Bulletin 1 (30) 2019

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Issue 1 (30) 2019

I. Vechtomov E. Ì. Binary relations and homomorphisms of Booleans

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The works deals with Binary relations between arbitrary sets A and B investigated in terms of corresponding complete V-homomorphisms from the Boolean B(A) to the Boolean B(B). The author proposes two duality theorems: for the category of all sets and binary relations between them considered as morphisms, and also for the category of all binary relations and their 2-morphisms.

Keywords: binary relation, Boolean, complete V-homomorphism, duality of categories.

References

  1. Kon P. Universalnaya algebra (Universal algebra), M.: Mir, 1968, 352 p.
  2. Arkhangelskiy A. V. Kantorovskaya teoriya mnozhestv (Cantor theory of sets), M.: Izd-vo MGU, 1988, 112 p.
  3. Birkgo G., Barti T. Sovremennaya prikladnaya algebra (Modern applied algebra), M.: Mir, 1976, 400 p.
  4. Vechtomov Ye. M. Binarnyye otnosheniya (Binary relations), Matematika v obrazovanii, 2007, v. 3, pp. 41-51.
  5. Vechtomov Ye. M. O binarnykh otnosheniyakh dlya matematikov i informatikov (On binary relations for mathematicians and computer scientists), Vestnik Vyatskogo gosudarstvennogo gumanitarnogo universiteta, 2012, 1 (3), pp. 51-58.
  6. Vechtomov Ye. M. Matematika: osnovnyye matematicheskiye struktury: uchebnoye posobiye dlya akademicheskogo bakalavriata (Mathematics: Basic Mathematical Structures: A Manual for Academic Baccalaureate), 2-ye izd, M.: Yurayt, 2018, 296 p.
  7. Kuk D., Beyz G. Kompyuternaya matematika (Computer Mathematics), M.: Nauka, 1990, 384 p.
  8. Maltsev A. I. Algebraicheskiye sistemy (Algebraic Systems), M.: Nauka, 1970, 392 p.
  9. Tsalenko M. SH. Modelirovaniye semantiki v bazakh dannykh (Simulation of semantics in databases), M.: Nauka, 1989, 288 p.
  10. Shreyder YU. A. Ravenstvo. Skhodstvo. Poryadok (Equality. Similarity. Order), M.: Nauka, 1971, 256 p.
  11. Grettser G. Obshchaya teoriya reshetok (The general theory of lattices), M.: Mir, 1982, 456 p.
  12. Plotkin B. I. Universalnaya algebra, algebraicheskaya logika i bazy dannykh (Universal algebra, algebraic logic and databases), M.: Nauka, 1991, 448 p.

For citation: Vechtomov E. Ì. Binary relations and homomorphisms of Booleans, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2019, 1 (30), pp. 3-15.

II. Pimenov R. R. Lineup markup as an introduction to group theory

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The article reveals the relationship between the ruler markup, the group of permutations of the three elements, involutive transformations and linear fractional functions. Threefold symmetry is shown, without which the ruler marking would be impossible. Examples and tasks useful for teaching mathematics at school and university are given.

Keywords: lineup markup, symmetry, group theory, involution, education.

References

  1. Pimenov R. R. Troystvennaya simmetriya Fraktal’nogo kaleydoskopa (Triple symmetry of a fractal kaleidoscope), Mat. Pros., Ser. 3, 20, MCCME, Moscow, 2016, pp. 57-110.
  2. Pimenov R. R. K logicheskim i naglyadno-geometricheskim svojstvam orientacii 1 (About logic and visual-geometric properties of orientation 1), Matematichesky vestnik pedvuzov i yniversitetov Volgo- Viatskogo regiona: periodichesky mejvuzovsky sbornik nauchno-metodicheskyh rabot, Kirov: Naucn. izd-vo ViatGU, 2016, v. 18, pp. 99-114.
  3. Koganov L. Dvoynoye otnosheniye kak prostoye (Cross-ratio as ane ratio), Problems of theoretical cybernetics, abstracts of 14 inter. conferences, Penza May 23-28, M, ed. MSU, 2005, pp. 1-4.
  4. Pimenov R. R. Esteticheskaya geometriya ili teoriya simmetriy (Aesthetic geometry or theory of symmetries), SPb, School league, 2014, 288 p.
  5. Bachmann F. Postroyeniye geometrii na osnove ponyatiya simmetrii (Aufbau der Geometrie aus dem Spiegelungsbegriff), Moscow, Nauka, 1969, 380 p.

For citation: Pimenov R. R. Lineup markup as an introduction to group theory, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2019, 1 (30), pp. 16-26.

III. Mingaleva A. E., Nekipelov S. V., Petrova O. V., Sivkov D. V., Sivkov V. N.   Apparatus distortion investigations in NEXAFS C1s-spectra on the example of fullerite C60

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The paper presents the results of the comparison of transmission and TEY methods in determining the absorption cross section in the NEXAFS C1s-spectra of the fullerite C60, as well as of «the thickness effect» modeling in the absorption cross section spectral dependences of the C60-films in the NEXAFS C1s-spectra. The calculations were performed with using absorption cross section spectra obtained in TEY mode as the true (undistorted) data. The modelling results are in good agreement with the experiment.

Keywords: absorption cross section, NEXAFS, fullerite, «thickness effect»,synchrotron radiation.

References

  1. St¨ohr J. NEXAFS Spectroscopy. Berlin: Springer Verlag, 1992. 403 p.
  2. Parratt L. G., Hempstead C. F., Jossem E. L. «Thickness Effect» in Absorption Spectra near Absorption Edges, Phys. Rev., 1957, V. 105, 1228 p.
  3. Sivkov V. N., Vinogradov A. S. Sila ostsillyatorov πg ― rezonansa formy v NK ― spektre pogloshcheniya molekuly azota (The oscillator strength of the πg― resonance form in the NK ― absorption spectrum of the nitrogen molecule), Opt. and spectrum, 2002, T. 93, 3, pp. 431-434.
  4. Sivkov V. N., Vinogradov A. S., Nekipelov S. V., Sivkov D. V.,Sluggish D. V., Molodtsov S. L. Sily ostsillyatorov dlya rezonansov formy v NK-spektre pogloshcheniya NaNO3, izmerennyye s ispol’zovaniyem sinkhrotronnogo izlucheniya (Oscillator strengths for form resonances in the NK absorption spectrum of NaNO3, measured usingsynchrotron radiation), Opt. and spectrum, 2006, T. 101, 5, pp. 782-788.
  5. Fedoseenko S. I., Vyalikh D. V., Iossifov I. E., Follath R.,Gorovikov S. A., P¨uttner R., Schmidt J.-S., Molodtsov S. L., Adamchuk V. K., Gudat W., Kaindl G. Commissioning results and performance of the high-resolution Russian-German Beamline at BESSY II, Nucl. Instr.and Meth. A., 2003, V. 505, pp. 718-728.
  6. Kummer K., Sivkov V. N., Vyalikh D. V., Maslyuk V. V., Bluher A., Nekipelov S. N., Bredow T., Mertig I., Molodtsov S. L. Oscillator strength of the peptide bond π∗ resonances at all relevant X-ray absorption edges, Phys. Rev., 2009, V. 80, pp. 155433-8 (2).
  7. Sivkov V. N., Obedkov A. M., Petrova O. V., Nekipelov S. V., Kremlin K. V., Kaverin B. S. , Semenov N. M., Gusev S. A. Rentgenovskiye i sinkhrotronnyye issledovaniya geterogennykh sistemna osnove mnogostennykh uglerodnykh nanotrubok (X-ray and synchrotron studies of heterogeneous systems based on multi-walled carbon nanotubes), Solid State Physics, 2015, 57, pp. 187-191.
  8. Gudat W., Kunz C. Close Similari between Photoelectric Yield and Photoabsorption Spectra in the Soft-X-Ray Range, Phys. Rev. Letters, 1972, V. 29, pp. 169-172.
  9. Petrova O. V. Raspredeleniye sil ostsillyatorov v ul’tramyagkikh rentgenovskikh spektrakh uglerodnykh nanostrukturirovannykh materialov i biopolimerov: dis. na soiskaniye uchonoy stepeni kand. fiz.- mat. nauk: 01.04.07 (Distribution of oscillator strengths in ultra-soft x-ray spectra of carbon nanostructured materials and biopolymers: dis. for the degree of Candidate Phys.-Mat. Sciences: 01.04.07), Mosk. state University, Moscow, 2018, 150 p.
  10. Maxwell A. J., Br¨uhwiler P. A., Arvanitis D., Hasselstr¨om J.,M¨artensson N. Carbon 1s near-edge-absorption fine structure in graphite, Chem. Phys. Lett., 1996, V. 260, pp. 71-77.
  11. Batson P. E. Carbon 1s near-edge-absorption fine structure in graphite, Phys. Rev., 1993, B. 48, pp. 2608-2610.

