Physics, mathematics, and technology

New exact solutions are obtained for a spatially non-local wave equation with sources. The results are set out in the terms of the heat transfer theory. The non-locality of the problem is determined by the value of the fourth spatial derivative. We considered two types of volume energy sources which are alter­na­ting with respect to the temperature. For a technical source the derivative is po­sitive, since «higher» temperatures arise from the energy release. For a bio­lo­gical source the source function is negative inclined, because a biological tis­sue gives off heat in the region of «lower» temperatures. The external inf­luen­ce on a non-local medium is simulated by spatially nonuniform energy source, and we have considered five types of such sources. The analytical solutions are pre­sented in the finite form. The effects of monotonous and nonmonotonous (im­pulsive) reonomic sources are compared. The conditions for a transonic transition are indicated for the wave of perturbation in the temperature set. Resonance occurrences in the system «medium — energy source» are studied. The limits of oscillation stability/instability are determined. We found a di­men­sionless criterion including the inclination of the source function and the pa­rameter of the medium non-locality. The criterion affects the correlation «os­cillation frequency — fading parameter».

A method for construction of exact cosmological solutions of Einstein equations is developed. The method is based on representation of these equations as a second-order linear differential equation. Particularly, the method allows to construct a more general solution, parametrized by two constants, using any known solution. Also it is shown, that in a specific case new classes of exact solutions have singularities with the following property: a geodesic, which begins or ends in the singularity, has an infinite length. Such a singularity leads to an absence of event horizons (if this is a future singularity). In this case it might prove possible to construct cosmological model, satisfying every consistency requirement during a universe lifetime.

The article presents the architecture, basic elements and implementation of the prototype of the tool for the development of functional hybrid intelligent systems with a heterogeneous visual field. Such systems are capable of simul­taneously simulating collective verbal-symbolic reasoning and activating the visual-figurative reasoning of users. The use of such systems in the practice of solving problems, in particular when managing regional electric networks, will allow users to «see» the problem situation and its possible approximate solutions, which can subsequently be justified and refined by the methods of logical-mathematical reasoning.

Complicating diagnostic tasks inevitably lead to the mistakes during de­cision-making and to the increasing complexity and workload of the features for automated decision in heterogeneous problem environment. Researches in this field are focused on formalization and exploration of the processes of find­ing, identifying of the heterogeneous diagnostic task and the synthesis of the method for its solving. This paper presents the results of the development of the algorithm for the synthesis of the method for solving of the heterogeneous diagnostic task, which establishes the integrated model under the approach of hybrid intelligent systems. Such model is relevant to diagnostic situation and combines the set of heterogeneous models of the theoretical, professional knowledge and the experience.

The article is devoted to the development of methods for optimizing the structural parameters of antenna systems, performed in order to improve the basic performance characteristics. Models are considered and estimated calcu­lations are carried out for structures implemented using symmetric vibrators. Conclusions about the feasibility of changing the geometric parameters of the antenna system, in terms of finding its optimal configuration in a specific fre­quency range.

The article is devoted to the development of a small-sized antenna system characterized by uniform input impedance over the entire operating frequency range, and structurally implemented on the basis of the fractal structure, as well as the optimization of its parameters in order to improve the basic opera­tional characteristics of the system.

The diffuse pollution is considered taking into account the lateral inflow. In the calculation scheme, the impurity has a small inertia, the deposition of particles is steady. Background values are set as initial conditions for the con­centration and in the initial section of the watercourse, and the intensity of the diffuse discharge along the shoreline is set. The results of solving the boundary value problem by numerical method in Mathcad are presented. The results of the study of the profiles of dimensionless concentration of the precip­itating admixture are shown. Graphs are presented in dimensionless varia­bles.