I. Yermolenko A. V. Scientific work with Yevgeny Ilyich
The article is devoted to the description of scientific work with the wellknown mathematician and mechanic, the honored worker of the Russian Federation, the doctor of physical and mathematical sciences, professor EvgenyIlyichMikhailovskii (1937–2013).
Keywords: refined theory of plates, contact problem.
References:
1. Vavilina N. N., Yermolenko A. V., Mihajlovskii E. I. Ustojchivost’ podkreplennojshpangoutamicilindricheskojobolochki (Stability of a cylindrical shell reinforced by frames), In the world of scientific discoveries, Krasnoyarsk: SIS, 2013, № 2.1 (38), pp. 43–55.
2. Yermolenko A. V. O poludeformacionnomvariantegranichnyhvelichin v teoriigibkihplastinKarmana (On the semi-deformational variant of boundary values in the theory of the flexible Karman plates), Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 1996, №2, pp. 235–242.
3. Yermolenko A. V. TeoriyaploskixplastintipaKarmana–Timoshenko–Nagdiotnositel’noproizvol’nojbazovojploskosti (The Karman– Timoshenko–Naghdi theory of plane plates relative to arbitrary base surface), In the world of scientific discoveries, Krasnoyarsk: SIS, 2011, № 8.1 (20), pp. 336–347.
4. Yermolenko A. V., Mihajlovskii E. I. Granichnyeuslovijadljapodkreplennogokraja v teoriiizgibaploskihplastinKarmana (Boundary conditions for the reinforced edge in the Karman theory of bending of flat plates), IOO, 1998, № 3, pp .73–85.
5. Mihajlovskii E. I., Badokin K. V., Yermolenko A. V. TeorijaizgibaplastintipaKarmana bez gipotezKirhgofa (The theory of bending of Karman-type plates without the Kirchhoff’s hypotheses), Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 1999, №3, pp. 181–202.
For citation:Yermolenko A. V. Scientific work with Yevgeny Ilyich, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 4–10.
II. Melnikov V. A. Methods for representing figures of general kind for a two-dimensional cutting problem
This article introduces representation of figures as rastr matrixes. Also the algorithm of additional data processing for reducing future computations difficulty is given. The last part describes principles of positioning figures on the workpiece.
Keywords: figures of general kind, cutting, two-dimensional space, bottomleft principle.
References:
1. Dyckhoff H. A typology of cutting and packing problems, European Journal of Operational Research, № 44, pp. 150—152.
2. Zalgaller V. A., Kantorovich L. V. Ratsionalnyi raskroi promyshlennyh materialov (Rational cutting of industrial materials), Novosibirks: Nauka, 1971, 300 p.
3. Nikitenkov V. L., Holopov A. A. Zadachi lineynogo programmiriovaniya i metody ih resesheniya (Linear programming problems and methods for their solution), Syktyvkar: Izdatelstvo Syktyvkarskogo universiteta, 2008, 143 p.
4. Prasolov V. V. Zadachi po planimetrii (Planning problems), 4th ed., dopolnennoe, M.: MCNMO, 2001, 584 p.
5. Shabat B. V. Vvedenie v kompleksnyi analiz (Introduction to complex analysis), M.: Nauka, 1969, 91 p.
6. Benell A. J., Olivera F. J. The geometry of nesting problems: A tutorial, European Journal of Operational Research, 2008, № 184, pp. 399—402.
7. Coordinate Systems, Transformations and Units // https:// www.w3.org: W3C. 6 мая 2017. URL: https://www.w3.org/TR/ SVG/coords.html.W3C (date of the application: 05.10.2017)
For citation: Melnikov V. A. Methods for representing figures of general kind for a two-dimensional cutting problem, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 11–24.
III. Kalinin S. I. GA-convex functions
The paper is devoted to the class of socalled GA-convex functions on the interval. A geometric characterization of such functions is given, their properties are studied, in particular, the Jensen inequality and its analogue are established. Sufficient conditions for the GA-convexity and GA-concavity of a function in terms of derivatives are formulated.
Keywords: GA-convex function, GA-concave function, Jensen’s inequality, analogue of Jensen’s inequality.
References:
1. Guan Kaizhong. GA-convexity and its applications, Anal. Math. 2013, 39, № 3, pp. 189–208.
2. Xiao-Ming Zhang, Yu-Ming Chu, and Xiao-Hui Zhang. The Hermite-Hadamard type inequality of GA-convex functions and its application, J. of Inequal. and Applics., Vol. 2010, Article ID 507560, 11 pages, doi:10.1155/2010/507560.
3. Kalinin S. I. (α,β)-vypuklye funkcii, ix svojstva i nekotorye primeneniya ((α,β)-convex functions, their properties and some applications), Ufa international mathematical conference. Abstracts / Executive editor R. N. Garifullin. Ufa: RITS Bashgu, 2016, pp. 75–76.