For citation: Mingaleva A. E., Nekipelov S. V., Petrova O. V., Sivkov D. V., Sivkov V. N. Apparatus distortion investigations in NEXAFS C1s-spectra on the example of fullerite C60, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2019, 1 (30), pp. 27-39.

IV. Mikhailov A. V., Tarasov V. N. The stability of the reinforced arches under the boundary conditions of the hinged support

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The paper solves problem of stability of elastic systems in the presence of one-sided constraints on displacement. The stability problems of circular arches under uniform pressure were previously discussed in the works of E. L. Nikolai, A. N. Dinnik and other authors. This paper discusses the stability problems of circular arches, supported by inextensible threads thatdo not withstand the compressive forces under the boundary conditions of hinged support. Both ends of the thread are attached to the axis of the arch, so that the distance between the points of attachment as a result of the deformation cannot increase. This problem is reduced to finding and studying the bifurcation points of solutions of a certain nonlinear programming problem.

Keywords: arch, stability, support by threads, hinged edge, spline, variational problem, one-sided constraints.

References

  1. Nikolai E. L. Trudy po mekhanike (Works on mechanics), M.: Izd. tekhniko-tekhnicheskoy literatury, 1955, 584 p.
  2. Dinnik A. N. Ustoychivost’ arok (The stability of the arches), M.: Gostekhizdat, 1946, 128 p.
  3. Zav’yalov Y. S., Kvasov B. I., Miroshnichenko V. L. Metody splayn-funktsiy (Methods of spline functions), M.: Nauka. Glavnaya redaktsiya fiziko-matematicheskoy literatury, 1980, pp. 96-101.
  4. Tarasov V. N. Metody optimisatsii konstruktivno-nelineinnykh zadach mekaniki uprugikh system (Optimization methods in the study of structurally non-linear problems of the mechanics of elastic systems), Syktyvkar, 2013, 238 p.
  5. Sukharev A. G. Global’nyy ekstremum i metody ego otyskaniya (Global extremum and methods for finding it), Matematicheskiye metody v issledovanii operatsiy, M.: Izd. MGU, 1983, 193 с.
  6. Tarasov V. N. Ob ustoychivosti uprugikh sistem pri odnostoronnikh ogranicheniyakh na peremeshcheniya (On the stability of elastic systems with one-sided constraints on displacements), Trudy instituta matematiki i mekhaniki. Rossiyskaya akademya nauk. Ural’skoye otdeleniye, Tom 11, № 1, 2005, pp. 177-188.
  7. Feodos’yev V. I. Izbrannyye zadachi i voprosy po soprotivleniyu materialov (Selected problems and questions on the resistance of materials), M.: Nauka, 1967, 376 p.

For citation: Mikhailov A. V., Tarasov V. N. The stability of the reinforced arches under the boundary conditions of the hinged support, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2019, 1 (30), pp. 40-52.

V. Cheredov V. N. Percolation-nanoclusters model of the crystallization front

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A new nanocluster model of a first-order liquid-solid phase transition is proposed based on the model of oscillating bonds and the percolation lattice of bonds and assemblies. The nanocluster structure at the water crystallization front, the conditions of its formation, and its relation to the percolation threshold of the liquid structure are studied. The relationship between the parameters of nanoclusters and the ratio of the thermodynamic and percolation characteristics of the structure of intermolecular fluid bonds has been revealed. Within the framework of the constructed model, the dynamics of the water structure and its phase transitions is studied. Quantitative characteristics of liquid phase nanoclusters at the water crystallization front are studied.

Keywords: intermolecular bonds, phase transitions, nanoclusters, percolation threshold, model of oscillating bonds.

References

  1. Cheredov V. N., Kuratova L. A. Dinamika setki mezhmolekulyarnyh svjazej i fazovyje perehody v kondensirovannyh sredah (Dynamics of a network of intermolecular bonds and phase transitions in condensed matter), Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, 4(25), pp. 20-32.
  2. Kaplan I. G. Mezhmolekuljarnye vzaimodejstvija. Fizicheskaja interpretacija, komp’juternye raschjoty i model’nye potencialy (Intermolecular interactions. Physical interpretation, computer calculations and model potentials), M.: BINOM, Laboratorija znanij, 2012, 400 p.
  3. Cheredov V. N. Statika i dinamika defektov v sinteticheskih kristallah fljuorita (Statics and dynamics of defects in synthetic fluorite crystals), SPb: Nauka, 1993, 112 p.
  4. Landau L. D., Lifshic E. M. Statisticheskaja fizika. Ch.1 (Statistical physics. Part 1), M.: Fizmatlit, 2010, 616 p.
  5. Enohovich A. S. Spravochnik po fizike i tehnike (Reference book on physics and techniques), M.: Prosveshhenie, 1989, 224 p.
  6. Zacepina G. N. Fizicheskie svojstva i struktura vody (Physical properties and structure of water), M.: MGU, 1998, 184 p.
  7. Jejzenberg D., Kaucman V. Struktura i svojstva vody (Structure and properties of water), M.: Direkt-media, 2012, 284 p.
  8. Dorsey N. E. Properties of ordinary Watter-Suvstance, New York: Reinhold Publishing Corporation, 1940, 673 p.
  9. Giauque W. F., Stout J. W. The entropy of water and the third law of thermodynamics. The heat capacity of ice from 15 to 273◦K, Journal of the American Chemical Society, 1936, V. 58, pp. 1144-1150.
  10. McDougall D. P., Giauque W. F. The production of temperatures below 1◦ A. The heat capacities of water, gadolinium nitrobenzene sulfonate heptahydrate and gadolinium anthraquinone sulfonate, Journal of the American Chemical Society, 1936, V. 58, pp. 1032-1037.
  11. Kirrilin V. A., Sychev V. V., Shendlin A. E. Tekhnicheskaya termodinamika (Technical thermodynamics), Ìoscow: Izdatelstvo MEI, 2008, 486 p.
  12. Tarasevich Ju. Ju. Perkoljacija: teorija, prilozhenija, algoritmy (Percolation: theory, applications, algorithms), M.: Librokom, 2012. 116 p.
  13. Jefros A. L. Fizika i geometrija besporjadka (Physics and geometry of disorder), M.: Nauka, 1982, 176 p.
  14. Stanley H. E. A polychromatic correlated-site percolation problem with possible relevance to the unusual behaviour of supercooled H2O and D2O (A polychromatic correlated-site percolation problem with possible relevance to the unusual behaviour of supercooled H2O and D2O), Journal of Physics A: Mathematical and General, 1979, V. 12, 12, pp. L329-L337.
  15. Stanley H. E., Teixeira J. J. Interpretation of the unusual behavior of H2O and D2O at low temperatures: Tests of a percolation model (Interpretation of the unusual behavior of H2O and D2O at low temperatures: Tests of a percolation model), The Journal of Chemical Physics, 1980, V. 73, 7, pp. 3404-3422.
  16. Stanley H. E., Teixeira J., Geiger A., Blumberg R. L. Interpretation of the unusual behavior of H2O and D2O at low temperature: Are concepts of percolation relevant to the «puzzle of liquid wate»? (Interpretation of the unusual behavior of H2O and D2O at low temperature: Are concepts of percolation relevant to the«puzzle of liquid water»?), Physica A: Statistical Mechanics and its Applications, 1981, V. 106, 1-2, pp. 260-277.

