accounts for all time-dependent multipole moments of an isolated astronomical system.Comment: 36 pages, no figure

Social Image of the Ural Region Mining Workers at the Post-Reform Time Period

The article dwells upon a transition character of the Ural proletariat at the post-reform time period. Both domestic and foreign historiography define the social image of the Russian worker of the 20th century second part as either proletarian or referring to a “half-worker and half-peasant” type, combining traditional pre-capitalist features with newer ones, characteristic of industrial manufacture. A manufacturer’s being connected to the land as well as forming a certain mentality combined with the professional skills are considered the main criteria while defining the Russian workers’ typology. Taking into consideration the Urals old tradition of industrial manufacture, the process of forming an independent class at the area progressed rather vigorously. Despite of land allotments availability, workers in the Urals got under influence of modernization. Treating scornfully peasant work, industrial workers purposefully separated themselves from peasants. Nevertheless, it will be wrong to speak about complete disappearance of traditional peasant psychology among the Ural proletariat of the said time period. The working class at the region used to belong to a transition type, therefore we can speak about its incomplete establishment as a bourgeois society class

NUMERICAL MODELING OF A STRESS-STRAIN STATE OF A GAS PIPELINE WITH COLD BENDING OFFSETS ACCORDING TO IN-LINE INSPECTION

Knowledge of the current stress-strain state of any section of the pipeline allows you to make informed decisions on its operation, maintenance and repair, as well as on the prediction of the technical condition. The task of determining the characteristics of the stress-strain state of a gas pipeline section that has cold bend offsets (CBO) according to in-line inspection (ILI) is considered. The bent part of CBO is characterized by the presence of residual stresses and deformations in the wall of the offset, which contribute to the overall level of the stress-strain state of the gas pipeline operating under external and internal loads. Using the results of in-line diagnostics, numerical modeling and a solution, the change in the values of longitudinal stresses, is determined and the need to take into account residual stresses in the zone of elastic-plastic deformations of cold bend offsets is shown

Mechanical system of layer protection and technology of its application to prevent clogging of bottomhole formation zone in performing geological and technical measures

One of the important tasks of effective well operation in oil fields is to prevent clogging of bottomhole formation zone in the process of various geological and technical measures. As one of the most promising means to prevent reservoir productivity decreasing a technology using downhole shutoff valves has been proposed. Summary of the technology consists in application of a deep reservoir protection system, which is hermetically mounted in the well and dividing the productive formation area and pumping equipment placement. The analysis showed that the known shutoff valves configurations (systems with hydraulic, mechanical, electric drive) does not allow to carry out research on monitoring the development of operated object. Accordingly, none of the configurations has not been accepted for industrial use so far. The paper proposes a new mechanical reservoir protection system (including the bottomhole shutoff valve), providing a hermetic separation of productive reservoir and area of killing fluid injection when the differential pressure is up to 10 MPa. The basis of the shutoff valve construction is the principle of ball valve, in closed position the ball is pressed to valve seat by pressure, which creates a resistance to its opening. In order to achieve a high equipment`s operating time in design a special attention was paid to ensure device operation with the presence of well complications. To solve this problem a special sludge trap was included in the equipment and it was placed between the hollow plunger and the pump unit with a back pressure valve and a perforated pipe inside. Calculations of sludge trap filling were made according to the different number of stops and at various concentrations of mechanical impurities. As a result of calculations conclusions about the strength conditions fulfillment for geometric dimensions specified for pairs of steel-polyamide and steel-Zedex materials were made. Proposed device construction ensures a reliable isolation between under and above packer space, preventing ingress of killing fluid in the bottomhole formation zone. Universal equipment configuration extends its application area and the possibility of its use in combination with any pump unit depending on well conditions

Mathematical model of the starter system for a three-stage synchronous generator with a damping cage

В данной статье рассматривается математическая модель стартерной системы для газотурбинных двигателей. Модель исследуемого трехкаскадного синхронного генератора была построена в системе d-q-координат. Полученная модель позволяет сконфигурировать параметры машины в широком диапазоне, а также получить информацию о токах и напряжениях основных электрических узлов машины. Математическое моделирование показало эффективность полученной модели и адекватность предложенного алгоритма электростартерного запуска синхронной машины.This paper, considers a mathematical model the starter system for gas turbine engines. Model of the investigated three-stage synchronous generator has been built in the dq-coordinates. The obtained model allows one to configure the machine parameters in a wide range, as well as receive information about currents and voltages major electrical components of the machine. Mathematical modeling shown efficiency of the resulting model and adequacy of the proposed algorithms electric starter mode synchronous machine

Ультрафиолетовое излучение импульсно–периодических разрядов высокого давления в ксеноне