4. Abramovich S., Klariˇci´c Bakula M., Mati´c M. and Peˇcari´c J. A variant of Jensen–Steffensen’s inequality and quasi-arithmetic means, J. Math. Anal. Applics., 307 (2005), pp. 370–385.
5. Mercer A. McD. A variant of Jensen’s inequality, J. Inequal. In Pure and Appl. Math., Vol. 4, Issue 4, Article 73, 2003, pp. 1–2.
For citation: Kalinin S. I. GA-convex functions, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 25–42.
IV. Lovyagin Yu. N. Some remarks on the problem of the normability of Boolean algebras
We study the connection between the property of normability of a Boolean algebra and the existence on it of a semi-additive (o) -continuous essentially positive function. Criteria are given, under which the seminormalized Boolean algebra has no measure.
Keywords: Boolean algebra, measure, problem D. Magaram.
References:
1. Poroshkin A. G. Teoriyameryiintegrala (Theory of measure and integral), Moscow: KomKniga, 2006, 184 p.
2. Poroshkin A. G. Uporyadochennyemnozhestva. Bulevyalgebry (Ordered sets. Boolean algebras), Syktyvkar: Syktu State University, 1987, 85 p.
3. Halmos P. Measure theory, Berlin-Haidelberg-New York: Springer, 1950, 304 p.
4. Kelley J. General topology, Toronto-London-New York: D van Nostard company, 1957, 432 p.
5. Vladimirov D. A. Bulevyalgebry (Boolean algebras), Moscow: Nauka, 1969, 318 p.
6. Vladimirov D. A. Teoriyabulevyhalgebr (The theory of Boolean algebras), St. Petersburg: Publishing house of the St. Petersburg University, 2000, 616 p.
7. Halmos P. Lectures on Boolean algebras, Prinston, New-Jersey. D. vanNostardcompany, 1963, 96 p.
8. Mayaram D. An algebraic characterization of measure algebras, Ann. Math., 1947, v. 48, № 1, pp. 154–167.
9. Popov V. A. Additivnyeipoluadditivnyefunkciinabulevyhalgebrah (Additive and semiadditive functions on Boolean algebras), Sibirsk. mat., 1976, vol. 17, No 2, pp. 331–339.
10. Alexyuk V. N. Teorema o minorante. Schetnost’ problemyMagaram (The Minorant Theorem. The countability of the problem of Magaramz), Mathematics, 1977, t. 21, No. 5, pp. 597–604.
11. Lovyagin Yu. N. Bulevyalgebry s dostatochnymchislomnepreryvnyhkvazimer (Boolean algebras with a sufficient number of continuous quasimers), Syktyvkar: Dep. in VINITI, № 3111-В97, 1997, 24 p.
12. Lovyagin Yu. N. O nekotoryhsvojstvahbulevyhalgebr (On some properties of Boolean algebras), Some actual problems of modern mathematics and mathematical education: Proceedings of the scientific conference «Herzen readings — 2009», SPb: RSPU them. A. I. Herzen, 2009, pp. 131–135.
13. Lovyagin Yu. N. Regulyarnyeipolunormirovannyebulevyalgebry (Regular and semi-normalized Boolean algebras), Some actual problems of modern mathematics and mathematical education: Proceedings of the scientific conference «Herzen readings — 2011», SPb: RSPU them. A. I. Herzen, 2011, pp. 146–148.
14. Lovyagin Yu. N. Primer regulyarnoj, no nenormirovannojbulevyalgebry (An example of a regular but not normalized Boolean algebra), Some actual problems of modern mathematics and mathematical education: Proceedings of the scientific conference «Herzen Readings — 2012», SPb: RSPU them. A. I. Herzen, 2012,pp. 129–130.
15. Lovyagin Yu. N. O problemenormiruemostibulevyhalgebr (On the problem of normability of Boolean algebras), Proceedings of the Russian Pedagogical University. A. I. Herzen, 2013, № 154, pp. 23–33.
16. Gaifman H. Cjncerning measure on Boolean algebras, Pacif. J. Math., 1964, v. 14, № 1, pp. 61–73.
For citation:Lovyagin Yu. N. Some remarks on the problem of the normability of Boolean algebras, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 43–55.
V. Pimenov R. R. The geometry of perpendicularity: obtuse and acutes angles in known theorems
In the article we introduce and research the conception of «the impossible configuration of obtuse and acute angles» and its relation to theorems about perpendicularity in the plane and Rn. We study two theorems, about intersection altitudes in triangle and about projections, the last we named as «the domino theorem». We generalise both theorems for arbitrary numbers of lines and discover related with them impossible configuration of angles. We show as using continuity and method of «small moving» we can derive theorems about perpendicular lines from impossible configurations of angles. We view at the right angle as the boundary between acute and obtuse angles for this. We consider the using of these methods in non-Euclidean geometry, in Rn and express them in terms of vector algebra.