For citation: Cheredov V. N. Percolation-nanoclusters model of the crystallization front, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2019, 1 (30), pp. 53-66.

VI. Belykh E. A. Car number plate segmentation based on averaged models

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This paper is devoted to the problem of dividing an image with a car number into images of individual characters, as well as recognizing these characters. The paper proposes a method for solving this problem by constructing an averaged image.

Keywords: symbol recognition, car plate, computer vision, image segmentation.

References

  1. Malygin E. S. Ustoychivaya k shumam segmentatsiya avtomobil’nykh nomerov v nizkom razreshenii: bakalavrskaya rabota (Low-noise, noise-free segmentation: bachelor’s work), St. Petersburg State the university. St. Petersburg, 2015, 26 p.
  2. Bolotova Yu. A., Spitsyn V. G., Rudometkin M. N. Raspoznavaniye avtomobil’nykh nomerov na osnove metoda svyaznykh komponent i iyerarkhicheskoy vremennoy seti (Recognition of license plates based on the method of connected components and hierarchical temporary network), Computer Optics, 2015, T. 39, 2, pp. 275-280.
  3. Serikov A. S. Segmentatsiya i raspoznavaniye avtomobil’nykh registratsionnykh nomerov (Segmentation and recognition of car registration numbers), Youth and modern information technologies: collectionof works XIV International Scientific and Practical Conference of Students, Postgraduates and young scientists, 2016, Tomsk: TPU publishing house, 2016, T. 2, pp. 219-220.
  4. Viola P., Jones M. Rapid Object Detection using a Boosted Cascade of Simple Features, 2013 IEEE Conference on Computer Vision and Pattern Recognition, 2001, Vol. 1, pp. 511-518.
  5. Belykh E. A. Optimizatsiya algoritmov raspoznavaniya avtomobil’nykh nomerov dlya raboty s videopotokom: vypusknaya kvalifikatsionnaya rabota (Optimization of license plate recognition algorithms for work with video stream: final qualifying work), Syktyvkar Pitirim Sorokin State University, Syktyvkar, 2017, 64 p.

For citation: Belykh E. A. Car number plate segmentation based on averaged models, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2019, 1 (30), pp. 67-76.

VII. Odyniec W. P. About Physicists Who Came to the URSS in the 1930s

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The article presents a slice of the development of physical science in the USSR in the 30s of twentieth century against the background of history of interaction with foreign physicists who came to the country.

Keywords: quantum and nuclear physics, low temperature physics, relativity theory, astrophysics, rigid body theory, statistical nuclear theory, A. Ioffe, V. Weisskopf, A. Weissberg, K. Weiselberg, F. G. Houtermans, M. Ruhemann, L. Tisza, G. Placzek, F. Lange, V. S. Spinel, V. A. Maslov, P. A. M. Dirac, L. Landau, A. Leipunsky, I. Obreimov, L. V. Schubnikow, V. Fomin, N. Rozen, B. Podolsky, V. A. Fock, I. Kurchatov.

References

  1. Ioffe A. F. Vstrechi s fizikami. Moi vospominaniya o zarubezhnykh fizikakh (Encounters with Physicists. Remeniscences of Foreign Physiciasts), Leningrad: Nauka, 1983, 262 p.
  2. Odyniec W. P. Immigratsiya v SSSR v dovoyennyy period: Profili matematikov (Immigration to the USSR in the pre-war period: Profiles of the mathematicians) / W.P. Odyniec, Syktyvkar: Syktyvkar State University named after Pitirim Sorokin, 2019, 124 p.
  3. Tolok V. T., Kozak V. S., Vlasov V. V. Fizika i Khar’kov (Physics and Kharkov), V.T. Tolok, Kharkov: Timchenko, 2009, 408 p.
  4. Fraenkel V. Ya. Professor Fridrikh Khoutermans: Raboty, zhizn’, sud’ba (Professor Friedrich Houtermans: Work, Life, Fate), St. Petersburg: PIYaPh RAN Press, 1997, 200 p.
  5. Khramov Yu. A. Fiziki: Biograficheskiy spravochnik (Biographical Handbook), eds. A.I. Akhiezer; 2nd ed.,enlarged and corrected, Moscow: Nauka, 1983, 400 p.
  6. Ranyuk Yu. Laboratoriya 1. Yaderna fizika v Ukraini (Laboratory No 1. Nuclear Physics in Ukraine), Yu. Ranyuk.-Kharkov: Añta, 2006, 590 p.
  7. Oleynikov P. V. German Scientists in the Soviet Atomic Project, The Nonproliferation Review/ Summer 2000, No 2, pp. 1-30.
  8. Khroniki. Uspekhi fizicheskikh nauk (Chronicles. Uspekhi Fizicheskich Nauk), Vol. XIV, 1934, pp. 516-520.
  9. Walther A. The second Union Conference on the atomic nucleus, Moscow: Physikalische Zeitschrift der Sowjetunion, Vol. 12, No. 5, 1937, pp. 610-622.

For citation: Odyniec W. P. About Physicists Who Came to the URSS in the 1930s, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2019, 1 (30), pp. 77-91 .

VIII. Sotnikova O. A. Teaching logical and mathematical analysis based on higher algebra material to future math teachers

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The ability to perform logical and mathematical analysis of math instruction material is considered to be one of the key methodological competences for a math teacher. Traditionally, the issue has been dealt with in the course of methods-of-teaching subjects. However, the author follows the principle of vocational and pedagogic focus of education and substantiates the reasonability and feasibility of dealing with the issue when studying higher algebra. The article provides the list of activities in order to perform logical and mathematical analysis of algebra instruction material.

Keywords: Math teacher training at university, logical and mathematical analysis, methodological skills.

References

  1. Lyachenko E. I., Zobkova K. V., Kirichenko T. F. I dr. Labaratornye i prakticheskie raboty po metodike prepodavania matematike: Uchebnoe posobie dla studentov fiz.-mat. spez. ped. Insnitutov(Laboratory and practical work on the methods of teaching mathematics: A manual for students of Phys.-Mat. specialist. ped. institutions), Pod ped. E.I. Lyachenko, Ì.: Prosvyachenie, 1988, 223 p.
  2. Mordkovich A. G. O professionalno-pedagogicheskoy napravlennosti matematicheskoy podgotovki budushix uchiteley (On the professional and pedagogical orientation of the mathematical preparation of future teachers), Matematika v shkole, 1984, ― 6, pp. 42-45.
  3. Gorskiy D. P. Opredelenie (Definition), Ì.: Ìysl, 1974, 310 p.
  4. Kondakov N. I. Logicheskiy slovar (Logical dictionary), Ì.: Nauka, 1971, 637 p.
  5. Boltyanskiy V.G. Kak ustroena teorema? (How does the theorem work?), Matematika v shkole, 1973, ― 1, pp. 41-50.
  6. Gradshteyn I. S. Pryamaya i obratnaya teoremy (Direct and inverse theorems), Ì.: Nauka, 1973, 128 p.

For citation: Sotnikova O. A. Teaching logical and mathematical analysis based on higher algebra material to future math teachers, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2019, 1 (30), pp. 92-112.

IX. Odyniec W. P. About the problems of mathematical training of physists

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Teaching physics relies heavily on the mathematical apparatus. Unfortunately, curricula in physics and mathematics are not always consistent. Therefore, in the process of giving lectures in physics, sections of mathematics that have not yet been studied have to either be offered to students to study on their own, or set forth directly in lectures in physics . The first option is actual for elite universities only, while the another is fraught with loss of generality in such disciplines as, for example, quantum logic. The development of new elective courses in physics (for example, in the framework of the magistracy) may require new supplementary courses in mathematics. It is noted that often due to the lack of required mathematics teachers and the reduction of study hours in physics and mathematics, it is not so easy to ensure the learning process. In our opinion,the following mathematical courses in signal processing theory, data compression, latticeanalysis, would be helpful such as: 1) wavelet analysis initiated by S. Mallat, (U.S.A.) and Y. Meyer (France) [3; 4]; 2) the theory of summation of divergent series [1]; 3) theory of fractal [2]. (The subject of the article was discussed at the round table of 15th International Conference «Physics in the system of modern education» (PSME-19) (3-6 June 2019, St. Petersburg)).

