Averaging and mixing
DOI:
https://doi.org/10.14529/ctcr180413Keywords:
charge mixture properties, composites, mixtures, committees, diagnostics, stability, selection, interpretation, statistics, balanceAbstract
Abstract
The article is devoted to the explanation of the role of averaging and mixing in applied problems in technology and economics. The article provides the examples of applied problems solved at the Mathematical Programming Department of the N.N. Krasovskii Institute of Mathematics and Mechanics and at the department of Econometrics and Statistics of the Graduate School of Economics and Management of the Ural Federal University named after the First President of Russia B.N. Eltsin.
These are the problems in geology, mining and metallurgy, placement and development of enterprises which were traditionally solved in the Urals. Besides, the problems in planning and operational management at ore-dressing and processing enterprises were solved. A new wave of operational management at enterprises started at the beginning of 2000’s should be noted. This operational management applied the committee method.
Being mathematicians, we specified certain inaccuracies in publications made before 1990 on this subject. It is noteworthy that the principal performers of this research – the research workers of the Mathematical Programming Department – were awarded with the medals of Exhibitions of Economic Achievements of USSR.
The set of research done by N. Bourbaki’s seminar participants was devoted to averaging and mixing. In general, the research performed at the Mathematical Programming Department and in N. Bourbaki’s seminar provided a better understanding of material averaging and activity combination processes.
Modern applied research requires a more detailed solution substantiation in terms of pragmatics that was also noted in the article.
When solving these problems a method of committee construction was applied. This is also a fundamentally important approach to solving incompletely formalized problems of optimal decisions.
References
Eremin I.I., Mazurov Vl.D. Nestatsionarnye protsessy matematicheskogo programmirovaniya [Nonstationary Processes of Mathematical Programming]. Мoscow, Nauka Publ., 1979. 291 p.
Kerimov T.K. Nerazreshimosti. [Unsolvabilities]. Moscow, Akademicheskiy proekt Publ., 2007. 218 p.
Khaykin V.P. Korrelyatsiya i statisticheskoe modelirovanie v ekonomicheskikh raschetakh [Correlation and Statistical Model Operation in Economic Calculations]. Moscow, Economica Publ., 1964. 213 p.
Benuni A.KH. Vyyavlenie i ispol'zovanie proizvodstvennykh rezervov tsvetnoy metallurgii [Identification and Use of Production Reserves of Nonferrous Metallurgy]. Moscow, Metallurgy Publ., 1962. 230 p.
Nemirovskiy A.S., Yudin D.B. Slozhnost' zadachi… [Complexity of a Task …]. Moscow, Nauka Publ., 1979. 384 p.
Esipov N., Tyagunov L.I. [Definition of Rational Extent of Enrichment of Coals. Solution of Applied Tasks: Forecasting of Quality of Coke by Method of Committees]. Method of Committees in Recognition of Images: Coll. of Works, Sverdlovsk, 1974, iss. 6, pp. 131–146. (in Russ.)
Borel Е. Sur les principles de la theorie cinetique des gaz. Annales scientifiques de l’Ecole normale superieure, 1906, 23, pp. 9–32.
Ramm A.N. Opredelenie tekhnicheskikh pokazateley domennoy plavki. Metodicheskoe rukovodstvo [Definition of Technical Indexes of Domain Melting. Methodical Manual]. Leningrad, LPI Publ., 1971. 215 p.
Attouch H. Homogénéisation. Séminaire Bourbaki: volume 1987/88, exposés 686–699, Astérisque, no. 161–162 (1987–1988), Talk no. 686, pp. 7–30. Available at: http://www.numdam.org/article/SB_1987–1988__30__7_0.pdf.
Smirnov A.I. Nekotorye modeli biologicheskoy dinamiki: kand. dis. [Some Models of Biological Dynamics. Cand. Sci. Diss.]. Sverdlovsk, 1985. 112 p.
Mazurov Vl.D. Metod komitetov v zadachakh optimizatsii i klassifikatsii [Method of Committees in Problems of Optimization and Classification]. Moscow, Nauka Publ., 1990. 248 p.
Benuni A.Kh., Gurfel' B.L. Matematicheskie metody v planirovanii i upravlenii tsvetnoy metallurgii [Mathematical Methods in Scheduling and Management of Nonferrous Metallurgy]. Moscow, Metallurgy Publ., 1974. 191 p.
Katkovnik V.Ya. Lineynye otsenki i stokhasticheskie zadachi optimizatsii [The Linear Estimators and Stochastic Problems of Optimization]. Moscow, Nauka Publ., 1976. 488 p