Keywords: perpendicularity, continuity, projection, orientation, altitude of triangle.
References:
1. Bachmann F. Postroeniegeometriinaosnoveponyatiyasimmetrii (Aufbau der GeometrieausdemSpiegelungsbegriff), М.: Nauka, 1969, 380 p. 2. Tabachnikov S. Skewers, Arnold Mathematical Journal,
2, 2016, pp. 171–193.
3. Pimenov R. R. K logicheskiminaglyadno-geometricheskimsvojstvamorientacii 1 (About logic and visual-geometric properties of orientation 1), MatematicheskyvestnikpedvuzoviyniversitetovVolgoViatskogoregiona: periodicheskymejvuzovskysborniknauchno-metodicheskyhrabot, Kirov: Naucn. izd-voViatGU, 2016, vyp. 18, pp. 99–114.
4. Pimenov R. R. K logicheskiminaglyadno-geometricheskimsvojstvamorientacii 2 (About logic and visual-geometric properties of orientation 2), MatematicheskyvestnikpedvuzoviyniversitetovVolgoViatskogoregiona: periodicheskymejvuzovskysborniknauchno-metodicheskyhrabot, Kirov: Naucn. izd-voViatGU, 2016, vyp. 18, pp. 115–126.
5. Pimenov R. R. ObobshcheniyateoremyDezarga: geometriyaperpendikulyarnogo (The generalization the Desargues’s theorem and geometry of perpendicularity), Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2016, №1 (21), pp. 28–43.
6. Pimenov R. R. TraktovkiteoremPappa: perpendikulyarnost’ iinvolyutivnost’ (The interpretation and generalizations the Pappus’s theorems: involutions and perpendicularity), Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, 2 (23), pp. 29–45.
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9. SkopenkovMichail. Naglyadnayageometriyaitopologiya (Visual geometry and topology), URL: http://skopenkov.ru/courses/geometry16.html.
For citation:Pimenov R. R. The geometry of perpendicularity: obtuse and acutes angles in known theorems, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 56–73.
VI. Gulyaeva S. T., Kabanova S. L., Mironov V. V. To a problem of increase in effectiveness of educational process when using the modern systems of the organization of videoconferences
In work topical issue of increase in effectiveness of educational process when using the modern systems of the organization of videoconferences is considered. The chart of business process of use of videoconferences is provided and technologies and most the videoconferences popular systems are considered.
Keywords: education, videoconference, effectiveness, business process, videoconferencing.
References:
1. Videokonferencsvjaz’. Avtor: KompanijaTrueConf // https:// trueconf.ru/: TrueConf 7.2 для Windows. URL: https:// trueconf.ru/ videokonferentssvyaz/070 (date of the application: 10.07.2017).
2. Chtotakoe VoIP? // http://aver.ru/: Vsyo o novinkaxtexniki. URL: http://aver.ru/all/chto-takoe-voip/ (date of the application: 10.07.2017).
3. Oborudovaniedljaprovedenijavideokonferencij // https:// www.insotel.ru/: Insotel. URL: http:// www.insotel.ru/article. php?id=31 (date of the application: 10.07.2017).
4. Obzorstandartovperedachidannyhispol’zuemyh v videokonferencsvjazi // http:// www.ipvs.ru/: IP Video Systems. URL: http:// www.ipvs.ru/information/videoconferencing/113-protocols-videoconferencing-data.html (date of the application: 10.07.2017).
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8. Videokonferencsvjaz’. Chast’ 1: Vvedenie v predmet // http://networklab.ru/: Setevayaakademiya CISCO. URL: http:// network-lab.ru/ videokonferentssvyaz-chast-1-vvedenie/ (date of the application: 10.07.2017).
9. Prodazhaoborudovanija Polycom // http:// www.polycom-spb.ru: Polycom. URL: http://www.polycom-spb.ru/Polycom_HDX_70001080 (date of the application: 10.07.2017).
For citation:Gulyaeva S. T., Kabanova S. L., Mironov V. V. To a problem of increase in effectiveness of educational process when using the modern systems of the organization of videoconferences, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 74–87.
VII. Odyniec W. P. On a history of some mathematical models in ecology
The prehistory of the appearance of some mathematical models and methods in ecology is briefly reviewed. History the five mathematical models reviewed in detail: the model, which based on multifractal analysis, the model of absorption by rain of pollution of atmosphere, the Lotka–Volterramodelsand their development, the model of the population stability by the genetic level.
Keywords:Margalef index, Hedervari estimation, multifractal analysis, the Lotka–Volterra models, repressilator.
