Issue 1 (26) 2018

I. Makarov P. A., Shcheglov V. I. On the application of the operators formalism to the solution of the electrodynamics problems for bigyrotropic media

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The operator formalism is developed to consider electromagnetic wave processes in stationary, homogeneous, bihyrotropic media. Wave equations are obtained in the general case, and also for waves propagating in paralleland perpendicular to the gyrotropy axis. The solutions of the wave equation and the dispersion relations for the gyroelectric and gyromagnetic waves are analytically obtained. The general method of the solution for waves propagating parallel to the gyrotropy axis is showed.

Keywords: electrodynamics, Maxwell’s equations, bihyrotropic medium, propagation of electromagnetic waves.

References

1. Shavrov V. G., Shcheglov V. I. Magnitostaticheskiye i elektromagnitnyye volny v slozhnykh strukturakh (Magnetostatic and electromagnetic waves incomplex structures), M.: FIZMATLIT, 2017, 360 p.
2. Veselago V. G. Elektrodinamika veshchestv s odnov remennootritsatelnymi znacheniyami ε i µ (The electrodynamics of substances with simultaneously negative values of ε µ), Uspekhi Fizicheskikh Nauk, v. 92, № 3, 1967, pp. 517–526.
3. Vinogradov A. P. Elektrodinamika kompozitnykh materialov (Electrodynamics of composite materials), M.: URSS, 2001, 207 p.
4. Shcheglov V. I. Raschetdinamicheskoy pronitsayemosti sredy, soderzhashchey magnitnuyu i elektricheskuyukom ponenty (The dynamic permittivity calculation of media having magnetic and electric components), Journal of radio electronics, URL: http://jre.cplire.ru/ win/contents.html: № 7. 2001. URL: http://jre.cplire.ru/win/aug01/ 4/text.html (date of the application: 29.03.2018).
5. Eritsyan O. S. Opticheskiye zadach ielektrodinamiki girotropnykhsred(Optical problems in the electrodynamics of gyrotropic media), Uspekhi Fizicheskikh Nauk, v. 138, № 4, 1982, pp. 645–674.
6. Barta O., et al. Magneto-optics in bi-gyrotropic garnet waveguide // Opto-electronics review. Vol. 9. № 3. 2001. Pp. 320–325.
7. Bukhanko A. F., Sukstanskii A. L. Optics of a ferromagnetic superlattice with noncollinear orientation of equilibrium magnetization vectors in layers // Journal of Magnetism and Magnetic Materials. Vol. 250. 2002. Pp. 338–352.
8. Dadoenkova N. N., et al. Complex waveguide based on a magnetooptic layer and a dielectric photonic crystal // Superlattices and Microstructures, vol. 100, 2016, pp. 45–56.
9. Eliseeva S. V., Sannikov D. G., Sementsov D. I. Anisotropy, gyrotropy and dispersion properties of the periodical thin-layer structure of magnetic-semiconductor // Journal of Magnetism and Magnetic Materials. Vol. 322. 2010. Pp. 3807–3816.
10. Rychly J. et al. Magnonic crystals — Prospective structures for shaping spin waves in nanoscale // Low Temperature Physics. Vol. 41. № 10. 2015. Pp. 745–759
11. Gurevich A. G., Melkov G. A. Magnitnyye kolebaniyai volny (Magneticoscillations and waves), M.: Nauka, 1994, 464 p.
12. Landay L. D., Lifhitz E. M. Teoreticheskaya fizika: T. VIII.Elektrodinamika sploshnykh sred (Theoretical physics: Vol. VIII.Electrodynamics of Continuous Media), M.: FIZMATLIT, 2005, 656 p.
13. Greer J. B., Bertozzi A. L., Sapiro G. Fourth order partial differential equations on general geometries // Journal of Computational Physics. Vol. 216. № 1. 2006. Pp. 216–246.
14. Elsgolz L. E. Differentsialnyy euravneniya i variatsionnoye ischisleniye(Differential equations and the calculus of variations), M.: URSS,2002, 320p.
15. Kuznetcov E. A., Shapiro D. A. Metody matematicheskoy fiziki:kurslektsiy (Methods of mathematical physics: Course of lectures),P.I, Novosibirsk State University, 2011, 131 p.

For citation: Makarov P. A., Shcheglov V. I. On the application ofthe operators formalism to the solution of the electrodynamics problems for bigyrotropic media, Bulletin of Syktyvkar University, Series 1: Mathematics.Mechanics. Informatics, 2018, 1 (26), pp. 3–16.

