Abstract:
Experimental validation of the Faraday's law of electromagnetic induction (EMI) is performed when an electromotive force is generated in thin copper turns, located inside a large magnetic coil. It has been established that the electromotive force (emf) value should be dependent not only on changes of the magnetic induction flux through a turn and on symmetry of its crossing by magnetic power lines also. The law of EMI is applicable in sufficient approximation in case of the changes of the magnetic field near the turn are symmetrical. Experimental study of the induced emf in arcs and a direct section of the conductor placed into the variable field has been carried out. Linear dependence of the induced emf on the length of the arc has been ascertained in case of the magnetic field distribution symmetry about it. Influence of the magnetic field symmetry on the induced emf in the arc has been observed. The curve of the induced emf in the direct section over period of current pulse is similar to this one for the turns and arcs. The general law of EMI for a curvilinear conductor has been deduced. Calculation of the induced emf in the turns wrapped over it and comparison with the experimental data has been made. The proportionality factor has been ascertained for the law. Special conditions have been described, when the induced emf may not exist in the presence of inductive current. Theoretical estimation of the inductive current has been made at a induced low voltage in the turn. It has been noted the necessity to take into account the concentration of current carriers in calculation of the induced emf in semiconductors and ionized conductors.

Abstract:
Measurements of magnetic induction near an ice rod in the strong electric field were carried out. Theoretical estimation of the magnetic induction was made. It was found that in the average the experimental values of magnetic induction were an order less than theoretical value. A conclusion about the non- equivalence of magnetic fields of bound charges current and conduction current was made. Therefore, the magnetic field near an energized conductor is caused not directly by moving charges but by their influence on the propagation medium. The similar effect could occur at diffusion of other particles through the medium.

Abstract:
The paper draws attention to the importance of the notion “luminiferous ether” in physics. There is a proposed method to register its flows generated by natural cosmic movements or created artificially. The work presents the results of ether wind searching with a prototype of the proposed installation located at the altitude of <30 m above sea level. Ether flows with speeds > 20 km/s are not found, which is consistent with the results of previous experiments.

The article considers physical properties of photon as a quantum of electromagnetic wave in luminiferous medium. An experimental evaluation method for its energy and mass based on radiation pressure effect was presented. The of “photon amplitude” concept was introduced, through which energy is represented similarly to quantum (phonon) energy of elastic mechanical wave. A model of photon as a wave packet in the medium was considered, which based its volume evaluation. The resulting equation for energy corresponds to commonly known, regarding the first degree frequency proportionality, while it is more informative.

Abstract:
We identify the leading term describing the behavior at large distances of the steady state solutions of the Navier-Stokes equations in 3D exterior domains with vanishing velocity at the spatial infinity.

Abstract:
We prove some new product representations for random variables with the Linnik, Mittag-Leffler and Weibull distributions. The main result is the representation of the Linnik distribution as a normal scale mixture with the Mittag-Leffler mixing distribution. As a corollary, we obtain the known representation of the Linnik distribution as a scale mixture of Laplace distributions. In turn, as a corollary of this representation we obtain the explicit representation of the distribution density of the ratio of two independent positive strictly stable random variables. Another corollary of the main representation is the theorem establishing that the distributions of random sums of independent identically distributed random variables with finite variances converge to the Linnik distribution under an appropriate normalization if and only if the distribution of the random number of summands under the same normalization converges to the Mittag-Leffler distribution.

Abstract:
We study weak ergodicity, bounds on the rate of convergence, and problems of computing of the limiting characteristics for an inhomogeneous $M_t|M_t|S$ queueing model with possible catastrophes.

Abstract:
Two approaches are suggested to the definition of asymmetric generalized Weibull distribution. These approaches are based on the representation of the two-sided Weibull distributions as variance-mean normal mixtures or more general scale-location mixtures of the normal laws. Since both of these mixtures can be limit laws in limit theorems for random sums of independent random variables, these approaches can provide additional arguments in favor of asymmetric two-sided Weibull-type models of statistical regularities observed in some problems related to stopped random walks, in particular, in problems of modeling the evolution of financial markets.

Abstract:
We prove a general transfer theorem for multivariate random sequences with independent random indexes in the double array limit setting. We also prove its partial inverse providing necessary and su?cient conditions for the convergence of randomly indexed random sequences. Special attention is paid to the case where the elements of the basic double array are formed as statistics constructed from samples with random sizes. Under rather natural conditions we prove the theorem on convergence of the distributions of such statistics to normal variance-mean mixtures.

Abstract:
We prove a version of a general transfer theorem for random sequences with independent random indexes in the double array limit setting under relaxed conditions. We also prove its partial inverse providing the necessary and sufficient conditions for the convergence of randomly indexed random sequences. Special attention is paid to the case where the elements of the basic double array are formed as cumulative sums of independent not necessarily identically distributed random variables. Using simple moment-type conditions we prove the theorem on convergence of the distributions of such sums to normal variance-mean mixtures.