Accelerating units for commercial resonator LINACs model UELR-10-10S designed for radiation sterilization development and results of testing

Some specific design features of the accelerating units for LINACs model UELR-10-10S designed for radiation sterilization and the electron beam characteristics obtained experimentally are considered.Описываются некоторые особенности конструкции ускорителей модели УЭЛР-10-10С, приводятся и обсуждаются характеристики электронного пучка, полученные экспериментально.Описуються деякі особливості конструкції прискорювачів моделі УЕЛР-10-10С, приводяться і обговорюються характеристики електронного пучка, отримані експериментально

Unbounded random operators and Feynman formulae

We introduce and study probabilistic interpolations of various quantization methods. To do this, we develop a method for finding the expectations of unbounded random operators on a Hilbert space by averaging (with the help of Feynman formulae) the random one-parameter semigroups generated by these operators (the usual method for finding the expectations of bounded random operators is generally inapplicable to unbounded ones). Although the averaging of families of semigroups generates a function that need not possess the semigroup property, the Chernoff iterates of this function approximate a certain semigroup, whose generator is taken for the expectation of the original random operator. In the case of bounded random operators, this expectation coincides with the ordinary one. © 2016 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd

Unbounded random operators and Feynman formulae

We introduce and study probabilistic interpolations of various quantization methods. To do this, we develop a method for finding the expectations of unbounded random operators on a Hilbert space by averaging (with the help of Feynman formulae) the random one-parameter semigroups generated by these operators (the usual method for finding the expectations of bounded random operators is generally inapplicable to unbounded ones). Although the averaging of families of semigroups generates a function that need not possess the semigroup property, the Chernoff iterates of this function approximate a certain semigroup, whose generator is taken for the expectation of the original random operator. In the case of bounded random operators, this expectation coincides with the ordinary one. © 2016 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd

Modeling the signal-to-interference ratio in amobile network with moving devices

The goal of the study is to analyze the signal-to-interference ratio (SIR) for device-to-device interaction of devices communication in the 5th generation mobile networks, taking into account the movement of the receiving and transmitting devices in the service area. The SIR value at the receiver of the associated pair is studied as a time-varying random process, and the mathematical model of motion is given by a kinetic equation taking into account the given average speed of the devices, their spatial density, and the maximum allowable communication radius. The measures of performance quality were studied by numerical analysis using SIR simulation of a key channel. The measures are the following: the signal interruption probability for the receiver-transmitter pair, the probability density function of the random variables for the duration of the availability period, and the period of absence of communication. It is shown that the signal interruption probability grows logarithmically as either the average device speed or the number of devices in the service area increases

МОДЕЛИРОВАНИЕ ОТНОШЕНИЯ СИГНАЛ/ИНТЕРФЕРЕНЦИЯ В МОБИЛЬНОЙ СЕТИ СО СЛУЧАЙНЫМ БЛУЖДАНИЕМ ВЗАИМОДЕЙСТВУЮЩИХ УСТРОЙСТВ

The goal of the study is to analyze the signal-to-interference ratio (SIR) for device-to-device interaction of devices communication in the 5th generation mobile networks, taking into account the movement of the receiving and transmitting devices in the service area. The SIR value at the receiver of the associated pair is studied as a time-varying random process, and the mathematical model of motion is given by a kinetic equation taking into account the given average speed of the devices, their spatial density, and the maximum allowable communication radius. The measures of performance quality were studied by numerical analysis using SIR simulation of a key channel. The measures are the following: the signal interruption probability for the receiver-transmitter pair, the probability density function of the random variables for the duration of the availability period, and the period of absence of communication. It is shown that the signal interruption probability grows logarithmically as either the average device speed or the number of devices in the service area increases.Целью исследования является анализ отношения сигнал/интерференция (SIR, signal-to-interference ratio) при прямом взаимодействии устройств в мобильных сетях 5-го поколения (5G) с учетом перемещения приемопередающих устройств в зоне обслуживания. Величина SIR на приемнике ассоциированной пары исследуется как изменяющийся во времени случайный процесс, а математическая модель движения задана кинетическим уравнением с учетом скорости перемещения устройств, их пространственной плотности и максимально допустимого радиуса взаимодействия. Задача численного анализа решается методом имитационного моделирования. В качестве функционала величины SIR исследуется плотность распределения случайной величины (СВ) длительности периода наличия (отсутствия) связи. Показано, что вероятность обрыва связи логарифмически растет с увеличением как скорости перемещения взаимодействующих устройств, так и их числа в заданной зоне обслуживания

On the Distribution of the Stationary Point of Significance Level for Empirical Distribution Function

We consider empirical distribution functions of nonstationary time-series, depending on set length. The local self- consistent significance level is introduced. The class of time- series, for which the distribution function of significance level is stationary, is considered. For example, the signal-to-interference ratio for random walking subscribers in D2D model of wireless connection belongs to this class of random processes. We introduce also the so-called Chernoff equivalence of the self-consistent significance level and derive the formula of averaging levels for various sets. © 2018 IEEE