Keywords: quantum logic,wavelet analysis, summation of divergent series, fractal theory.

References

  1. Novikov I. Ya., Protasov V. Yu., Skopina M. A. Teoriya vspleskov (The wavelet theory), Moscow: Fizsmatlit, 2006, 616 p.
  2. Odyniec W. P. Ob istorii nekotorykh matematicheskikh metodov, ispol’zuyemykh pri prinyatii upravlencheskikh resheniy: uchebnoye posobiye (On the history of some mathematical methods used in the makingof managerial decisions), Syktyvkar: Pitirim Sorokin University Press, 2015, 108 p.
  3. Cook R. G. Beskonechnyye matritsy i prostranstva posledovatel’nostey (Infinite matrices and sequence spaces), London: MacMillan and Co.,1950, 360 p.
  4. Mandelbrot B. Fraktal’naya geometriya prirody (Fractals: form, chance and dimension), San Francisco: W.H. Freeman and Co., 1977, 365 p.

For citation: Odyniec W. P. About the problems of mathematical training of physists, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2019, 1 (30), pp. 113-115.

Bulletin 2 (31) 2019

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Issue 2 (31) 2019

I. Beznosov A. O., Ustyugov V. A. Development of the software for nanocomposite films granulometric analysis

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The article discusses the mathematical foundations of the image clustering procedure, which allows splitting the original image into sections, selected according to the principle of similarity of their elements. The agglomerative hierarchical clustering method is described. A software package was developed for clustering AFM images of nanogranular films, and the results of various parts of the algorithm are presented.

Keywords: atomic force microscopy, nanogranulated film, clustering.

References

  1. machinelearning.ru Klasterizatsiya ― [Web-page]. ― URL: machinelearning.ru/wiki/index.php?title=Klasterizatsiya (date of the application: 09.01.2019).
  2. aiportal.ru ― Mera rasstoyaniya [Web-page]. URL:http://www.aiportal.ru/articles/autoclassification/measure-distance.html (date of the application: 17.05.2019).
  3. scipy.org ― SciPy [Web-page]. ― URL: https://www.scipy.org/ (date of the application: 25.05.2019).
  4. scikit-learn.org ― sklearn.cluster.AgglomerativeClustering [Web-page]. ― URL: https://scikit-learn.org/stable/modules/generated/sklearn.cluster.AgglomerativeClustering.html#sklearn.cluster.Agglomerative Clustering.fit (date of the application: 11.01.2019).

For citation: Beznosov A. O., Ustyugov V. A. Development of the software for nanocomposite fims granulometric analysis, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2019, 2 (31), pp. 3 ― 17.

II. Maslyaev D. A. About the semiring of the Laurent skew polynomials and the expansion of Jordan

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The article shows that the study of semirings of Laurent skew polynomials is reduced to the case when endomorphism is an automorphism. Namely, let φ be the injective endomorphism of the semiring S. Then we construct the extension Sφof the semiring S and the auto morphism φ¯ of the semiring S, which is a continuation of the original endomorphism of φ. It is shown that semirings of Laurent skew polynomials S[x–1, x, φ] and Sφ[x–1, x, φ¯] are isomorphic.

Keywords: semiring of Laurent skew polynomials, extension of Jordan.

References

  1. Jordan D. A. Bijective extensions of injective ring endomorphisms, J. London Math. Soc., 1982, 25:3, pp. 435-448.
  2. Vestomov E. M., Lubyagina E. N., Chermny V. V. Elementy teorii polukolets (Elements of the theory of semirings), Kirov: Raduga ― press, Kirov, 2012, 228 p.
  3. Golan J. S. Semirings and their applications, Kluwer Academic Publishers, Dordrecht; Boston; London, 1999, 380 p.

For citation: Maslyaev D. A. About the semiring of the Laurent skew polynomials and the expansion of Jordan, Bulletin of SyktyvkarUniversity. Series 1: Mathematics. Mechanics. Informatics, 2019, 2 (31), pp. 18-25.

III. Gorev A. V., Ustyugov V. A. Development of the speech recognition systems for home automation

Text

The article describes the mathematical foundations necessary for the speech recognition systems development. An embodiment of a speech recognition algorithm based on a comparison of the mel-frequency cepstral coecients of audio signal samples is described. The implementation of thesoftware speech activity detector is presented.

Keywords: speech recognition, mel-frequency coecients, kepstrum.

References

  1. Lindsei P., Norman D. Pererabotka informatsii u cheloveka (Humans information processing), Mir, 1974, 546 p.
  2. Huang X., Acero A. Spoken Language Processing: A Guide to Theory Algorithm, and System Development, Prentice Hall, 2001, 965 p.
  3. Lyons R. G. Understanding Digital Signal Processing, Addison Wesley Pub. Co, 2006, 656 p.
  4. Bracewell R. N. The Fourier Transform and its Applications, McGraw Hill, 2000, 620 p.
  5. Ganchev T., Fakotakis N. Comparative evaluation of various MFCC implementations on the speaker verification task, 10th International Conference on Speech and Computer, Patras, Greece, 2005.
  6. Moattar M. H., Homayounpour M. M. A ecient real-time voice activity detection algorithm, Laboratory for Intelligent Sound and Speech Processing (LISSP), Computer Engineering and Information Technology Dept., Amirkabir University of Technology, Tehran, Iran, 24.10.2009.
  7. Nandhini S., Shenbagavalli A. Voiced/Unvoiced Detection using Short Term Processing, International Journal of Computer Applications, 0975 ― 8887, 2014.
  8. Bachu R., Kopparthi S., Adapa B., Barkana B. Voiced/Unvoiced Decision for Speech Signals Based on Zero-Crossing Rate and Energy, AdvancedTechniques in Computing Sciences and Software Engineering, 2010, pp. 279-282.

For citation: Gorev A. V., Ustyugov V. A. Development of the speech recognition systems for home automation, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2019, 2 (31), pp. 26 ― 41.

IV. Khozyainov S. A. Identication of the relative cost of technically complex devices: An evaluation of graphics cards

Text

The article describes a method for determining the relative cost of technically complex devices using normalization of parameter values and additive criterion for evaluating the eciency of computers.

Keywords: complex devices, graphics cards, additive criterion, efficiency of computers, tender.

References

  1. Sobranie zakonodatel’stva Rossiiskoi Federatsii (Collected Legislation of the Russian Federation), 2011, No 46, Article 6539 (In Russian).
  2. Korporativnye zakupki ― 2016: praktika primeneniya Federal’nogo zakona № 223-FZ: sbornik dokladov (Corporate procurement ― 2016: practice of application of the Federal law No 223-FL. The collection of reports), Moscow, Book on Demand Publ., 2016, 232 p. (In Russian).
  3. Orlov S. A., Tsilker B. Ya. Organizatsiya EVM i sistem : uchebnik dlya vuzov (Organization of computers and systems: textbook for high schools), St. Petersburg, Piter Publ., 2011, 688 p. (In Russian).
  4. Orlov S., Vishnyakov A. Pattern-oriented architecture design of software for logistics and transport applications, Transport and Telecommunication, 2014, Vol. 15, No 1, pp. 27-41.
  5. Orlov S., Vishnyakov A. Pattern-oriented decisions for logistics and transport software, Transport and Telecommunication, 2010, Vol. 11, No 4, pp. 46-58.

For citation: Khozyainov S. A. Identification of the relative cost of technically complex devices: An evaluation of graphics cards, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2019, 2 (31), pp. 42-57.