II. Petrakov P. A., Cheredov V. N. The contribution of «hot» phonons to the internal energy of solids

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A mixed thermodynamic model of a solid is constructed, including the interpretation of the energy of acoustic branches of oscillations on the basis of the Debye model, and the branches of optical vibrations and librational rotations based on the Einstein model. In the framework of the development of the theory of thermal oscillations (phonons) of the lattice of solids, the contribution of «hot» phonons, as harmonic oscillators with modes of thermal oscillations with values of indices higher than the predetermined value, to the internal energy of solids is studied. Dependences of the contribution to the internal energy of a molecule caused by acoustic and optical thermal vibrations with modes above the limiting one are studied. The curves of the fraction of the internal energy of solids with a lattice excited by «hot» phonons are obtained, depending on the level of the limiting mode of the oscillator for ice crystals.

Keywords: thermal vibrations, phonons, internal energy, crystal lattice, solid.

References

1. Cheredov V. N., Kuratova L. A. Dinamika setki mezhmolekulyarnykh svyazey i fazovyye perekhody v kondensirovannykh sredakh (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. Rodnikova M. N., Chumaevskiy N. A. O prostranstvennoysetkevodorodnykhsvyazey v zhidkostyakh i rastvorakh (On the spatial grid of hydrogen bonds in liquids and solutions), Journal of Structural Chemistry, 2006, v. 47, pp. 154–166.
3. Malenkov G. G. Struktura i dinamika zhidkoyvody (Structure and dynamics of liquid water), Journal of Structural Chemistry, 2006, v. 47, pp. 5–35.
4. Bushuev Yu. G. Svoystvasetki vodorodnykh svyazey vody (Properties of a network of hydrogen bonds of water), Proceedings of the Russian Academy of Sciences, Chemical series, 1997, № 5, pp. 928–931.
5. Landau L. D., Lifshitz E. M. Statisticheskaya fizika (Statistical physics), Part 1, Moscow: Fizmatlit, 2010, 616 p.
6. Wang Kuo-Ting, Brewster M.Q. An Intermolecular Vibration Model for Lattice Ice //International Journal of Thermodynamics. 2010. V. 13. № 2. Pp. 51–57.
7. Eisenberg D., Kautsman V. Struktura i svoystvavody (Structure and properties of water), Moscow: Direct-Media, 2012, 284 p.
8. Enochovich A. S. Spravochnik po fizike i tekhnike (Reference book on physics and techniques), Moscow: Prosveshenie, 1989, 224 p.
9. Zatsepina G. N. Fizicheskiye svoystva i strukturavody (Physical properties and structure of water), Moscow: Moscow State University, 1998, 184 p.
10. Bertie J. E., Whalley E. Optical Spectra of Orientationally Disordered Crystals. II. Infrared Spectrum of Ice Ih and Ice Ic from 360 to 50 cm⁻¹ //The Journal of Chemical Physics. 1967. V. 46, № 4. Pp. 1271–1281.
11. Wang Kuo-Ting, Brewster M. Q. An Intermolecular Vibration Model for Lattice Ice //International Journal of Thermodynamics. 2010. V. 13. № 2. Pp. 51–57.

For citation: Petrakov P. A., Cheredov V. N. The contribution of «hot» phononsto the internal energy of solids, Bulletin of Syktyvkar University. Series 1:Mathematics. Mechanics. Informatics, 2018, 1 (26), pp. 17–28.

III. Tarasov V. N. On the elastic line of the rod compressible by longitudinal force located between two rigid walls

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The problem of determining the elastic line compressible by longitudinal force of the rod, located between two rigid walls is considered. The dependence of the elastic line on boundary conditions is studied.

Keywords: elastic line, critical force, boundary conditions, stability, Euler equation.

References

1. Mihailovskii E. I., Tarasov V. N., Holmogorov D. V. Sakriticheskoepovedeniestersniaprisestkimiogranisheniiaminaprogib (Supercritical thebehavior of longitudinally compressed rod with hard constraints at adeflection of), PMM, 1985, t. 49, vip. 1, pp. 156–160.
2. Nikolai E. L. Trudi po mexanike (Works on mechanics), M.: Isdatelstvotexniko-teoretiteskoiliteraturi, 1955, 376 p.
3. Tarasov V. N. Ob ustoichivostiuprugihsistempriodnostoronnihogranicheniyahnaperemescheniya (On stability of elastic systems with one-sided restrictions on the movement), Trudy institute matematiki i mehaniki, Rossiskaya akademiya nauk, Uralskoeotdelenie, Tom 11, No. 1, 2005, pp. 177–188.
4. Feodosiev 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: Tarasov V. N. On the elastic line of the rod compressible by longitudinal force located between two rigid walls, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2018, 1 (26), pp. 29–46.

IV. Rychkov S. L. Some integral principal values

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A method of evaluation of principal values of integrals  is considered. The plasma dispersion functions of plasmas having quasipower electron energy distribution can be calculated using integrals of such a type. The suggested method differs from previously known ones and results in formulas more convenient for usage. The integrals are represented in terms of Gauss hypergeometric functions for z > 0 and ν > 5/2. Simple asymptotic approximations for values z ≫ 1 are obtained. Graph plots of the results are given.

