Mordovia University Bulletin

13-23

Authors: Shiryayev Viktor Dmitriyevich (professor of Fundamental Informatics chair of Ogarev Mordovia State University (68, Bolshevistskaya Str., Saransk, Russia), Candidate of Sciences (PhD) degree holder in Physicomathematical sciences, docent, Shiryayevvd@mail.ru) Anoshchenkova Ekaterina Vasilyevna (lecturer of Fundamental Informatics chair of Ogarev Mordovia State University (68, Bolshevistskaya Str., Saransk, Russia), anoshehnkovaev@mail.ru) Bikmurzina Ravilya Ryashitovna (associate professor (docent) of Fundamental Informatics chair of Ogarev Mordovia State University (68, Bolshevistskaya Str., Saransk, Russia), Candidate of Sciences (PhD) degree holder in Pedagogical sciences, bravilya@mail.ru)

Static models of hierarchical systems of management are considered in this research. The practice of creating and functioning of various organizational systems (including economic systems) shows that the process of their management should be based on the hierarchical principle. The goals of analysis and synthesis of hierarchical systems go beyond general optimal control theory, as with subsystems interacting, the very notion of optimality gets ambiguous. As a rule, the management within the scope of an economic system implies the presence of a hierarchical structure, the individual elements of which have their own goals, that could be different from the goal of the system’s development in whole. Tree-structure and diamond-structure systems of management are studied in this research. Conflict-controlled systems with hierarchical structure are added up to hierarchical games. In rather general conditions the analysis of a two-level model of hierarchical system of management comes to finding of the solution for a game. Tree-structure system of man- agement is formalized as a non-cooperative game (n+1) of a player (administrative center and operating departments В1, …, Вn). Diamond-structure system of management is formalized as a non-cooperative game with four players in its normal form. Nash equilibrium is used as a principle of optimality in a noncooperative game. Constructive methods of finding optimal solutions for these kinds of systems are provided. Multiplicity of Nash equilibria encountered is determined by dominating role of the core А0 in the game. It goes without saying that the existence of a dominant player is possible in other tasks of conflict management. In our research, however, we confine ourselves to studying tree – structure and diamond-structure system of management only.

30-36

Authors: Kharitonova Irina Vladimirovna ( associate professor (docent) of Algebra and Geometry chair of Ogarev Mordovia State University (68, Bolshevistskaya Str., Saransk, Russia), Candidate of Sciences (PhD) degree holder in Pedagogical sciences, ira6318@yandex.ru)

The article considers the conditions of organization of independent work of students in the implementation of a differentiated approach to teaching mathematics. Particular attention is paid to the factors that contribute to the effectiveness of teaching to mathematics. The article highlights the most common signs of independence of students. It is emphasized that the problem of differentiation of instruction in terms of collective action is quite complicated and, in turn, requires the implementation of the learning process of new methods that allow to improve the mathematical training. There is a close relationship concepts of differentiation and individualization of instruction a the conditions that must be fulfilled for the successful and effective implementation of a differentiated instruction. At the organization level differentiation a teacher should not forget about the great variety of forms and methods of achieving it. For example, one of the ways of implementing the training level differentiation may be the formation of mobile teams of students. That being said, a teacher can simulate the process of organization of independent work from two sides – from the work of a teacher and by activities of students.

39-47

Authors: S. I. Malozemov.

The article considers the problem of food security in the context of the globalization and current state of providing food security taking into account the prospects specified in the Food Security Doctrine.

48-52

Authors: R. S. Tarasov, M. I. Rutkovskaya, N. V. Raslova.

The metallurgical industry of a country is one of the leading branches that provide ma¬chine building, roads and railways building as well as the military power of the country. The policy of the government should be oriented at support and development of Russian industry. That was especially topical in the 19th century. To solve the problems of develop¬ing metallurgical industry the requests on its state all over the country were made. Politi¬cal events regulated the process of taking the effective measures for the development of industry. The economic policy was oriented towards acquisition of income in the treasury and therefore was limited to supporting protective duties.

59-70

Authors: Skryabin Vladimir Aleksandrovich ( professor of Machine Engineering Technology chair of Penza State University (40, Krasnaya Str., Penza, Russia), Doctor of Sciences degree holder in Engineering sciences, vs_51@list.ru) Reyes Almeyda Maksim Antoniovich ( post-graduate student of Machine Engineering Technology chair of Penza State University (40, Krasnaya Str., Penza, Russia), max-reyes@yandex.ru)

The authors report the results of finish treatment researches of surfaces of pistons made of aluminium alloys. It is shown that centerless polishing and polishing before coverage of surface with nickel-phosphorus alloy provides good durability of coupling of alloy with aluminium basis, and a chemical nickelage and polishing provide the increase of wearproofness and inoxidizability of coverage with the elastic circles of alloy. Results of the work reflected in the article are inculcated as technology of the chemical besieging and finish abrasive treatment of protective-decorative coverage of alloy nickel-rhenium-phosphorus in. “Compressor” Association LLC (city of Penza), application of which allowed to promote wearproofness and inoxidizability of working surfaces of details. An economic effect from introduction of development is attained by the increase of resource of work in 1,3–1,5 times.