V. Odyniec W. P. About Four Phsicist who participated in the USSR Ftomic Project

Text

The article deals with the life and work of Alexander Leypunsky (1903-1972), Ovsei Leypunsky (1904-1990), Dora Leypunsky (1912-1977) and Konstantin Petrzak (1907-1998). That what unites them is not only their participation in the USSR Atomic project, but also the fact that they all were born in the territory of the polish Kingdom of the Russian Empire (now part of the Republic of Poland).

Keywords: A. I. Leypunsky, O. I. Leypunsky, D. I. Leypunsky, K. A. Petrzhak, fast neutron reactor, diamond synthesis, radiation levels, neutron-activatting analysis, spontaneous fission of uranium.

References

  1. Gorobec B. S. Sekretnye fiziki iz Atomnogo proekta SSSR (Secret physicists from the Atomic project of the USSR), Sem’ya Lejpunskih, M.: Izd-vo Librokom, 2008, 512 p.
  2. Yaroslavskoe vosstanie. Iyul’ 1918 (Russia. The Ecyclopaedia), Red.-sost. V.ZH. Cvetkov i dr., Moskva: Posev, 1998, 112 p.
  3. Khramov Yu. A. Fiziki: Biograficheskij spravochnik, The Physicists. The biographies handbook, Pod red. A.I. Ahiezera, izd. 2., dop. i isp., M.: Nauka, 1983, 400 p.
  4. Odyniec W. P. O fizikah, priekhavshih v SSSR v dovoennoe vremya (On Physicists who came to the USSR in pre-war period), Vestnik Syktyvkarskogo universiteta, Ser. 1, Vyp. 1 (30), 2019, pp. 77-92.
  5. Frenkel V. Ya. Georgij Gamov: liniya zhizni 1904-1933 (George Gamov: The line of life 1904-1933), UFN, 1994, T. 164, vyp. 8, pp. 847-865.
  6. Biografii, Nacional’naya Akademiya Nauk SSHA (Biographers. National Academy of Sciences USA). URL: http://www.nap.edu/readingroom/books/biomems/frossini.html Frederick Dominic Rossini. (data obrashcheniya: 11.09.2019).
  7. Leypunsky O. I. Ob iskusstvennyh almazah (Upon synthetic diamond), Uspekhi Himii, T. VIII, vyp. 10, pp. 1519-1534.
  8. Rossiya. Enciklopedicheskij slovar’ (Russia. The Ecyclopaedia), pod red. K.K. Arsen’eva i F.F. Petrushevskogo, reprintnoe izdanie F. A. Brokgauz i I. E. Efron, 1898, L.: Lenizdat, 1991, 922 p.
  9. Petrzhak K. A., Flerov G. N. Spontannoe delenie urana (Spontaneous Fission of Uranium), ZHETF, 1940, T. 10, vyp. 9-10,pp. 1013-1017.

For citation: Odyniec W. P. About Four Phsicist who participated in the USSR Ftomic Project, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2019, 2 (31), pp. 58-78.

VI. Popov V. A. Tasks for researcher in the studying course of mathematical analysis: preliminary-continuity

Text

The characteristic of a set of research problems developed by the author on the subject of sections of mathematical analysis of the function of one variable formulated with the help of the concept of preliminary-continuity of the function at the point by him is given.

Keywords: research problem,the preliminary-continuity of the function at the point on the left (right).

References

  1. Yarkov V. G. Sushchnost’ i funktsii issledovatel’skikh zadach v obuchenii matematike studentov pedvuza (Essence and functions of research problems in teaching mathematics to students the University), Modern problems of science and education, 2013, No 6, URL: http://science-education.ru/ru/article/view?id=11061 (date accessed: 30.10.2018).
  2. Gelbaum B., Olmsted J. Kontrprimery v analize (Counterexamples in analysis), Moscow: Mir, 1967, 251 p.
  3. Shibinsky V. M. Primery i kontrprimery v kurse matematicheskogo analiza: uchebnoye posobiye (Examples and counterexamples in the course of mathematical analysis: textbook), Moscow: Higher school, 2007, 544 p.
  4. Boss In. Lektsii po matematike (Lectures on mathematics), T. 12, Counterexamples and paradoxes: a Textbook, Moscow: Librokom, 2009, 216 p
  5. Popov V. A. Issledovatel’skiye zadachi v kurse matematicheskogo analiza: prednepreryvnost’ (Research problems in the course of mathematical analysis: pre-continuity), Mathematical modeling and information technologies: national (all-Russian) scientific conference (6 – 8 December 2018 , G. Syktyvkar): collection of materials, Rev. edited by A. V. Yermolenko. Syktyvkar: Publishing house of SSU. Pitirima Sorokina, 2018, pp. 71-73.
  6. Popov V. A. Soglasovannyye funktsii (Coordinated functions), Bulletin of the Komi state pedagogical Institute, Vol. 2. Syktyvkar: KSPI publishing house, 2005, pp. 110-114.
  7. Popov V. A. Prednepreryvnost’. Proizvodnyye. P-analitichnost’ (pre-Continuity. Derivative. P-analyticity: a monograph), Syktyvkar: Komi pedagogical Institute, 2011, 228 p.
  8. Popov V. A. Integriruyemost’ po Rimanu i kontaktnost’ funktsii (Riemann Integrability and function contact), Teaching mathematics in schools and universities: problems of content, technology and methods: materials of the all-Russian scientific and practical conference,Glazov: Glazovsky state pedagogical University.in-t, 2009, pp. 22-26.

For citation: Popov V. A. Tasks for researcher in the studying course of mathematical analysis: preliminary-continuity, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2019, 2 (31), pp. 79-90.

VII. Popov V. A., Kaneva E. A. «Long» arithmetic in studies of statistics of the first digits of powers of two, Fibonacci numbers and primes

Text

The paper deals with educational and research problems of statistical regularities of the first digits of natural powers of two, Fibonacci numbers and Prime numbers in the programming environment PascalABC.NET. At the same time, elements of the theory of «long» arithmetic are used, which allow to significantly expand the volume of sets of the studied arraysof natural numbers and can be useful in the classroom for the study of programming languages by students.

Keywords: Benford’s law, powers of two, Fibonacci numbers, prime numbers, PascalABC.NET programming environment, «long» arithmetic.

