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

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

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

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

Orbital effects of a monochromatic plane gravitational wave with ultra-low frequency incident on a gravitationally bound two-body system

We analytically compute the long-term orbital variations of a test particle orbiting a central body acted upon by an incident monochromatic plane gravitational wave. We assume that the characteristic size of the perturbed two-body system is much smaller than the wavelength of the wave. Moreover, we also suppose that the wave's frequency is much smaller than the particle's orbital one. We make neither a priori assumptions about the direction of the wavevector nor on the orbital geometry of the planet. We find that, while the semi-major axis is left unaffected, the eccentricity, the inclination, the longitude of the ascending node, the longitude of pericenter and the mean anomaly undergo non-vanishing long-term changes. They are not secular trends because of the slow modulation introduced by the tidal matrix coefficients and by the orbital elements themselves. They could be useful to indepenedently constrain the ultra-low frequency waves which may have been indirectly detected in the BICEP2 experiment. Our calculation holds, in general, for any gravitationally bound two-body system whose characteristic frequency is much larger than the frequency of the external wave. It is also valid for a generic perturbation of tidal type with constant coefficients over timescales of the order of the orbital period of the perturbed particle.Comment: LaTex2e, 24 pages, no figures, no tables. Changes suggested by the referees include

Molecular and electronic structure of terminal and alkali metal-capped uranium(V) nitride complexes

Determining the electronic structure of actinide complexes is intrinsically challenging because inter-electronic repulsion, crystal field, and spin–orbit coupling effects can be of similar magnitude. Moreover, such efforts have been hampered by the lack of structurally analogous families of complexes to study. Here we report an improved method to U≡N triple bonds, and assemble a family of uranium(V) nitrides. Along with an isoelectronic oxo, we quantify the electronic structure of this 5f1 family by magnetometry, optical and electron paramagnetic resonance (EPR) spectroscopies and modelling. Thus, we define the relative importance of the spin–orbit and crystal field interactions, and explain the experimentally observed different ground states. We find optical absorption linewidths give a potential tool to identify spin–orbit coupled states, and show measurement of UV···UV super-exchange coupling in dimers by EPR. We show that observed slow magnetic relaxation occurs via two-phonon processes, with no obvious correlation to the crystal field

An ancient bison from the mouth of the Rauchua River (Chukotka, Russia)

An incomplete carcass of an extinct bison, Bison ex gr. priscus, was discovered in 2012 in the mouth of the Rauchua River (69°30'N, 166°49'E), Chukotka. The carcass included the rump with two hind limbs, ribs, and large flap of hide from the abdomen and sides, several vertebrae, bones of the forelimbs and anterior autopodia, stomach with its contents, and wool. The limb bones are relatively gracile, which is unusual in bison, and a SEM study of the hair microstructure suggests higher insulating capacity than in extant members of the genus. Additionally, mitochondrial DNA analyses indicate that the Rauchua bison belonged to a distinct and previously unidentified lineage of steppe bison. Two radiocarbon dates suggest a Holocene age for the bison: a traditional 14C date provided an estimate of 8030±70 14C yr BP (SPb-743) and an AMS radiocarbon date provided an age of 9497±92 14C yr BP (AA101271). These dates make this the youngest known bison from Chukotka. Analysis of stomach contents revealed a diet of herbaceous plants (meadow grasses and sedges) and shrubs, suggesting that the early Holocene vegetation near the mouth of the Rauchua River was similar to that of the present day: tundra-associated vegetation with undersized plants