82-95

Authors: Skryabin Vladimir Aleksandrovich ( professor of Machine Engineering Technology chair of Penza State University (40, Krasnaya Str., Penza, Russia), Doctor of Sciences degree holder in Engineering sciences, vs_51@list.ru)

The subject of the article are regularities of the process of co-operation of details made of powder-like materials with a discrete abrasive layer. It is shown that many known methods of finish do not allow to a full degree to provide high quality of surfaces, of details of powder-like materials. There are numerous pores on the surfaces of such details, foods of wear debris of processing environment and also directly abra- sive grains can be charged in. The basic parameters of finish treatment of smooth and geometrically-complex surfaces are estimated: size of arc of contact, position of arc of contact in relation to the surface of detail, distribution of pressure on the arc of contact, size of force operating on single abrasive grain treatments, such as brands and gritness of abrasive filler, and » also composition of working liquids. On the basis of the analytical dependences and charts, acquired as a result of theoretical and experimental researches of process of detail with an abrasive layer, recommendations are given on the practical use of abrasive details made of powder-like materials, both on the stage of planning of equipment in the plan of achievement set the productivity and treatment and on the stage of the industrial use of present options.

101-104

Authors: Yufkin Yurij Gavrilovich ( associate professor (docent) of Machine Tools and Systems chair of Ruzaevka Machine Engineering Institute, branch of Ogarev Mordovia State University (93, Lenin Str., Ruzaevka, Russia), Candidate of Sciences (PhD) degree holder in Engineering sciences, yuriyfkinn@mail.ru) Vesnushkina Nina Nikolayevna ( associate professor (docent) of Machine Engineering Technology chair of Ruzaevka Machine Engineering Institute, branch of Ogarev Mordovia State University (93, Lenin Str., Ruzaevka, Russia), nina.vesnushkina@mail.ru )

The article discusses the operation of fine boring with self-positioning tools as tools with a constructively implemented adaptation system. The authors establish the main sources of error of the technological system; sources of error shape of the holes in the workpiece; error of the workpiece in the machine. The mathematical model describing the process of boring selfaligning tools is created basing on a mathematical model of processing in the form of a closed technological system. Floating cutter blocks are regarded as completely rigid body relative to the tool body having one degree of freedom. General parameters characterizing the structure of a boring tool with floating cutter blocks are their number; the pressing force of each of the insical unit in the tool body; friction coefficients of cutting blocks in the tool body; the number of cutting elements disposed on each side of the incisal block. Components of the cutting forces are presented in the form of fixed and variable parts. The variable part of the components of the cutting force is presented in the form of a Fourier series. The formalization of the profile of the hole takes into account its error in the radial section (ovality, cut). Current coordinate describing the profile at a given point of the hole is a central angle. The resulting dynamic model of the boring tool with floating cutting blocks, which takes into account the variability of the components of the cutting force acting on each cutting element, can adequately describe his work in real time.

110-127

Authors: Besolov Vladimir Butusovich (director of North Caucasian Academic Centre of the International Academy of Architecture (94, Alagirskaya Str., Alagir, Russia), archgrad101@yandex.ru) Besolov Aristarkh Vladimirovich ( post-graduate student of Caucasus Studies, the history of the ancient world and the Middle Ages of North Ossetia State University named after K. L. Hetagurov (46, Vatutin Str., Vladikavkaz, Russia), archgrad101@yandex.ru)

Over the course of history the architectural morphotype of the ancient centric dwelling has been continuously transformed and developed, for the Indo-European masters paid special attention to the improvement of the Domeconcept, i.e. planned composition, spatial and tectonic structure and shape. Initial place of emergence and development of the creative ideas for the dome on a square occurred in architecture of the ancient centric dwelling and subsequently held its brilliant transformation into central dome structures of memorial and religious architecture in Early Medieval Christian Eastern countries and historical Byzantium. Undoubtly, for many centuries there was a crystallization of the artistic and creative concept of the domeon on a square, arisen in ancient times. Evidences of this are the architectural creations of the centric composition, the structures and forms, built of local building materials, constituents inseparable unity, organic whole with the Caucasus-Pamir mountain mega region landscape. There is no doubt that the architectural morphotype of the ancient centric dwelling with-pyramidal-ledged ceiling andlight-fluehole over an open hearth was the original basis and creative impulse in the process of forming the composition and structure of the internal space and external forms architectonic in memorial and religious structures in the early Middle Ages with Central dome, i.e. in Christian regions and the Muslim East, including the architecture of the Early and High Middle Ages in countries as Aghvan, Armenia, Georgia, Abkhazia and Alanya – all in the Caucasus, as well as Azerbaijan, Middle and Central Asia.