Keywords: integral principal value, hypergeometric functions, nonequilibrium plasma, quasipower dispersion function, kappa–dispersion.

References

1. Pierrard V., Lazar M. Kappa distributions: theory and applications in space plasmas // Solar Physics. 2010. V. 267. Pp. 153–174.
2. Podesta J. J. Plasma dispersion function for the kappa distribution, Report NASA/CR-2004-212770. https://ntrs.nasa.gov/archive/nasa /casi/ntrs.gov/20040161173.pdf (date of the application: 26.03.2018).
3. Bateman H., Erdelyi A. Vysshiye transtsendentnyye funktsii. Gipergeometricheskayafunktsiya. Funktsii Lezhandra (Higher transcendental functions. Hypergeometric function. Legendre functions), M, Science, 1965, 296 p.

For citation: Rychkov S. L. Some integral principal values, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2018, 1 (26), pp. 47–57.

V. Kotelina N. O. Two-dimensional ternary search and its application in competitive programming

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In this paper the application of ternary search in one problem of competitive programming is considered.

Keywords: two-dimensional ternary search, competitive programming.

References

1. Distantcionnaya podgotovka po informatike (Distance training in computer science). URL: http://informatics.mccme.ru (date of usage: 29.10.2017).
2. MAXimal. Sayt M. Ivanova (MAXimal. Site of M. Ivanov) URL: http://e-maxx.ru (date of usage: 12.09.2017).
3. Knuth D. E. Iskusstvo programmirovaniya (The Art of Computer Programming. Vol. 3. Sorting and Searching) M. :Williams (2007). 832 p.
4. Konspektystudentovkafedrykomp’yuternykhtekhnologiyUniversiteta ITMO (Conspects of students of ITMO) URL: http://neerc.ifmo.ru/wiki (date of usage: 12.09.2017).
5. Mathews J. H., Fink K. D. Chislennyyemetody. Ispol’zovaniye MATLAB (Numerical Methods: Using MATLAB) 3rd Edition. Spb.: Williams, 2001, 716 p.
6. Olimpiady po informatike (Olympiads on informatics) URL: https://neerc.ifmo.ru/school. (date of usage: 12.09.2017).

For citation: Kotelina N. O. Two-dimensional ternary search and its application in competitive programming, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2018, 1 (26), pp. 58–63.

VI. Melnikov V. A. Application of genetic algorithms for finding the optimal nesting sequence

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Keywords: genetic algorithms, optimization, genom, individuals.

References

1. MacLeod C. An Introduction to Practical Neural Networks and Genetic Algorithms For Engineers and Scientists, p. 85.
2. He Y., Liu H. Algorithm for 2D irregular-shaped nesting problem based on the NFP algorithm and lowest gravity-center principle, Journal of Zhejiang University, 2006, № 7, pp. 571–574.
3. Panchenko T. V. Geneticheskie algotritmy (Genetic algorithms), pod red. U. U. Tarasevicha, Astrahan: Izdatelskiydom «Astrahanskiyuniversitet», 2007, p. 16.
4. Kudryavcev L. D. Matematicheskiyanaliz (Mathematical analysis), 2-e izd, M.: Vyshayashkola, 1973, v. 1, 687 p.
5. Coordinate Systems, Transformations and Units [Electronic resource] / W3C. 6 мая 2017. URL: https://www.w3.org/TR/SVG/coords.html (date of the application: 25.12.2017).
6. Melnikov V. A. Metodypredstavleniyafigurobshchegovidadlyazadachidvumernogoraskroya (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.

For citation: Melnikov V. A. Application of genetic algorithms for finding the optimal nesting sequence, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2018, 1 (26), pp. 64–72.

VII. Kotelina N. O., Popova N. K. The preparation of the online round of the championship on programming on Yandex.Contest platform

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The paper discusses the online round of the open programming championship of Pitirim Sorokin Syktyvkar State University conducted as part of a project «Development of network interaction in the field of mathematics, physics, computer science and robotics between educational organizations of the Finno-Ugric republics of the Russian Federation».Keywords: online round, Yandex.Contest, competitive programming.

References

1. Arkhiv materialov olimpiad / Olimpiady po informatike (Archive of materials of Olympiads / Computer science Olympiads) URL: https://neerc.ifmo.ru/school/archive/index.html (date of usage: 19.02.2018).
2. Ofitsial’nyysaytVserossiyskoykomandnoyolimpiadyshkol’nikovpoprogrammirovaniyu / Olimpiady po informatike (Official site of the all-russian team Olympiad in programming / Computer science Olympiads) URL: https://neerc.ifmo.ru/school/russia-team/ index.html (date of usage: 19.02.2018).
3. Pravila sorevnovaniy / Sorevnovaniya po programmirovaniyu 2.0 (Competition rules / Programming competitions 2.0) URL: http:// codeforces.com/blog/entry/4088?locale=ru (date of usage: 19.02.2018).
4. Sorevnovaniya po programmirovaniyu 2.0 (Programming competitions 2.0) URL: http://codeforces.com (date of usage: 19.02.2018).
5. Tablitsa rezul’tatov internet-turaotkrytogochempionataSyktyvkarskogogosudarstvennogouniversitetaim. Pitirima Sorokina po programmirovaniyu / Yandeks.Kontest (Table of results of the online roundof the open programming championship of Pitirim Sorokin Syktyvkar State University / Yandex. Contest) URL: https://contest.yandex. ru/contest/7113/standings/ (date of usage: 19.02.2018).
6. Timus Online Judge / Arkhivzadach s proveryayushchey sistemoy (Timus Online Judge / The problems’ archive with the testing system) URL: http://acm.timus.ru/ (date of usage: 19.02.2018).