References

  1. Okulov S. M. «Dlinnaya» arifmetika («Long» arithmetic), Informatics, M.: The first of September, 4, 2000, pp. 19-23.
  2. Okulov S. M. Algoritmy komp’yuternoy arifmetiki (Algorithms of computer arithmetic), S. M. Okulov, A. V. Lyalin, O. A. Pestov, E. V. Razova, 2nd ed. (El.), Electronic Text Data (1 pdf file: 288 p.), M.: BINOM. Knowledge Laboratory, 2015.
  3. Koptenok E. V., Kuzin A. V., Shumilin T. B., Sokolov M. D. Razrabotka sposoba predstavleniya dlinnykh chisel v pamyati komp’yutera (Development of a presentation method long numbers in computer memory), Young scientist, 2017, No 46, pp. 26-30. The same URL https://moluch.ru/archive/180/46418/ (accessed September 14, 2018).
  4. Dlinnaya arifmetika ot Microsoft (Long arithmetic from Microsoft), URL: https: // habrahabr.ru/post/207754 (accessed: 03.07.2016).
  5. Popov V. A., Kaneva E. A. Issledovatel’skiye zadaniya na zanyatiyakh po ovladeniyu komp’yuternymi tekhnologiyami (Research tasks in the lessons on mastering computer technologies), Mathematical modeling and information technology: a collection of articles of the International Scientific Conference, November 10-11, 2017, city Syktyvkar / otv. ed. A. V. Ermolenko, Syktyvkar: SSU named after Pitirim Sorokin, 2017, pp.109-113.
  6. Weil G. O ravnomernom raspredelenii chisel po modulyu odin (On the uniform distribution of numbers modulo one), Selected Works.Maths. Theoretical physics. Series « Classics of Science », M.: Nauka, 1984, pp. 58-93.
  7. Postnikov A. G., Parshin A. N. Kommentarii k stat’ye Veylya G. «O ravnomernom raspredelenii chisel po modulyu odin» (Comments on Weil G. «On the uniform distribution of numbers modulo one»), Weil G. Selected Works. Maths. Theoretical physics. Series «Classics of Science», M.: Nauka, 1984, pp. 451-455.
  8. Arnold V. I. «Zhestkiye» i «myagkiye» matematicheskiye modeli («Hard» and «soft» mathematical models), Ed. 2nd, stereotype, M.: MCCNMO, 2008, 32 p.
  9. Kuvakina L. V., Dolgopolova A. F. (Zakon Benforda: Sushchnost’ i primeneniye) Benford’s Law: Essence and Application, Modern high technology, 6, 2013, pp. 74-76. [Electronic resource] URL: https://www.top-technologies.ru/ru/article/view?id=31987 (date of access: 07.21.2017).
  10. Akulich I. Vsego lish’ stepeni dvoyki (Only powers of two), Quantum, 2, 2012, pp. 38-42.
  11. Mario L. φ ― chislo Boga. Zolotoye secheniye ― formula mirozdaniya (φ is the number of God. Golden section ― formula of the universe), trans. A. Brodotskaya, M.: Publishing group «AST», 2015, 432 p, URL:https://e-libra.ru/read/377938-chislo-boga-zolotoe-sechenie-formula-mirozdaniya.html(accessed March 7, 2016).
  12. Don Z. Pervyye 50 millionov prostykh chisel (The first 50 million primes), UMN, 39: 6 (240), 1984, pp. 175-190.
  13. Ribenboym P. Rekordy prostykh chisel (novaya glava v knige rekordov Ginnesa) (Records of primes (a new chapter in the GuinnessBook of Records)), UMN, 42: 5 (257), 1987, pp. 119-176.
  14. Poundstone W. Kamen’ lomayet nozhnitsy. Kak perekhitrit’ kogo ugodno: prakticheskoye rukovodstvo (The stone breaks the scissors. How to outwit anyone: a practical guide), trans. from English Yu. Goldberg, M.: ABC Business, ABC-Atticus, 2015, 352 p.

For citation: Popov V. A., Kaneva E. A. «Long» arithmetic in studies of statistics of the first digits of powers of two, Fibonacci numbers and primes, Bulletin of Syktyvkar University. Series 1: Mathematics.Mechanics. Informatics, 2019, 2 (31), pp. 91-107.

VIII. Popov N. I. Scientific and methodological seminar of the department of physical, mathematical and information education

Text

The article reveals modern activities of the scientific and methodological seminar at the Department of Physical, Mathematical and Information Education of the Pitirim Sorokin Syktyvkar State University.

Keywords: scientific and methodological activities of the seminar, participants of the scientific and methodological seminar.

References

  1. Popov N. I. Fundamentalizatsiya universitetskogo matematicheskogo obrazovaniya: monografiya (Fundamentalization of university mathematics education: monograph), Yoshkar-Ola: Mari State University Publishing House, 2012, 136 p.
  2. Popov N. I., Nikiforova E .N. Metodicheskiye podkhody pri eksperimental’nom obuchenii matematike studentov vuza (Methodical approaches in experimental teaching of mathematics to university students), Integration of Education, 2018, V. 22, ― 1, pp. 193-206.DOI: 10.15507 / 1991-9468.090.022.201801.193-206.
  3. Pevny A. B., Yurkina M. N. Metod kasatel’nykh pri nakhozhdenii maksimuma (Tangent method for finding the maximum) Mathematics in School, 2019, ― 4, pp. 32-34.
  4. Popov V. A. Kafedra matematiki Komi pedinstituta: istoriya stanovleniya i razvitiya (Department of Mathematics, Komi Pedagogical Institute: History of Formation and Development), Syktyvkar: Komi Pedagogical Institute, 2012, 216 p.
  5. Popov V. A. Ivan Semenovich Brovikov (k 100-letiyu so dnya rozhdeniya) (Ivan Semenovich Brovikov (on the 100th anniversary of his birth)), Mathematical education, 2016, ― 3 (79), pp. 93-97.
  6. Popov N. I., Kalimova A. V. Vyyavleniye spetsial’nykh sposobnostey budushchikh uchiteley matematiki, fiziki i informatiki (Identification of special abilities of future teachers of mathematics, physics and computer science), News of Saratov University. New series. Acmeology of education. Developmental psychology, 2019, V. 8, Issue 1 (29), pp. 12-18. DOI: https://doi.org/10.18500/2304-9790-2019-8-1-12-18.
  7. Yakovleva E. V., Popov N. I. Realizatsiya kognitivno-vizual’nogo podkhoda pri obuchenii matematike studentov vuza (Implementation of the cognitive-visual approach in teaching mathematics to university students), Informatization of continuing education ― 2018 = Informatization of Continuing Education ― 2018 (ICE-2018): proceedings of the International Scientific Conference, Moscow, October 14-17, 2018, V. 2 , Moscow: RUDN, 2018, pp. 240-243.
  8. Popov N. I., Shasheva N. S. The use of didactic units in the organization of computer testing, Informatization of continuing education ― 2018 = Informatization of Continuing Education ― 2018 (ICE-2018): proceedings of the International Scientific Conference, Moscow, October 14-17, 2018, V. 1, Moscow: RUDN, 2018, pp. 109-112.
  9. Popov N. I., Shustova E. N. Ob effektivnosti ispol’zovaniya metodicheskikh podkhodov pri izuchenii elementarnykh funktsiy budushchimi uchitelyami matematiki (On the effectiveness of the use of methodological approaches in the study of elementary functions by future teachers of mathematics), Bulletin of Omsk State Pedagogical University, Humanities research, 2018, ― 1 (18), pp. 139-144.

For citation: Popov N. I. Scientific and methodological seminar of the department of physical, mathematical and information education, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2019, 2 (31), pp. 108-116.

Bulletin 3 (32) 2019

by

Issue 3 (32) 2019

I. Yermolenko A. V. On the series of conferences «Mathematical modeling and information technology»

Text

The article is devoted to a series of conferences on mathematical modeling and information technology at the Syktyvkar University. The significance of the conference for the development of science and the involvement of young people in scientific research is substantiated.

Keywords: scientific conference, Syktyvkar, mathematical modeling, information technology.

References

  1. Matematicheskoye modelirovaniye i informatsionnyye tekhnologii : materialy Mezhdunarodnoy nauchnoy konferentsii (Mathematical modeling and information technology: materials of the International Scientific Conference), November 10-11, 2017, Syktyvkar / Ed. A. V. Yermolenko, Syktyvkar: Publishing House of SSU named after Pitirim Sorokin, 2017, 162 p.
  2. Yermolenko A. V. Nauchnaya rabota s Yevgeniyem Il’ichem (Scientific    work with YevgenyIlyich), Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, № 3 (24), pp. 4–10.
  3. Mikhailovskii E. I.Shkola mekhaniki akademika Novozhilova (The Novozhilov School of Mechanics). Syktyvkar: Publishing House of the Syktyvkar University, 2005, 172 p.
  4. Chernykh K. F., Mikhailovskii E. I., Nikitenkov V. L. Ob odnoy vetvi nauchnoy shkoly Novozhilova (Novozhilov – Chernykh –Mikhaylovskiy – Nikitenkov) (About one branch of the scientific school of Novozhilov (Novozhilov — Chernykh – Mikhailovsky – Nikitenkov)). Syktyvkar: Publishing House of the Syktyvkar University, 2002, 47 p.
  5. Matematicheskoye modelirovaniye i informatsionnyye tekhnologii: Natsional’naya (Vserossiyskaya) nauchnayakonferentsiya (Mathematical modeling and information technology: materials of the International Scientific Conference), December 6-8, 2018, Syktyvkar / Ed. A. V. Yermolenko, Syktyvkar: Publishing House of SSU named after Pitirim Sorokin, 2018, 161 p.
  6. Matematicheskoye modelirovaniye i informatsionnyye tekhnologii: Natsional’naya (Vserossiyskaya) nauchnaya konferentsiya (National (AllRussian) Scientific Conference), November 7-9, 2019, Syktyvkar: a collection of materials in [Electronic resource]: a textual scientific electronic publication on a CD / rev. ed. A.V. Yermolenko, Syktyvkar: Publishing house of SSU im.Pitirim Sorokin, 2019.1 opt. compact disk (CD-ROM).

