# Optimization Models and Algorithms for Network Problems of Resours’ Distribution

The efficient algorithms for nonlinear programming problems for calculating networks have been offered, as well as the new network models to determine the optimal flows and distribution of resources have been constructed. The problems with nonlinear objective functions of general form and network structure of restrictions, which allow reaching quite a wide range of networks using common approach, were considered. For calculations the modifications of well-known methods of nonlinear programming were applied.

# Identification of Low Frequency Oscillations Using Synchrophasor Measurements

The actual questions of the study of low-frequency oscillations of power in the interconnected power system (IPS) of Ukraine in terms of introduction of modern Wide Area Measuring System (WAMS) are considered. The algorithm for identifying modes of oscillations by means of using recordings from the Phasor Measurement Units of a WAMS using spectral analysis and calculation of the main characteristics of identified fluctuations is developed.

# Comparative Analysis of Models of Heat Transfer in the Cylinder of Stationary Gas Engine 11GD100M

Heat transfer process in the cylinder of a stationary gas engine pre-chamber – torch ignition of lean fuel-air mixtures and qualitative power regulation was studied and mathematically modelled. During the investigation of heat transfer in the cylinder of the gas engine the components obtained by the results of experimental research of internal thermal balance were analyzed. It was shown that heat transfer in the cylinder 11GD100M has distinctive features compared to the known petrol and diesel engines.

# The Efficiency of the Heat Pump in the Heating System Using Heat from Exhaust Gases after the Condensing Boiler

The thermodynamic efficiency of heat pump hot water supply schemes using heat from exhaust gases after the condensing boiler was determined. It was established, that there is the optimum degree of cooling of the flue gases in the evaporator heat pump, which corresponds to the maximum specific useful effect received from the exhaust gases heat utilization by HP based on the cost to the heat pump compressor drive.

# Visualization of Surface Conduc¬tivity Distribution by Conductivity Zones Method

The usage of modification method for direct EIT problem solving is substantiated. The voltages on phantom contour with known current approximation of surface conductivity distribution are calculated. The classical algorithm with Newton–Raphson method for inverse EIT problem solving is shown. That is “refinement” of surface conductivities by results of analysis. The conductivity zones method to reduce the order and time of calculations is described (transition from solution of the equation with 1000 order to 16 times solving the equations with 14 order). The regularization method by A.N.

# Behavior of Surface Spin Waves at Reflection from Uniaxial Multilayer Ferromagnet

The purpose of this article is to review the reflective properties of multilayer ferromagnet for surface spin waves. It was calculated the reflection coefficient of surface spin waves from multilayer ferromagnet with uniaxial magnetic anisotropy in non-ideal boundary conditions at the interface between layers. The problem is solved in the exchange approximation. Graphics shows us the dependence of the reflection coefficient on the frequency, of the external magnetic field, the exchange interaction constant and uniaxial magnetic anisotropy.

# Sound Generation by Taylor and Scully Vortexes and the Blade of the Varying Cross Section

A problem of the blade vortex interaction noise (BVI) generation has been solved for incoming flux and Taylor, Scully vortexes. Solution for this problem is a closed system of the aeroacoustical equations, which is based on perfect compressible gas model. A behavior of the generated noise has been studied for the different flow velocities and blade thicknesses. Results of the calculations show existence of the two frank regions of the sound existence on the blade shape. The first of it is more resistant for the parameters changing. The second one is a flow region of the instability.

# Inertial Stability as a Result of the Relation Between Transport and Relative Fluid Rotations

The aim of the paper is fluid inertial stability nature determination through the representation of potential (non-rotational) motion as the compensation of two rotations, transport one and relative one. Theoretical methods are used. It is based on well-known description of fluid motion as a sum of three types (Cauchy–Helmholz theorem), but uses theoretical mechanics approach. The motion is considered as a sum of transport and relative ones. Thransport angular velocity corresponds to macroscopic motion, while relative one is caused by fluid parcel deformation.

# Definition Peculiarities of Energy of Vacancy Formation In 4d-Transition Metals from First Principles

In this paper a study of the temperature dependence of the vacancy formation energy in bulk fcc 4d-transition metals Ag and Pd using DFT was presented. Peculiarity of this work is the use of experimental values of the lattice parameters for the respective temperatures. This paper discusses the various contributions to the vacancy formation energy and shows that they can play an important role. It was shown that thermal excitation has a significant impact on the vacancy formation energy at high temperatures. The possibility of the existence of the compensation effect, i.e.

# Propagation of Spin Wave Through the Anisotropic Boundary of Two Uniaxial Ferromagnets in an External Magnetic Field

This paper represents the investigation of the reflection of bulk spin waves at the interface of two uniaxial ferromagnetic media that propagate at an angle to the interface and their penetration from one ferromagnetic medium to another one. Thereby, the interaction similar to the interaction of two antiferromagnets is taken into account at the boundary interface between two media in an external constant uniform magnetic field. The problem is solved in the formalism of spin density based on equations of Landau–Lifshitz in the absence of dissipation in the system.