For citation: Kotelina N. O., Popova N. K. The preparation of the online round of the championship on programming on Yandex.Contest platform, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2018, 1 (26), pp. 73–79. 

VIII. Odyniec W. P. The 1929–1936 Immigration to the USSR: Profiles of Mathematicians. Part 1.

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Keywords: boundary-value problems, singular integral equations, Bessel functions, the Oryol central prison, Fritz Noether, M¨untz theorem, Herman (Chaim) M¨untz, kernel function, Stefan Bergman.

References

1. Arkhiv Sankt-Peterburgskogo gosudarstvennogo universiteta (St. Petersburg State University Archive), File 7240.14 № 191 (Order № 11 from 14/1–1932 . On assigning of thesis advisor).
2. Arkhiv Sankt-Peterburgskogo gosudarstvennogo universiteta (St. Petersburg State University Archive), File 7240.14 № 191 (Order № 352а from 20/X–1932).
3. Bergmann S. Uberdie Kernfunktioneines Bereichs und ihrVerhalten am Rande. Teil 1 // J. furreine und angewandte Math. Bd. 169. Heft 1. 1932. S. 1–42.
4. Bergmann S. Uberdie Kernfunktioneines Bereichs und ihrVerhalten am Rande. Teil 2 // J. furreine und angewandte Math. Bd. 172. Heft 2. 1934. S. 89–128.
5. Bergmann S. Zur Theorie von pseudokon formen Abbildungen, Matem. Sbornik, t. 1 (43), No. 1, 1936, pp. 79–96.
6. Bergman S. O funktsiyakh, udovletvoryayushchikh lineynym differentsial’nym uravneniyam v chastnykh proizvodnykh (Upon the Functions Satisfying Certain Linear Partial Differential Equations), DokladyAkad. ofSci, USSR, vol. 15, No. 5, 1937, pp. 227–230.
7. Bergmann S. Zur Theorie der linearen Integral — und Funktional gleichun genimcomplexen Gebiet, Izvestiya NIIMM TGU, Tomsk, vol. 1, issue 3, 1937, pp. 242–257.
8. Bergmann S. The Kernel Function and Conformal Mapping.- Cambridge (Massachusetts): Amer. Math. Society, 1950. 161 p.
9. Bergman S., Schiffer M. M. Kernel functions and elliptic differential equations in mathematical physics. New York: Academic Press, 1953. 432 p.
10. Bergmann S. Integral operators in the theory of linear partial differential equations. Berlin-New York: Springer, 1961, 2thed., 1969.
11. Brewer J. W., Smith M. K. (eds.) Emmy Noether: a tribute to her life and work. New York: Marcel Dekker, Inc., 1981. 237 p.
12. Del О. А. Nemetskiye emigranty v SSSR v 1930-ye gody. Avtore feratdi ssertatsiinasoiskani yeuchenoy stepenikandi datnauk (German Emigrants in the USSR during the 1930’s. Abstracts of Dissertation for the Degree of a Candidate of Sciences (History)), Moscow: the Russian Academy of State Service., 1995, 22 p.
13. Juravlev S. V., Tyazhelnikova V. S. Inostrannaya koloniya v SovetskoyRossii v 1920-1930-ye gody (Postanovka problemy i metody issledovaniya) (The Foreign Colony in Soviet Russiaduring the 1920’s– 1930’s), Otechestvennayaistoriya, 1994, No. 1, pp. 179–189.
14. Lyapunov А. М. Obshchaya zadacha obustoychivosti dvizheniya (General Problem of the Stability of Motion), Ed. H. M. M¨untz, M.- L.: ONTI, 1935, 386 p.
15. Matematika v SSSR zasorok let. 1917-1957 (Mathematics in the USSR for 1917–1957), vol. 2, Bibliography, M.: State Phiz.-Math. Lit. Publ., 1959, 819 p.
16. Muntz Ch. Zum Randwertproblem der partiellen Differential gleichung der Minimal flachen // J. fur Reineund Angew. Math. 139. 1911. S. 52–79.
17. Muntz Ch. Uber den Approximationssatz von Weierstrass / H. A. Schwarz–Festschrift. Berlin: 1914. S. 303–312.
18. Muntz Ch. Die Losung des Plateauschen Problems uberkonvexen Bereichen // Math. Ann., 94. No. 1–2. 1925. S. 53–96.
19. Gottfried Noether, 76: Educator in Statistics // New York Times. August 27, 1991. P. 22. (Obituary).
20. Noether Fr. O rekurrentnykh funktsiyakh Besselya i Ermita (Upon Recurrent Functions of Bessel and Hermite), Izvestiya NIIMM TGU, Tomsk: 1935, Vol. 1, issue 2, pp. 121–125.
21. Noether Fr. Asymptotische Darstellungen und Geometrische Optik, Izvestiya NIIMM TGU, Tomsk: 1937, t. 1, issue 3, p. 175–189.
22. NoetherFr. Zur Kinematik des starren Korpers in der Relativtheorie // Annalen der Physik. 336 (5). 1910. S. 914–944.
23. Noether Fr. Bemerkunguber die Losungszahlzueinan deradjungierten Randwertaufgaben beilinearen Differentialgleichungen // Sitzungsberichte der Heidelberger Akad. der Wissenschaft. Math. Nat. Klasse. 1920, I. Abhandlung. S. 37–52.
24. Noether Fr. Ubereine Klassesingularer Integralgleichungen // Math. Ann. Bd. 82. 1921. S. 42–63.
25. Odyniec W. P. Arnol’dVal’fish — zhizn’ voprekistereotipam (k 125-letiyu so dnyarozhdeniya) (Arnold Walfisz – a Life Defying Stereotypes (the 125th anniversary of his birth)), Mathematics in higher education, issue 14, Moskow – Nizhni Novgorod – St. Petersburg, 2016, pp. 105–112.
26. Ortiz E. L., Pinkus A. Herman Muntz: A Mathematician’s Odyssey //Mathem. Intellig. Berlin. 27. 2005. S. 22–30.
27. Segal, Sanford L. Mathematicians under the Nazis. Princeton: Princeton University Press, 2003. 536 p.
28. Siegmund-Schulze R. Mathematiker auf der Fluchtvor Hitler.- Wiesbaden: Vieweg Verlag, 1998. 324 s.
29. Trudy Vtorogo Vsesoyuznogo matematicheskogo s’yezda. Leningrad. 24-30 iyunya 1934 g. T. 1. Plenarnyye i obzornyye doklady (Proceedings of the Second All-Union Mathematical Congress, Leningrad, June 24- 30, 1934, T. 1, Plenary and overview reports), Moscow-Leningrad: Acad. Sci. USSR Press, 1935, 371 p.