For citation:Yermolenko A. V. On the series of conferences «Mathematical modeling and information technology», Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2019, 3 (32), pp. 3–12.

II. Golchevskiy Yu. V., Yermolenko A. V., Kotelina N. O., Osipov D. A. On the series of conferences «Mathematical modeling and information technology»

Text

About WorldSkills Championship at Syktyvkar University The article describes the experience of the Komi Republic V Open Regional Championship «Young Professionals» (WorldSkills Russia) at the Syktyvkar University.

Keywords: WorldSkills, championship.

For citation:Golchevskiy Yu. V., Yermolenko A. V., Kotelina N. O., Osipov D. A. About WorldSkills Championship at Syktyvkar University, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2019, 3 (32), pp. 13–19.

III. Belyaeva N. A., Nadutkina A. V. Nonisothermal flow of a viscous fluid

Text

A mathematical model of the nonisothermal pressure flow of a viscous fluid in a round pipe is considered. The numerical analysis of the dimensionless model is based on the application of the sweep method. Graphical results of numerical experiments are presented.

Keywords: nonisothermal pressure flow, variable viscosity, numerical analysis, sweep method.

References

  1. Belyaeva N. A.Matematicheskoye modelirovaniye: uchebnoye posobiye (Mathematical modeling: a training manual), Syktyvkar: Publishing House of the Syktyvkar State University, 2014, 116 p.
  2. Belyaeva N. A.Osnovy gidrodinamiki v modelyakh: uchebnoye posobiye (Fundamentals of hydrodynamics in models: a training manual), Syktyvkar: Publishing House of the Syktyvkar State University, 2011, 147 p.
  3. KhudyaevS. I. Porogovyye yavleniya v nelineynykh uravneniyakh (Threshold phenomena in nonlinear equations), M.: Fizmatlit, 2003, 272 p.

For citation:Belyaeva N. A., Nadutkina A. V. Non-isothermal flow of a viscous fluid, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2019, 3 (32), pp. 20–30.

IV. ChernovV. G. Decision making in conditions of uncertainty with fuzzy, linguistic assessments of the situation

Text

The solution of the decision-making problem is considered under conditions of uncertainty, when the elements of the payment matrix are presented in the form of fuzzy, linguistic statements. A method is proposed for finding the best solution based on a linear order relation on a set of fuzzy integral estimates of alternatives constructed from linguistic estimates.

Keywords:uncertainty, fuzzy set, membership function, fuzzy linguistic estimate, linear order relation.

References

  1. Ventzel E. S.Issledovaniyeoperatsiy. Zadachi, printsipy, metodologiya (Operations research. Tasks, principles, methodology), M.: Drofa, 2004, 208 p.
  2. Seagal A. V.Teoretiko-igrovaya model’ prinyatiya investitsionnykh resheniy (Game-theoretic model of investment decision making), Scientific notes of the Taurida National University named after V.I. Vernadsky, a series of «Economics and Management», v. 24 (63), No. 1, 2011, pp. 193–205.
  3. Vovk S. P.Igradvukhlits s nechetkimistrategiyami i predpochteniyami (A game of two persons with fuzzy strategies and preferences), Almanac of modern science and education, No. 7 (85), pp. 47–49.
  4. Seraya O. V., Katkova T. N.Zadachateoriiigr s nechetkoy platezhnoymatritsey (The task of the theory of games with a fuzzy payment matrix), Mathematical Machines and Systems, 2012, No. 3, pp. 29–36.
  5. Zaichenko Y. P. Igrovyye modeli prinyatiya resheniy v usloviyakh neopredelennosti (Game models of decision making in conditions of uncertainty), Proceedings of the V international school-seminar «Theory of decision-making», Uzhgorod, UzhNU, 2010, 274 p.
  6. Bector C. R., Suresh Chandra. Nechetkoye matematicheskoye programmirovaniye i nechetkiyematrichnyyeigry (Mathematical Programming and Fuzzy Matrix Games), Springer, 2010, 236 p.
  7. Piegat A. Nechetkoye modelirovaniye i upravleniye (Fuzzy modeling and control), M.: BINOM. Laboratoriyaznaniy, 2013, 798 p.
  8. Melikhov A. N., Bernshtein L. S., Korovin S. Y.Situacionnye sovetuyushchiesistemy s nechetkojlogikoj (Situational advisory systems with fuzzy logic), M.: Science, The main edition of the physical and mathematical literature, 1990, 272 p.
  9. Chernov V. G., Andreev I. A., Gradusov D. A., Tretyakov D. V. Resheniyebizneszadach s pomoshch’yunechetkoyalgebry (The solution of business problems by means of fuzzy algebra), M.: TorahCenter, 1998, 87 p.
  10. Chernov V. G. Sravneniye nechetkikh chisel na osnove postroyeniya lineynykh otnosheniy poryadka (Comparison of fuzzy numbers based on the construction of a linear relationship order), Dynamics of complex systems, XXI century2018, No. 2, pp. 81–87.
  11. Chernov V. G.Entropiynyykriteriyprinyatiyaresheniy v usloviyakh polnoyneopredelennosti (Entropy criterion for decision making under conditions of complete uncertainty), Information Management Systems, 6 (7), 2014, pp. 51–56.

For citation: Chernov V. G. Decision making in conditions of uncertainty with fuzzy, linguistic assessments of the situation, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2019, 3 (32),pp. 31–45.

V. Garbuzov P. A., Gashin R. A. Design, development and implementation of complex automated car fleet management system

Text

The process of design, development and implementation of complex automated car fleet management system is described. Some problems encountered by the developers and ways to solve them were discussed.

Keywords: complex automated system, car fleet management, MVC architecture, MySQL, PHP.

References

  1. 1C: Predpriyatiye 8. Upravleniye Avtotransportom (1C: Enterprise 8. Car Fleet Management), URL: https://rarus.ru/1c-transport/1c8-avtotransport-standart/ (date of the application: 11.11.2019).
  2. Upravleniye avtotransportom | Kompaniya SIKE (Car Fleet Management | SIKE company), URL: http://autopark.sike.ru/ Bureau of special projects «Bornika» (date of the application: 11.11.2019).
  3. Programma «Avtobaza» – effektivnoye i ekonomichnoye resheniye dlya avtopredpriyatiy (The «Automobile depot» – an effective and economical solution for automobile enterprises), URL: http://www.bornica.ru/autobase/ (date of the application: 11.11.2019).
  4. Upravleniye transportom (TMS) i kur’yerskoy dostavkoy | AllianceSoft (Transport Management (TMS) and courier delivery | AllianceSoft), URL: https://asoft.by/resheniya/upravlenie-transportom-tms-ikurerskoy- dostavkoy (date of the application: 11.11.2019).
  5. Seydametov G. S., Ibraimov R. I. Analiticheskiy obzor shablona MVC (Analytical review of the MVC template), Informatsionnokomp’yuternyyetekhnologii v ekonomike, obrazovanii i sotsial’noysfere, 2018, No. 3 (21), pp. 45–51.
  6. Belykh E. A., Golchevskiy Yu. V. Podkhod k proyektirovaniyu yazyka podstanovok dlya generatsii elektronnykh dokumentov, soderzhashchikh slozhnyye tablitsy (An approach to designing a substitution language for generating electronic documents containing complex tables), VestnikUdmurtskogouniversiteta. Matematika.Mekhanika. Komp’yuternyyenauki, 2019, vol. 29, issue 3, pp. 422–437. DOI: 10.20537 / vm190311.

For citation: Garbuzov P. A., Gashin R. A. Design, development and implementation of complex automated car fleet management system, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2019, 3 (32), pp. 46–61.

VI. Nosov L. S., Pipunyrov E. Y.  Stream encryption based on FPGA

Text

It is proposed to use a soft-processor, which described in Verilog language, and FPGA to create a universal stream cipher, which could be programmed and quickly adapted at the hardware level.