Pulsed quartz-jacketed high-pressure xenon lamps, operating in the periodic pulse repetition modes, despite the appearing UV radiation sources of other types, remain a critical component of the processing equipment used in photochemistry, photo-medicine, nanoelectronics, biology, etc. Their main advantages, namely high power and radiation energy are slightly devalued by a relatively low efficiency of the shortwave radiation. Available literature data concerning the influence of various factors on the energy level of short-wave radiation in xenon need to be systematised and generalised because they have been obtained under conditions of uncontrolled quartz-jacketed transmission. The transmission of quartz can degrade after a while and, in addition, undergo great changes during the pulse. Besides, as a rule, in the literature, there is no detailed description of a complete kit of experimental setting. As a result, to analyse the factors affecting the efficiency of studying in the UV range is difficult, and there arises a relevant problem to optimise this type of discharge parameters to increase the efficiency in the range of 220-400 nm. A mathematical model of the radiation source, realistically describing the processes in the xenon plasma and in the stabilising envelope, can be a reliable ground for such a study. The paper shows an impact of the discharge channel diameter and length, the filling pressure of xenon, the pulse duration, the parameters of discharge circuit, and the current of pilot arc on the radiation yield. Based on the simulation-found relationship of internal plasma parameters (temperature distributions, fields of particle concentration and radiation, dynamics of electrical resistance of discharge channel, and plasma emission spectra) with radiation characteristics of discharge, are determined conditions to ensure the greatest radiation yield in the UV region.  The experimental data prove the computational results. A material obtained gives practice-critical guidelines for development and correct selection of the short-wave radiation source.Импульсные ксеноновые лампы высокого давления в кварцевой оболочке, работающие в режимах периодического следования импульсов, несмотря на появление источников УФ- излучения других типов остаются важнейшим компонентом технологического оборудования, применяемого в фотохимии, фотомедицине, наноэлектронике, биологии и т.д. Главные их достоинства -  высокая мощность и энергия излучения - несколько обесценивает относительно низкая эффективность излучения в коротковолновой области. Имеющиеся литературные данные о влиянии различных факторов на уровень энергии коротковолнового излучения разрядов в ксеноне нуждаются в систематизации и обобщении, т.к. они получены в условиях неконтролируемого значения пропускания кварцевой оболочки. Пропускание кварца может деградировать со временем и, кроме того,  сильно меняться в течение импульса. Кроме того,  в литературе отсутствует, как правило, детальное описание полного набора условий проведения эксперимента. В итоге анализ факторов, влияющих на  эффективность изучения в УФ- области затруднен, и возникает актуальная задача оптимизации параметров разрядов указанного типа с целью увеличения КПД в области 220-400 нм. Надежной основой для проведения такой работы может служить расчетно- теоретическое исследование с помощью  математической модели источника излучения, реалистично описывающей процессы в плазме ксенона и стабилизирующей оболочке. В работе  показано влияние на  выход излучения диаметра и длины разрядного канала, давления наполнения ксенона, длительности импульса, параметров разрядного контура, тока дежурной дуги. На основе устанавливаемой при моделировании связи внутренних параметров плазмы (температурных распределений, полей концентрации частиц и радиации, динамики электрического сопротивления канала разряда и спектров излучения плазмы) с радиационными характеристиками разряда определены условия, обеспечивающие наибольший выход излучения в УФ- области. Результаты вычислений  подтверждены экспериментальными данными. Полученныйматериал дает важные для практики ориентиры для разработки и правильного выбора источника излучения коротковолнового диапазона

Inferring possible magnetic field strength of accreting inflows in EXor-type objects from scaled laboratory experiments

Aims. EXor-type objects are protostars that display powerful UV-optical outbursts caused by intermittent and powerful events of magnetospheric accretion. These objects are not yet well investigated and are quite difficult to characterize. Several parameters, such as plasma stream velocities, characteristic densities, and temperatures, can be retrieved from present observations. As of yet, however, there is no information about the magnetic field values and the exact underlying accretion scenario is also under discussion. Methods. We use laboratory plasmas, created by a high power laser impacting a solid target or by a plasma gun injector, and make these plasmas propagate perpendicularly to a strong external magnetic field. The propagating plasmas are found to be well scaled to the presently inferred parameters of EXor-type accretion event, thus allowing us to study the behaviour of such episodic accretion processes in scaled conditions. Results. We propose a scenario of additional matter accretion in the equatorial plane, which claims to explain the increased accretion rates of the EXor objects, supported by the experimental demonstration of effective plasma propagation across the magnetic field. In particular, our laboratory investigation allows us to determine that the field strength in the accretion stream of EXor objects, in a position intermediate between the truncation radius and the stellar surface, should be of the order of 100 G. This, in turn, suggests a field strength of a few kilogausses on the stellar surface, which is similar to values inferred from observations of classical T Tauri stars