MATHEMATICAL MODELING OF THE MECHANICAL CHARACTERISTICS OF ELECTRIC MOTORS WITH A PHASE ROTOR UNDER STABLE MOTION OF MECHANISMS OF LIFTING AND TRANSPORTATION MACHINES

A method of mathematical synthesis of the equations of the mechanical characteristics of an electric motor with a phase rotor, corresponding to various resistance steps in the rotor circuit and approximated by straight lines, when simulating the unsteady movement of the mechanisms of hoisting-and-transport machines, is presented.

Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems

In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long-range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations, and agent-based models—reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first-passage time distributions. Research has lead us to question whether the observed long-range memory is a result of the actual long-range memory process or just a consequence of the non-linearity of Markov processes. As our most recent result, we discuss the long-range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the auto-regressive fractionally integrated moving average (ARFIMA) sample series. Our newly obtained results seem to indicate that new estimators of self-similarity and long-range memory for analyzing systems with non-Gaussian distributions have to be developed.

Understanding the Nature of the Long–Range Memory Phenomenon in Socio–Economic Systems

In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long–range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long–range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations and agent–based models. Reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first–passage time distributions. Research has lead us to question whether the observed long–range memory is a result of actual long–range memory process or just a consequence of non–linearity of Markov processes. As our most recent result we discuss the long–range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the ARFIMA sample series. Our newly obtained results seem indicate that new estimators of self–similarity and long–range memory for analyzing systems with non–Gaussian distributions have to be developed.

Stochastic Technical Stability Test of a Passenger Railroad Car Crossing a Turnout

This article presents a definition of stochastic technical stability that was applied to test a mathematical model of a passenger railroad car crossing a turnout with the speed exceeding 160 km/h. Stability defined in this way allows testing of Lyapunov’s stability with disturbances from the track and for a nonlinear system. The STS test of a nonlinear mathematical model of a passenger car was carried out by perturbing the motion of the mathematical model with irregularities originating from the track gauge change and wheelset motion in the direction transverse to the track axis. The main aim of this paper was to determine the influence of various factors and technical conditions on the assessment of the stability of various means of transport. The analysis presented can be used to assess the dynamics of electric vehicles, whose mechanical parameters differ from those of combustion vehicles at present. The area of stable motion in the Lyapunov sense was defined using the STS method. Simulations were performed to determine the trajectory of the wheelset transverse motion. The probability of finding the wheelset in the stable motion area in relation to the rail for a single-point contact was determined. In practice, this is a one-point contact of the wheel with the rail. Conclusions from the conducted research are presented.

Creation of a Visual Model of the Atomic Structure as a Possible Element of a Quantum Computer

Using only the laws of classical mechanics, a possible physical model of the structure of an atom as an element of a quantum computer—- a cube is proposed. The stable motion of an electron in an atom is substantiated, which is provided not only by the motion in the main elliptical or circular orbit but also by the additional motion of the electron around the main trajectory along the trajectory (helical line), the projection of which on the plane of the main orbit has the form of a cosine. It is shown why the trajectory of the electron is “smeared”, and the electron does not fall on the nucleus and, in general, what keeps it in the sphere of influence of the nucleus.

Local asymptotic self-similarity for heavy-tailed harmonizable fractional Lévy motions

In this work we characterize the local asymptotic self-similarity of harmonizable fractional Levy motions in the heavy tailed case. The corresponding tangent process is shown to be the harmonizable fractional stable motion. In addition, we provide sufficient conditions for existence of harmonizable fractional Levy motions.