Keywords: information security, FPGA, stream cipher.

References

  1. P. Pal Chaudhuri. Computer organisation and design, Delhi: PHI Learning, 2014, 897 p.
  2. David M. Harris and Sarah L. Harris. Digital Design and Computer Architecture, Boston: Morgan Kaufman, 2007, 570 p.
  3. GOST R 34.12-2015 Informatsionnayatekhnologiya. Kriptograficheskayazashchitainformatsii. Blochnyyeshifry (Information technology. Cryptographic information security. Block ciphers), M.: Standartinform, 2015, 25 p.
  4. IEEE 1364-2001 IEEE Standard Verilog Hardware Description Language. USA: The Institute of Electrical and Electronics Engineers, 2001, 778 p.
  5. Pong P. Chu. FPGA prototyping by Verilog examples Xilinx Spartan-3 Version. New Jersey:John Wiley & Sons, 2008, 488 p.
  6. Spartan-3A/3AN FPGA Starter Kit Board User Guidei. v. 1.1.XILINX, 2008, 140 p.
  7. SamodelovА. Kriptografiya v otdel’nom bloke: kriptograficheskiy soprotsessor semeystva STM32F4xx. Ofitsial’nyysaytkompanii «Kompel» (Cryptography in a separate block: cryptographic coprocessorSTM32F4xx family. The official website of the company «Kompel»),URL: http: //www.compel.ru/lib/ne/2012/6/4-kriptografiya-votdelnom-bloke-kriptograficheskiy-so-protsessor-semeystva-stm32f4xx.(date of the application: 03.12.2016).

For citation: Nosov L. S., Pipunyrov E. Y. Stream encryption based onFPGA, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2019, 3 (32), pp. 62–76.

VII. Dorofeev S. N., Nazemnova N. V. Methodological features of teaching high school students to recognize geometric images

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The article deals with the problem of teaching students to recognize geometric images. It is noted that this quality in the process of learning geometry has a personality-oriented character, the fact that learning to recognize geometric images will be most effective if you use the activity approach is substantiated.Keywords:teaching mathematics, recognition of geometric images, activity approach, vector-coordinate method, teaching students the discovery of «new» knowledge.

References

  1. 1. Ananyev B. G. Psikhologiyachuvstvennogopoznaniya (Psychologyof sensory cognition), M, 1960, 488 p.
  2. Ananyev B. G. Novoye v uchenii o vospriyatiiprostranstva (New in the doctrine of perception of space), Questions of psychology, 1960, No 1, pp. 18–29.
  3. Borodai Yu. M. Voobrazheniye i teoriyapoznaniya (Imagination and theory of knowledge), M, 1966, 192 p.
  4. Dorofeev S. N. Trudnosti metodiki obucheniya resheniyu zadach vektornym metodom i putiikhpreodoleniya (Difficulties of teaching methods to solve problems by vector method and ways to overcome them), Materials of interregional scientific and practical conference, Penza, 1997, pp. 389–390.
  5. Nazemnova N. V. Mnogokomponentnoye uprazhneniye kak sredstvo formirovaniya u uchashchikhsya deystviyaporaspoznavaniyuobraza (Multicomponent exercise as a means of forming students ’ actions on image recognition), University education: sat. nauch. works submitted to the international exhibition. science.-method.Conf. Penza: Privolzhsky house of knowledge, MKUO, 2004, pp. 326–329. 

For citation: Dorofeev S. N., Nazemnova N. V. Methodological features of teaching high school students to recognize geometric images, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2019, 3 (32), pp. 77–88.

VIII. Mansurova E. R., Nizamova E. R. Generalization in analysis as a means of improving the quality of mathematical preparation of students

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The article considers the role of generalization in analysis in improving the level of mathematical training of secondary school students on the example of the topic «Primitive and integral». Tasks on the topic are presented from textbooks on algebra and the principles of analysis currently used in the school course in mathematics, as well as from didactic materials for specialized classes and materials of the exam.Keywords: generalization, analysis, school, profile, integral, antiderivative, derivative, function, USE.

References

  1. Davydov V. V. Vidyobobshcheniya v obuchenii (Types of generalization in learning), M.: Pedagogical Society of Russia, 2000, pp. 157–173.
  2. Kolyagin Yu. M. Metodika prepodavaniya matematiki v sredney shkole. Obshchaya metodika (Methods of teaching mathematics in high school), General technique. Cheboksary: Publishing house of Chuvash. Univ., 2009, pp. 86–95.
  3. Sawyer W. W. Prelyudiya k matematike (Prelude to mathematics), M.: Education, 1972, pp. 37–47.
  4. Prozorovskaya S. D., Filipova T. I., Kropacheva N. Yu. Formirovaniye osnovnykh ponyatiy matematicheskogo analiza na osnove teoreticheskogoobobshcheniya (Formation of the basic concepts of mathematical analysis based on theoretical generalization), Siberian Pedagogical Journal, 2012, № 8, pp. 88–92.
  5. Pratusevich M. Ya. Algebra i nachala matematicheskogo analiza. 11 klass (Algebra and the beginning of mathematical analysis, Grade 11), M.: Education, 2010, 463 p.
  6. Nathanson I. P. Teoriya funktsiy veshchestvennoy peremennoy (The theory of functions of a real variable), St. Petersburg: Doe, 2018, 560 p.
  7. Merzlyak A. G. Algebra. 11 klass (Algebra. Grade 11), Kharkov: Gymnasium, 2011, 431 p.
  8. Muravin G. K. Algebra i nachala matematicheskogo analiza. 11 kl (Algebra and the beginning of mathematical analysis. 11 cl), M.: Bustard, 2013,253 p.
  9. Ryzhik V. I. Didakticheskiye materialy po algebre i matematicheskomu analizu dlya 10-11 klassov (Didactic materials on algebra and mathematical analysis for grades 10-11), M.: Education, 1997, 144 p.
  10. Mordkovich A. G. Algebra i nachala analiza. 10 kl (Algebra and the beginning of analysis. 10 cl), M.: Mnemozina, 2009, 443 p.
  11. Mordkovich A. G. Algebra i nachala analiza. 10-11 kl (Algebra and the beginning of analysis. 10-11 cl), Ch. 2, M.: Mnemozina, 2003, 315 p.
  12. Nikolsky S. M. Algebra i nachala matematicheskogo analiza. 11 klass (Algebra and the beginning of mathematical analysis, Grade 11), M.: Education, 2009, 446 p.
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For citation: Mansurova E. R., Nizamova E. R. Generalization in analysis as a means of improving the quality of mathematical preparation of students, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2019, 3 (32), pp. 89–100.

IX. Kotelina N. O., Matwiichuck B. R. Image clustering by k-means

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The paper deals with the problem of data clustering by the k-means method on the example of a raster image. The solution of the problem will be a program that implements the k-means method and as a result of the work, produces images divided into k clusters. The quality of clustering is estimated.Keywords: k-means method, clustering, cluster.

References

  1. Kotov A., Krasilnikov N. Klasterizatsiyadannykh (Data clustering), M., 2006, 16 p.
  2. Chubukova I. A. Data Mining, M.: Binom, 2008, 326 p.
  3. Obzor algoritmov klasterizatsii dannykh (Overview of data clustering algorithms), URL: tt https://habr.com/en/post/101338/ (date of theapplication: 12.02.2019).
  4. Tyurin A. G., Zuev I. O. Klasternyyanaliz, metody i algoritmyklasterizatsii (Cluster analysis, methods and algorithms of clustering), Vestnik MGTU MIREA, No 12, M.: Publishing house of MSTU, 2014,12 p.
  5. Ian Eric Solem Programmirovaniye komp’yuternogo zreniya na yazyke Python (Programming computer vision in Python), M.: DMK
  6. Press, 2016, 312 p.

For citation: Kotelina N. O., Matwiichuck B. R. Image clustering by kmeans, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics.Informatics, 2019, 3 (32), pp. 101–112.