For citation: Odyniec W. P. The 1929–1936 Immigration to the USSR: Profiles of Mathematicians. Part 1., Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 1 (26), pp. 80–96.

IX. Kalinin S. I., Leonteva N. V. (1/2; 1)-convex functions.Part 1.

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The article deals with the class of (1/2 ; 1)-convex functions. The authors give a geometric characterization of such functions, derive sufficient conditions for the membership of the function to the class under discussion in terms of derivatives.Keywords:(1/2 ; 1)-convex function, (1/2 ; 1) -concave function, 1/2 -parabolic a

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. andApplics. Vol. 2010. Article ID 507560, 11 pages, doi:10.1155/2010/507560.
3. 3. Kalinin S. I. (α; β)-vypuklyye funktsi i, ikh svoystva i nekotoryye primeneniya ((α; β)-convex functions, their properties and some applications), Ufa International Mathematical Conference. Collection of abstracts, otv. red. R. N. Garifullin, Ufa: RIC BashGU, 2016, pp. 75–76

For citation: Kalinin S. I., Leonteva N. V. (1/2; 1)-convex functions. Part 1., Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2018, 1 (26), pp. 97–104.

Issue 3 (28) 2018

I. Kotelina N. O., Popova N. K., Yurkina M. N. About open championship of SSU on programming

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The article is devoted to the jubilee, XV Open Syktyvkar State University Programming Championship. It tells about the experience of the event, as well as about the people who have made a significant contribution to the olympiad movement.

Keywords: sports programming, ACM, ICPC.

References

1. Kotelina N. O., Popova N. K. Podgotovka internet-turch empionatapo programmirovaniyuna Yandex. Contest (The preparation of the online round of the championship on programming on Yandex.Contest platform), Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2018, 1 (26), pp. 73–79.
2. Komiinform. https://komiinform.ru. Pervyygorodskoy otkrytyy chempionat poprogrammirovaniyu proshel v Syktyvkare v vykhodnyye (The first city open programming championship was held in Syktyvkar at the weekend). https://komiinform.ru/news/4351 (the date of circulation: 12.12.2018).
3. Kiryukhin V. M. Metodika provedeniya i podgotovki k uchastiyu v olimpiada po informatike. Vserossiyskaya olimpiada shkol’nikov (Methods of carrying out and preparing for participation in computer science competitions. All-Russian School Olympiad). M.: BINOM. Laboratory of Knowledge, 2011, 271 p.

