Vol 17, No 2 (2013)

The problem of equally-stressed reinforcing of bending metal-composite plates in conditions of steady-state creep, is solved by the help of methods of the perturbation theory. The opportunity of existence of several alternative solutions of a considered problem which can be reliably determined using the developed algorithm is shown. Concrete projects are constructed for equally-stressed reinforcing doubly connected plates with different density of reinforcing on an internal contour.

The numerical calculation and the analysis of influence on the real and imaginary parts of effective piezoelectric and piezomagnetic factors of magnetoelectric piezocomposite (is PVF with unidirectional ferrite fibers) of size of filling by fibers and of frequency of the enclosed electric field taking into account Maxwell–Wagner relaxation are carried out.

The model of neural network based on artificial neuron with dynamic synaptic weights was constructed. As main model processes for changing the synaptic weights were chosen: weakening of a synaptic weight in the absence of synapse stimulation, and modulation of synapse with synchronous irritation of some other synaptic junction.

The new method of measurement of integral characteristics on instant values of the harmonic signals divided both in space and in time is considered. Results of the analysis of method error because of a deviation of real signal from harmonic model are contained.

Representation of conditions of separability of integer weight factors from the sequences organizing a basis of enciphering is described. Two aspects of such sequences are considered: a geometrical progression and sequence with equal powers of natural numbers. These sequences of constant signs and alternating sequences are used when generating the relative summarized residuals, expression of each of which is located in a central part of a double inequality. Definition of conditions of separability involving the residual sequence — a geometrical progression is made with reference to its common ratio, and conditions of separability involving the the residual sequence containing equal powers of natural numbers, are found using the accompanying function introduced with reference to integer arguments of formed values of relative summarized residuals.

In this paper the nonlocal boundary value problem for the pseudo-parabolic equation of the third-order in a multidimensional domain is considered. Using an iterative method, the solving process of the nonlocal boundary value problem is reduced to solving the series of some local problems. An a priori estimate for the convergence of the iterative method in the norm $W_2^1(G)$ is obtained.

The Higgs model with friction is considered. The hyperbolic analog of the KrylovBogoliubov averaging method is used to obtain an approximate solution. The obtained solution is compared to a numerical solution of the considered equation.

The deformation of three-layer elastoplastic beam under the cyclic loading in a temperature field is considered. For the description of kinematics of asymmetrical on the package thickness beam the hypotheses of broken normal are accepted. The method of solving the corresponding boundary-value problems is given. The analytical solutions of thermoelasticity and thermo-elasto-plasticity problems under the direct and reverse loading are received. The numeric analysis is conducted.

We investigate the evolution of a quantum system described by the two-atom Jaynes–Cummings model with an intensity-dependent couplings by displaying the linear atomic entropy and the asymptotic behavior of state vector. The possibility of the system being initially in a pure disentangled state to revive into this state during the evolution process is shown. Conditions and times of disentanglement are derived.

The description of interacting multilevel quantum system and quantum electromagnetic field in terms of statistical density matrix is considered in path integral approach. The statistical operator and probability transitions of quantum system are represented as mean of electromagnetic field influence functional. The influence functionals are defined for specific models of electromagnetic field. The explicit form for singleand multimode electromagnetic field is concretized in cases when initial state of the field is represented by vacuum and pure coherent.

The cosmological Friedmann equation for the Universe, filled by scalar field with the quadratic potential, is reduced to the system of two first-order equations, one having the separable variables. The boundary-value problem with data at infinity is formulated for the second equation. The solution of this problem is represented in form of generalized Dirichlet series. The existence of classical solution in this form at the neighborhood of infinity is proved.

A new approach to the problem of scattering the plane electromagnetic TE wave on a homogeneous dielectric layer is presented, which does not predict, unlike the standard model, the Hartman effect for the tunneling time in the case of scattering the TE wave in the regime of a frustrated total internal refection (FTIR). The basic idea of this approach is that a correct definition of the tunneling velocity and time is possible if only the dynamics of both its subprocesses — transmission and reflection — is known at all stages of the scattering process investigated. It is shown that the Wigner (group) tunneling time was introduced without taking into account of this requirement, and, as a consequence, both this characteristic itself and the associated with it Hartman effect have no relation to transferring the light energy through the layer. The dwell transmission time, which is directly related to it, does not lead to the Hartman effect.

Absorbing process of ultrahigh-energy gamma-quanta in a cosmic space is investigated. It is shown that the main absorbing mechanism is the reactions arising at collisions of cosmic-ray photons with microwave and radio background ones. Estimate of the mean free path of a photon for different energies gives evidence that gamma-quanta with energies E > 1019 eV running from Active Galactic Nuclei seem to reach the Earth vicinity. This result is in agreement with the recent observations of extensive air shower array experiments realized by AGASA and Yakutsk.

In an approach of the Poincaré-invariant quantum mechanics in a modified relativistic impulse approximation performed construction of the operator of the electromagnetic current for different forms of dynamics (instant form, point form and dynamics of the light-front). The current operator is constructed according to the conditions of Lorentz covariance and conservation. It is shown that the analytical expressions for the form factor are identical in all forms of dynamics. Numerical calculations of the pion form factor with the wave function obtained by the variational method are in good agreement with experiment.

The caption of massive quantum particle by the infinite string is considered. It is demonstrated that the appearance of the cuspidal point on the string leads to the collapse of particle wave function in this point.