The goal of this work is to propose a new approach to the calculation of electromagnetic field that excited by the eddy current induced in the conductive environment the influence of an external magnetic field source. The quasistationary approximation accepted, that is, the bias currents do not take into account. Method. The main feature of the method is the introduction of so-called conditional boundary. This name is given for mental surfaces, which can be done in the area, free of conductive environment. Boundary form is arbitrary and dictated by considerations of calculations convenience. The agreement that the same boundary conditions, like on the conductor-vacuum boundary are performed. We prove that this task change leads to a change in its decisions only outside of the conductor and the only for part of the electric field. Magnetic induction vector throughout the space, as well as electric field tension vector in the conductive environment do not change. At the same time, a good choice of conditional boundary in some cases allows to simplify the task with calculation point of view. In addition to the conditional boundaries introduction, some formal basic conversion ratios are proposed, describing quasistationary electromagnetic field. These changes had the same goal to simplify calculations. The result. The new formulation of task of quasistationary electromagnetic field calculation is received in the form of differential equations system and boundary conditions, including both known ratio and the newly received. The new formulation is equivalent to traditional (with the above proviso). However, it has some advantages in terms of ease of calculation. The practical significance. In practice of specific calculations the method would be useful, particularly in cases when the form guide is close to some "simple" form.

A system of electrodynamics suspension (EDS) in which the primary source of the field (electromagnet) is moving in a straight line parallel to the surface of the track and his speed makes small oscillations around a mean value is considered. The approximation of an infinitely wide track is allowed, the primary source of the electromagnetic field acts as a so-called periodic source. This problem is a special case of the general problem of the rate of the transients in the EDS, caused by uneven movement. Named speed determines the amount of time constants that make sense, and in contrast to the simplest case of a one-dimensional linear oscillator system EDS characterizes not by a single time constant, but by infinite set of values. The method of calculation of levitation and braking forces acting in this oscillatory motion on carriage electromagnet is worked out and simple explicit formulas to calculate these forces are got. On the basis of the calculation of time constants the rate of the transients in the EDS, caused by uneven movement is assessed. The calculations of levitation and braking forces according to the developed technique are made. The results obtained allow to delimit the applicability of the so-called quasi-static approach which consists in that the irregularly moving of electromagnet replaced by concurrent, i.e., the same electromagnet, similarly disposed and uniformly moving with a speed coinciding with the instantaneous value of the actual longitudinal speed of the electromagnet. In the quasi-static approximation, fluctuations of levitation and braking forces are in phase with oscillations of speed and amplitude of the forces oscillations do not depends on the frequency of the speed oscillation. The calculations show that in reality there is phase shift between the forces oscillations and speed oscillations depending on the frequency. Amplitudes of levitation and braking forces oscillations also depend on the oscillation frequency, and for each speed value a resonance frequency exists at which they reach the maximum value.

Aim: the probability of correctness of collective decision is studied in this paper, whereby the decision is made by majority vote of some team (group), consisting of an odd number of members, provided that the probability of correctness of individual decision of each member of the group is known.Мethods: the Bernoulli scheme, asymptotic representation, estimation by virtue of geometric progression, exponential series expansion, Wallis' product, a power scale of averages, Kolmogorov mean.Result: it was found, that if for each member of the group the probability of the correct decision is more than ½, then with an unlimited increase of the number of members of the group, the probability of the right collective decision tends towards one. The asymptotic representation and a number of two-sided assessments which characterise the speed of this tending were obtained. For a non-homogeneous group (i.e. the group the members of which make the right individual decision with different probability) the notion of a collective average was introduced here as an averaged characteristic that can be used to replace individual probability of each group member saving the probability of the right collective decision. The existence and uniqueness of a collective average was proved.A collective inequality was identified which shows that a collective average of some set of numbers is no less than the geometric mean of the same numbers, and the equality is present if and only if all members are equal at that. A collective inequality serves as analogue and addition to the known set of inequalities establishing connection between two different average values (for instance, the AM-GM inequality).Conclusion: thus, the results of the study fully meet the aim of determining the probability of correct decision made by a majority of votes under the assumptions taken. As a result, asymptotic representation and bilateral estimates characterising the speed of tending to the correct decision was obtained. For a non-homogeneous group, the existence and uniqueness of the concept of collective average as an averaged characteristic were introduced and firmly proved, which can be used to replace an individual probability of each group member, whereby preserving the probability of correctness of the collective decision. It was found that the collective average is no less than the geometric mean. Potential applications of the results obtained can be the quantitative evaluation of election procedures and the solution of problems associated with improving the reliability of recognition of weak signals of control sensors in various transport systems, including high-speed transport systems on magnetic suspension. 1 Санкт-Петербургский государственный университет 2 Петербургский государственный университет путей сообщения Императора Александра I (Санкт-Петербург, Россия) ВЕРОЯТНОСТЬ ПРАВИЛЬНОСТИ РЕШЕНИЯ, ПРИНИМАЕМОГО БОЛЬШИНСТВОМ ГОЛОСОВ Цель. Исследуется вероятность правильности коллегиального решения, которое принимается большинством голосов некоторого колле...