For citation: Kotelina N. O., Popova N. K., Yurkina M. N. About open championship of SSU on programming, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 3 (28), pp. 3–18.

II. Makarov P. A. On the application of the vector graphics language Asymptote for illustrating educational, methodical and scientific works of physics and mathematics

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The possibility of using the Asymptote vector graphics language to illustrate the physics and mathematics educational and scientific works is explored. A few of images illustrating the solution of problems from various fields of physics and mathematics have been developed. It is shown that the Asymptote language has convenient high-level syntax and a fairly developed object-oriented architecture.

Keywords: vector graphics, Asymptote, high-level programming language.

References

1. Lamport L. LATEX: a document preparation system. 2 ed., AddisonWesley, 1994. 291 p.
2. Lvovski S. M. Nabor i verstka v sisteme LATEX (Typesetting in the LATEXsystem), 3rd ed, M.: MCNMO, 2003, 448 p.
3. Kotelnikov I. A., Chebotarev P. Z. LATEX 2_εpo-russki (LATEX 2ε in Russian), 3rd ed, Novosibirsk: Siberian chronograph, 2004, 496 p.
4. Znamenskaya O. V., Znamenski S. V., Leinartas D. E., Trutnev V. M. Matematicheskaya tipografiya: Kurslektsiy (Mathematical typography: The course of lectures), Krasnoyarsk: SFU, 2008, 421 p.
5. Knut D. E. Vse pro TEX (All about TEX), M.: Williams, 2003, 560 p.
6. Hammerlindl A., Bowman J., Prince T. Asymptote: the Vector Graphics Language, 2016. 189 p.
7. KryachkovYu. G. Yevklidova geometriya na yazyke vektornoygra fiki ASYMPTOTE (Euclidean geometry with a symptote), Volgograd: VGSPU, 2015, 88 p.
8. Goossens M., Rahtz S., Mittelbach F. The LATEX graphics companion: illustrating documents with TEX and PostScript. Addison Wesley, 1997. 299 p.
9. Goossens M., Rahtz S., Mittelbach F. Putevoditel’ popaketu LATEX i yegogra ficheskimrasshireniyam. Illyustrirovaniye dokumentov pripomoshchi TEX’a i PostScript’a (The LATEX graphics companion. Ilustrating documents with TEX and PostScript), M.: Binom, 2002, 621 p
10. KiryutenkoYu. A. TikZ&PGF. Sozdaniyegrafiki v LATEX 2εdokumentakh (TikZ& PGF. Creating graphics in LATEX 2ε-documents), Rostov-on-Don, 2014, 277 p.
11. Tantau T. The TikZand PGF Packages. Manual for version 2.10. Institutf¨ ur Theoretische Informatik Universit¨ atzuL¨ubeck, 2010. 880 p.
12. Taft E., Chernicoff S., Rose C. PostScript language reference manual. 3 ed. Adobe Systems Incorporated, 1999. 912 p.
13. Reid G. C. Thinking in PostScript. Addison-Wesley Publishing Company, 1990. 239 p.
14. PostScript language. Tutorial and cookbook. Addison-Wesley Publishing Company, 1985. 247 p.
15. Casselman B. Mathematical illustrations: a manual of geometry and PostScript. Cambridge University Press, 2004. 264 p.
16. Kryachkov Yu. G. Asimptotadlyan achinayushchikh. Sozdaniye risunkov na yazyke vektornoy grafiki Asymptote (Asymptote for beginners. Creating pictures in the vector graphics language Asymptote), Volgograd: VGSPU, 2015, 131 p.
17. Hobby J. D. METAPOST. Rukovodstvopol’zovatelya (METAPOST. User guide), 2008, 106 p. URL: http://mirrors.ibiblio.org/CTAN/info/ metapost/doc/russian/mpman-ru/mpman-ru.pdf (date of the application: 20.12.2018).
18. Baldin E. M. Sozdaniye illyustratsiy v METAPOST (Creating illustrations in METAPOST), Linux Format, № 6–10, 2006.
19. Knut D. E. Vse pro METAFONT (All about METAFONT), M.: Williams, 2003, 376 p.
20. Volchenko Yu. M. Nauchnaya grafikanayazyke Asymptote (Scientific graphics in the Asymptote language), 2018, 220 p. URL: http://www.math.volchenko.com/AsyMan.pdf (date of the application: 20.12.2018).
21. Guibe O., Ivaldi P. geometry.asy. Euclidean geometry with asymptote. 2011. 95 p.
22. Belyaev Yu. N. Vektornyy i tenzornyyanaliz (Vector and tensor analysis), Syktyvkar: Syktyvkar State University, 2010, 298 p.
23. Kabardin O. F. Tranzistornaya elektronika. Spetspraktikum (Transistor electronics. Special Practice), M.: «Education», 1972, 207 p.
24. Zherebtsov I. P. Osnovyelektroniki (Fundamentals of Electronics), 5th ed, L.: Energoatomizdat, 1989, 352 p.

