Applied Mathematics and Control Sciences

It is shown that, in accordance with a priori approach to establishing physical phenomena construction formal mathematical model may be preceded by the experimental data obtained. The aim is to construct a mathematical model of a formal analogue of the wave function of the particle-free inert and compare it with the actual wave function. Reasons why this is the fact that the logic of wave-generalization, lies at the origin of the current version of the description of the wave function, it is not certain. The formal analogue of the wave function is obtained from a series of successive transformations of the classical equation of rectilinear uniform motion of a free nonrelativistic particle inert. Further transformations possible to obtain an analog of the Schrodinger equation for a free particle. His comparative analysis of the existing version of the Schrödinger equation revealed a contradiction in the existing version and half to adjust the value of the phase velocity.

The results of numerical modeling the technological process of plastic metal working of a large size ingot made of steel 30HGSA are presented. The modeling process has been carried out in accordance with a manufacturing scheme that involves the air cooling of the ingot during its transportation from the furnace to the deforming equipment, and two metal forming operations - free upsetting and open-die forging, during which the ingot is shaped into a circular configuration. The ingot was upset between the upper flat and lower annular dies to reach a diameter of 1060 mm. Then, using a combination of different dies the ingot was pressed to the desired dimensions no less than 860 mm. Examination of changes in the ingot shape and its heat and stress-strain states was carried out using an engineering software Deform-3D. A compression force required for implementation of forming operations during the technological process of plastic metal working was calculated.

Prediction of physical and mechanical properties of nanostructured materials is usually realized within discrete atomistic simulation. Such approach often provides a unique way of studying nanomaterials and requires some restrictions for the used interatomic potentials. A huge amount of different potentials has been used, i.e. pairwise, many-particle potentials, embedded atom method, covalent bond potentials etc. It is well known that computed mechanical properties in some cases may differ from experimental data, even qualitatively. The paper aims at the demonstration of different potentials ability to explain elastic anisotropy by studying invariant representation of tensor of elastic moduli in the exact form which has been built using different potentials of interatomic interaction. It makes it possible to study the prospects of different potentials for describing anisotropy of material elastic response. The authors demonstrated the abilities of two-particle or multi-particle potentials of interatomic interaction based on the Morse potential in describing anisotropy of materials elastic properties using the obtained invariant representation by the examples of two-dimensional quasi-crystalline structures. The pair-wise potentials in contrast to the many-particle embedded atom potential are shown to be unable to explain elastic anisotropy.

In article the problem of a choice of factors of management of technological process of production of an autoclave aerated concrete by criterion of quality is considered. By results of an expert assessment it is established that the best results on improvement of quality of a ready-made product will be reached at management of process of dispensing of components of an autoclave gas concrete. Justification of a choice of factors of quality management of an autoclave gas concrete at a dispensing stage, among which ratios of n, Cb and the content of active silicon dioxide (SiO2) in sand is given.

The new problem definition of shopping malls management taking into account consumer appeal where as criterion function the profit of tenants of trade and entertaining rooms is used is formulated. This problem definition corresponds to economic reality as in practice of management of commercial real estate the form of interaction between management company and tenants in the form of the fixed rental rate and percent from sales of tenants is widespread. The accounting of consumer appeal is provided thanks to modeling of preferences of shopping mall visitors. For search of optimum control the graphic-analytical method of the analysis of economic efficiency of the decisions made at commercial real estate objects management based on the analysis of sensitivity of indicators of efficiency to change of controlled factors is offered. Efficiency of application of this method and a possibility of finding of optimum control of shopping mall is visually shown.