References:
1. Abdurakhmanov A. I., Firstov P. P., Shirokov V. A. Vozmozhnayasvyaz’ vulkanicheskihizverzhenij s ciklichnost’yusolnechnojaktivnosti (A possible connection of volcanic eruption and the cyclicity of the sun activity), Bul. vulcanol. stancii, № 52, 1976, pp. 3–11.
2. Bagotskii S. V., Bazykin A. D., Monastyrskaya N. P. Matematicheskiemodeli v ehkologii (Mathematical models in ecology), Bibliographicheskiiukazatel’ otechestvennyhrabot, Moscow: VINITI, 1981, 224 p.
3. Bo¨ckman C. Hybrid regularization method for the ill-possed inversion of multiwave length lidar data to determine aerosol size distribution, Applied Optics, 40 (2001), pp. 1329–1342.
4. Borisenkov E. P., Paseckii V. M. Ekstremal’nyeprirodnyeyavleniya v russkihletopisyah XI–XVII vv (Extremal natural phenomena in the Russian chronicles), Leningrad: Gidrometeoizdat, 1983, 241 p.
5. Bullard F. M. Volcanoes in history, in theory, in eruption, Austin: Univ. Texas Press, 1962, 441 p.
6. Vlodavets V. I. VulkanyZemli (Volcanoes of the Earth), Moscow: Nauka, 1973, 169 p.
7. Volterra V. The changes and variations in the number of a coexisting animal species, Mem. R. Accad. Naz. deiLincei, Ser. 2., 1926, pp. 31–113.
8. Gelashvili D. B., Yakimov V. N., Iudin D. I., Dmitriev A. I., Rosenberg G. S., Solncev L. A. Mul’tifraktal’nyjanalizvidovojstrukturysoobshchestvamelkihmlekopitayushchihNizhegorodskogoPovolzh’ya (Multifractal analysis of species structure of company of the small mammal situated on Volga around from Nizhny Novgorod), Ecologiya, № 6, 2008, p. 456–461.
9. Georgi I. About the self-in flammableend of city dump of Revel, In: The selection of economical work’s which support for German language the Free Economical Society of St. Petersburg, vol. 3, St. Petersburg, 1791, pp. 330–331.
10. Glyzin S. D., Kolesov A. Yu., Rozov N. Kh. Sushchestvovanieiustojchivost’ relaksacionnogociklaimatematicheskojmodelirepressilyatora (The existence and stability ofa relaxation cycle and mathematical model of a repressilator), Matemat. Zametki, vol. 101, № 1, 2017, pp. 58–76.
11. Gulamov M. I. Teoretiko-gruppovojpodhod k issledovaniyuvzaimodejstviyaehkologicheskihfaktorov (A Group – The oretic Approach towards the Study in Interaction of Environmental Factors), Ecologicheskayachimiya, 21 (1), 2012, pp. 1–9.
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13. Kolmogorov A. N. Kachestvennoeizucheniematematicheskihmodelejdinamikipopulyacij (Qualitative research of mathematical models of dynamics of population), Problemycybernetiki, № 25, Moscow: Nauka, 1972, pp. 100–106.
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For citation:Odyniec W. P. On a history of some mathematical models in ecology, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 88–103.
VIII. Ustyugov V. A., Chufyrev A. E. The percolation problem
The article gives an overview of algorithms for solving the problem of finding a spanning cluster on a square lattice. A technique for determining the percolation threshold is described. The singular behavior of the last dependence in the vicinity of the critical concentration is explained. The solution of the problem in the form of a program in Python programming lagnuage is given.
Keywords: percolation, spanning cluster, Hoshen-Kopelman algorithm.
References:
1. Giordano N. J. Computational physics / N. J. Giordano, H. Nakanishi, Pearson/Prentice Hall, 2006, 544 p.
2. Gould H., Tobochnik J. Komp’yuternoemodelirovanie v fizike (Computer modelling in physics), M.: Mir, 1990, 400 p.
3. Tarasevich Yu. Yu. Perkolyaciya: teoriya, prilozheniyaialgoritmy (Percolation: theory, application, algorithms), M.: Editorial URSS, 2002, 112 p.
For citation:Ustyugov V. A., Chufyrev A. E. The percolation problem, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 104–113.
IX. Vechtomov E. M. Yevgeny IlyichMikhailovsky (to the fiftieth anniversary from the birthday)
The article is devoted to the prominent scientist, the deserved figure of science of the Russian Federation, the head of the school of mechanics of the Komi Republic, the doctor of physics and mathematics, professor EvgenyMikhailovsky.
For citation:Vechtomov E. M. Yevgeny IlyichMikhailovsky (to the fiftieth anniversary from the birthday), Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 114– 117.