For citation: Makarov P. A. On the application of the vector graphics language Asymptote for illustrating educational, methodical and scientific works of physics and mathematics, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 3 (28), pp. 19–37.

III. Ustyugov V. A. The queue on the microcontrollers

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The article substantiates the need to study the algorithms and data structures for developers of the software for embedded systems. The advantages obtained by the rational organization of the program code are considered. An embodiment of a simple data structure — a queue is described.

Keywords: microcontroller, embedded system, data structure, queue.

References

1. Polikarpova N. Avtomatnoye programmirovaniye (Automata programming), SPb: Piter, 2011, 176 p.
2. Morton J. Mikrokontrollery AVR. Vvodnykurs (AVR microcontrollers. Introductory course), M.: Dodeka, 2010, 271 p.
3. Shpak Yu. Programmirovaniye na yazyke C dlya AVR i PIC mikrokontrollerov (C programming for AVR and PIC microcontrollers), SPb:Korona-Vek, 2011, 546 p.

For citation: Ustyugov V. A. The queue on the microcontrollers, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 3 (28), pp. 38–46.

IV. Gromov N. A., Kostyakov I. V., Kuratov V. V.  Complex moment, Minkowski geometry and light propagation in metamaterials

Text

It is shown that the classical equations of motion of a two-dimensional particle on a Euclidean plane with an imaginary moment are equivalent to the equations of motion of a particle on a pseudo-Euclidean plane with a real moment. A similar equivalence is preserved in the quantum case for the Schr¨odinger equations on the Euclidean plane and the Minkowski plane. An ansatz for solving Maxwell’s equations is proposed, in which the propagation of electromagnetic waves in metamaterials with anisotropic dielectric constant of a different sign is described by the Schr¨odinger equation for a free particle on the Minkowski plane.

Keywords: Minkowski geometry, Schr¨odinger equation, metamaterials

References

1. Remnev M. A., Klimov V. V. Metapoverhnosti: novyj vzglyad na uravneniya Maksvella i novye metody upravleniya svetom (Metasurfaces: a new look at Maxwell’s equations and new methods of controlling light), UFN, 2018, t. 188, N 2, pp. 169–205
2. Smolyaninov I. I. Hyperbolic metamaterials, ArXiv:1510.07137 [physics. optics].
3. Katanaev M. O. Geometricheskie metody v matematicheskoj fizike (Geometric methods in mathematical physics), ArXiv:1311.0733[mathph].
4. Shabad A. E. Singulyarnyj centrkaknegravitacionnaya chernaya dyra (Singular center as a non-gravitational black hole), TMF, 2014, t. 181, N 3, pp. 603–613.
5. Perelomov A. M., Popov V. S. «Padenienacentr» v kvantovoj mekhanike («Fall on the center» in quantum mechanics), TMF, 1970, t. 4, N 1, pp. 48–65.
6. Gitman D. M., Tyutin I. V., Voronov B. L. Samosopryazhenny y erasshireniya v kvantovoymekhanike: obshchayateoriya i prilozheniya k uravneniyamShredingera i Diraka s singulyarny mipotentsialami (Self-Adjoint Extensions in Quantum Mechanics: General Theory and Applications to Schrodinger and Dirac Equations with Singular Potentials), Progress in Mathematical Physics, 2012, v. 62, Birkh¨auser, New York, 2012, 511 p. In: Progress in Mathematical Physics, vol. 62, Birkh¨auser: New York, 2012, 511 p.
7. Case K. M. Singular potentials, Phys. Rev., 1950, vol.80, pp. 797–806.
8. Neznamov V. P., Safronov I. I. Padeniechasticna centr. Gipoteza Landau-Lifshica i chislennyeraschety (Particles fall on the center. Landau-Lifshitz hypothesis and numerical calculations), Voprosy atomnoj nauki i tekhniki: teoreticheskaya i prikladnaya fizika, N 4, 2016, pp. 3–8.
9. Gromov N. A., Kuratov V. V. Kvantovaya chastica naploskosti Minkovskogo (The quantum part on the Minkowski plane), IzvestiyaKomi NC UrO RAN, vyp. 3(35), Syktyvkar, 2018, s. 5–7.

For citation: Gromov N. A., Kostyakov I. V., Kuratov V. V. Complex moment, Minkowski geometry and light propagation in metamaterials, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 3 (28), pp. 47–55.

V. Efimov D. B. The hafnian of Toeplitz matrices of special type, perfect matchings and Bessel polynomials

Text

In this paper, we present a simple and convenient analytic formula for exact computing of the hafnian of Toeplitz matrices of a special type. An interpretation of the obtained results in the language of perfect matchings and Bessel polynomials is given.

