Physics, mathematics, and technology

The paper studies design and development of expenditure accounting system of an online shop using the fuzzy sets theory and fuzzy logic. It has also considered the construction principles of complex information systems and formulated the requirements for the system under design. Apart from that the authors dwell upon the fuzzy problem of multi-criteria optimization on basis of interval estimation. The program interface has been designed and main principles of work created by informational system have been described.

The paper introduces internal affine (tangent) and normal (centroprojective) connections on normalized (Norden’s framed) hypersurface n-1()  Pn in its various subbundles. Coverages of the corresponding curvature 2 forms and curvature tensors of its connections are given.

The article describes the development of the structure and functional nodes of the receiving antenna of the short-wave range for moving objects. The authors define the ways to solve the problem of improving the range properties, increasing the sensitivity of the radio reception and ensuring the electromagnetic compatibility of radio electronic means located within limited space of the mobile object and integrating the antenna into the object’s housing elements.

The article presents the analysis of activity regulation issues in the regional power supply complex and the main ways to improve the efficiency of its subjects. The authors also focus on the issues of automated tariffs setting for production, transportation and transfer heat and electric power. Main attention is paid to automated registration of losses during producing and transferring heat and electric energy.

The authors identify the required characteristics of wind turbines for mobile installations, carry out the classification of wind turbines, analyze wind turbines with a horizontal and a vertical axis of rotation, and define the optimum types of wind turbines for use in conditions of low wind loadings.

The article presents the results of the universal program complex PT-Q-1 for the automated setting and the analysis of tariffs in district heating system. The authors study the feasibility of the SaaS model application which provides for the simplest data interchange in the relevant information space and allows reducing significantly the software implementation cost and maintenance. The structural organization, information and the software of the program PTQ- 1 complex features are given.

The latest results of space and ground-based mission WMAP, Planck, BICEP2 discussed widely by the scientific community and indicate the need for research on new models of inflation, other than the basic model of inflation, based on a single self-interacting scalar field. In this paper we consider the inflationary model based on chiral cosmological model, which takes into account the various forms of kinetic interaction between the phantom and the canonical field. This study determines the dynamics and interaction of the fields in the short time at the stage of early inflation, when the potential fields of cooperation remains constant (as seen in the model of the "new" inflation). We present a general algorithm for solving dynamic equations on chiral (scalar) fields and examine special cases when it is possible to find a solution in elementary functions.

This is a treatise on a two-dimensional supersymmetric hamiltonian H whose components consists of two scalar (h0, h1) and one matrix-valued hml  quantum-mechanical Hamiltonians with constant terms added to the mix. In particular, the article discusses the ways to utilize a known solution of the spectral problem for operator h0 in the multi-dimensional generalization of the factorization method in order to pro-duce such  hml and h1 that their ground-state eigenvalues will be identical to each other but lower than that of h0. Then we propose a new scheme designed for the task of construction of supersymmetric Hamiltonian H with a degenerate eigenvalue E = 0 and provide the corresponding (0 + 1) super-multiplet with a broken U1 symmetry. Next, we describe the algorithm for production of the algebra of an extended supersymmetry. We determine the important connection that relates the Moutard formula with a problem of «insertion» of a new ground-state eigenvalue to the spectrum of the matrix-valued component of H. And, finally, we discuss the Moutard transformations and their viability for the higher dimensional cases when d > 2.

The article gives the account of steady flow of a perfect gas in a vertical channel having some other parameters set. The flow is supposed to be highspeed, subsonic and design, that is the gas pressure at the outlet equal to the pressure (back pressure), while the forces of gravity can be neglected. The boundary value problem is solves with the standard numerical method, the Mathcad in particular. The least squares method was used to find the empirical dependence of the heat nitrogen on the temperature. Third order polynomial approximation gives the average deviation from experimental data of less than 0.5 %. The paper also shows that with increase of the wall temperature of channel increases the required pressure at the inlet of the lance and the speed of the output. The latter fact is important in the process to increase the influence of the purge. The developed method allows applying the Mathcad to solve the boundary problem of gas dynamics of a perfect gas in the channel with heat supply. The authors also show the dependence of the viscosity and heat capacity on the gas temperature.