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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.

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...

Aim:to propose a technical solution to ensure the lateral stabilization of the vehicle with an electrodynamic suspension. Development of a method for calculating the levitation characteristics of a transport installation with an electrodynamic suspension in the presence of a longitudinal joint in the track. Analysis of the results of theoretical studies. Мaterials and methods: The article used the methods of the electromagnetic field theory, generalized functions, Fourier transform, analytical and numerical methods for determining quadratures. The program for PC was developed in the Fortran language. Result: to ensure lateral stabilization of the vehicle with an electrodynamic suspension, it was proposed to introduce a longitudinal insulating joint into the structure of the track bed. A mathematical model is proposed for this system of electrodynamic suspension in approximation of an infinitely wide track structure of rectangular cross section. A mathematical model is proposed for this system of electrodynamic suspension in approximation of an infinitely wide track structure of rectangular cross section. Numerical integration of these equations was performed by applying the Gauss formula and the Philo method. The results of the calculations allowed us to obtain a number of graphical dependencies of the levitation characteristics on the magnitude of the lateral displacement of the carriage electromagnet from a relatively symmetrical position. Conclusion: thus, the obtained results of the study fully meet the goal of determining the parameters of the side stabilization of the vehicle with an electrodynamic suspension with a track, containing a longitudinal joint under the assumptions made. Comparison of the proposed method with other proposed stabilization methods does not reveal the decisive advantages or disadvantages of the new method. In most cases, its most serious drawback is its low levitation quality. However, it is significantly reduced if the movement of the high speed ground transportation vehicle occurs predominantly at high speed, at which the force of aerodynamic drag prevails over the force of electrodynamic braking. Same relative is and the dignity of the system-high lateral rigidity. The reason for this is that the demands on the lateral stiffness can be quantified only formulated in relation to a particular track HSGT taking into account the timetable and other factors. In fact, the main destabilizing influences in sideways are inertia at motion on component and crosswind. Its role in choosing the stabilization system could play and other tasks the system subsystems HSGT. For example, installing additional stabilizing magnets can make it difficult to escape the passenger compartment from the magnetic field. Plays a role also principle and system design of traction. From the above it is clear that the final choice of the lateral stabilization of the research at this stage would be premature. Proposed and studied in this article a new way to stabilize should be regarded as another possible along with the preceding. The answer to the question on the competitiveness of the new method must be bound to the characteristics of specific trails HSGT. Necessary and further refinement of results associated with the more strict account of edge effect, as well as consideration of the case of uninsulated interface.