Vol 50, No 1 (2017)

We consider the problem of local parameter identifiability for a hybrid system with components that are continuous and discrete in time. The set of observations is the vector-solution (depending on the parameter that is continuous in time) of the discrete component. Sufficient conditions of local parameter identifiability have been formulated using the earlier introduced notion of normalized separability of the set of parameters from the kernel of a special functional. An example where the condition of normed separability is reduced to some rank criterion is given.

In his recent paper published in Vestnik St. Petersburg University, Ser. Mathematics, V.V. Petrov found new sufficient conditions for the fulfillment of the strong law of large numbers for sequences of random variables stationary in the broad sense. These conditions are expressed in terms of second moments. In this paper, by using the ergodic theorem, similar problems are solved for sequences of random variables stationary in the narrow sense. In the absence of second moments, the statements of conditions involve the truncated second moments of truncated random variables. At the end of the paper, an example of a stationary sequence of random variables which is not ergodic but obeys the strong law of large numbers is given.

A family of one-dimensional continuous-time Markov processes is considered, for which the author has earlier determined the transition probabilities by directly solving the Kolmogorov–Chapman equation; these probabilities have the form of single integrals. Analogues of the first and second Kolmogorov equations for the family of processes under consideration are obtained by using a procedure for obtaining integro-differential equations describing Markov processes with discontinuous trajectories. These equations turn out to be equations in fractional derivatives. The results are based on an asymptotic analysis of the transition probability as the start and end times of the transition approach each other. This analysis implies that the trajectories of a given Markov process are divided into two classes, depending on the interval in which they start. Some of the trajectories decay during a short time interval with a certain probability, and others are generated with a certain probability.

In this study, we consider an approximation of entire functions of Hölder classes on a countable union of segments by entire functions of exponential type. It is essential that the approximation rate in the neighborhood of segment ends turns out to be higher in the scale that had first appeared in the theory of polynomial approximation by functions of Hölder classes on a segment and made it possible to harmonize the so-called “direct” and “inverse” theorems for that case, i.e., restore the Hölder smoothness by the rate of polynomial approximation in this scale. Approximations by entire functions on a countable union of segments have not been considered earlier. The first section of this paper presents several lemmas and formulates the main theorem. In this study, we prove this theorem on the basis of earlier given lemmas.

This paper deals with a class of elastic systems with structural damping subject to nonlocal conditions. By using a suitable measure of noncompactness on the space of continuous functions on the half-line, we establish the existence of mild solutions with explicit decay rate of exponential type. An example is given to illustrate the abstract results.

This paper continues the studies on the construction of the first order approximation of equations for a boundary layer in the vicinity of a surface Rayleigh wave front in shells of revolution under normal shock surface loading. Since the first order asymptotic approximation is insufficient for determination of all components of the stress-deformed state, we obtain refined asymptotic equations for construction of solutions for all components of displacements and stresses with an asymptotic error of the order of the relative shell thickness.

In this paper, we address the stability of an elastic thin annular plate stretched by two point loads that are located on the outer boundary. A roller support is considered on the outer boundary while the inner edge of the plate is free. Muskhelishvili’s theory of complex potentials has been applied to obtain a solution of the plane problem in the form of a power series. The buckling problem has been solved using the Rayleigh–Ritz method, based on the energy criterion. The critical Euler force and the respective buckling mode have been computed. Dependence between the critical force and the relative orifice size has been illustrated. Analysis of the results has shown that a symmetric buckling mode takes place for a sufficiently large hole, with the greatest deflection observed around the hole along the force line. However, an antisymmetric buckling mode occurs for relatively small holes, with the greatest deflection being along a line that is orthogonal to the force line.

This paper considers nonstationary monochromatic radiative transfer in an infinite onedimensional homogeneous medium. The medium is considered to be illuminated by a momentary isotropic point energy source. The optical properties of the medium are characterized by the absorption coefficient α, the single-scattering albedo λ, the mean time t₁ of photon stay in the absorbed state, and the mean time t₂ of its stay on the path between two consecutive scatterings. The exact solution of the nonstationary radiative transfer equation has been obtained for the case t₁ = t₂. Asymptotic expressions have been derived for the source function, for the average intensity, and for radiation flux when points of the medium are located at large optical distances from the power source |τ| ≫ 1 and for small absorption of light in the medium (1 − λ ≪ 1), assuming that t₁ ≫ t₂, t₁ ≪ t₂, or t₁ = t₂. These expressions are more precise than the ones previously known.