Keywords: hafnian, perfect matching, Bessel polynomial.

References

1. Caianiello E. R. On quantum field theory – I: Explicit solution of Dyson’s equation in electrodynamics without use of Feynman graphs // IL Nuovo Cimento. 1953. V. 10 (12). Pp. 1634–1652.
2. Bjorklunя A., Gupt B., Quesada N. A faster hafnian formula for complex matricesandits benchmarking on the Titansupercomputer // arXiv:1805.12498v2 [cs.DS] 25 Sep 2018.
3. Vyaly M. N. Pfaffiany, iliiskusstvorasstavlyat’ znaki (Pfaffians, or the art to set signs), Matematich eskoeprosv eshchenie, 2005, vyp. 9, pp. 129–142.
4. Schwarz M. Efficiently computing the permanent and Hafnian of some banded Toeplitz matrices // Linear Algebra and its Applications. 2009. V. 430. Pp. 1364–1374.
5. Efimov D.B. The hafnian and a commutative analogue of the Grassmann algebra // Electronic Journal of Linear Algebra. 2018. V. 34. Pp. 54–60.
6. Sloane N. J. A., editor The On-Line Encyclopedia of Integer Sequences, published electronically at https://oeis.org.
7. Krall H. L., Frink O. A new class of orthogonal polynomials: The Bessel polynomials // Transactions of the American Mathematical Society. 1949. V. 65. Pp. 100–115.
8. Chatterjea S. K. On the Bessel polynomials // Rendicontidel Seminario Matematicodella Universit`a di Padova. 1962. V. 32. Pp. 295–303

For citation: Efimov D. B. The hafnian of Toeplitz matrices of special type, perfect matchings and Bessel polynomials, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 3 (28), pp. 56–64.

VI. Kalnitsky V. S., Matveeva I. A. About the book, signed by Karl Weierstrass, from the library of St. Petersburg State University

Text

The article outlines several possible versions, as a geometry textbook of the German mathematician Paul von Zech, signed by Karl Weierstrass, could get into the library of St. Petersburg State University. This book, apparently from the personal library of Weierstrass. In this intriguing story several well-known scientists are directly involved, among them V.I. Schiff, SofyaKovalevskaya, and Magnus Mittag-Leffler.

Keywords: Karl Weierstrass, V.I. Schiff, SofyaKovalevskaya, Magnus Mittag-Leffler.

References

1. Gallica. http://gallica.bnf.fr (date of the application: 05.10.2018)
2. Poiskovo-istoricheskiy forum ( Poiskovo-istoricheskiy forum) http:// smolbattle.ru Smolenskiye dvoryane ShiffizBel’skogouyezda (Smolensk nobles Schiff from Belsky). http://smolbattle.ru/threads/Смоленскиедворяне-Шифф-из-Бельского-уезда.44170/ (date of the application: 05.10.2018).
3. Vachromeyeva O. B. Dukhovnoy eprostranstvo universiteta: Vysshiyezhenskiye (Bestuzhevskiye) kursy. 1878–1918 gg (Spiritual space of the university: Higher Women (Bestuzhev) Courses. 1878–1918), Invest. and Materials, Diada-SPb, St.P., 2003.
4. Depman I. Ya. S.-Peterburgskoye matematicheskoy eobshchestvo (S.-Petersburg Mathematical Society), Historical-mathemftical investigation, 13, 1960, pp. 11–106.
5. Protokoly S.-Peterburgskogom atematicheskogo obshchestva (S.-Petersburg Mathematical Society protocols), St.P., 1899.
6. Brockhaus F. A., Efron I. A. Enciclopedia, Ripol Classic, Moscow, 2013.
7. Biblioteka Bestuzhevskikh kursov: Istoricheskayakhronika v svidetel’stvakh i dokumentakh (Library of Bestuzhev Courses: Historical Chronicle in Testimonies and Documents), Ed. Vostrikov A. V., St.P.,StPSU Publ. Hause, 2009.
8. Government of Saint-Petersburg, Law N 88/1-rp 11.07.2005.
9. Galanova Z. S., Repnikova N. M. Vera Schiff — professor of mathematics on the Bestuzhev Courses Proc. XIII Internetional Kolmogorov readings, 782, Yaroslavl, 2015, pp. 258–263.
10. Kochina P. Ya. S. V. Kovalevskaya, Moscow, Nauka, 1981.
11. Ushakova V. G. Zhenshchiny v Sankt-Peterburgskom gosudarstvennom univercitete: istoriko-sotsiologicheskiya spekt (Women in SaintPetersburh state university: hystorical-sociological aspect), A woman in Russian society, 1, 1996, pp. 57–59.

For citation: Kalnitsky V. S., Matveeva I. A. About the book, signed by Karl Weierstrass, from the library of St. Petersburg State University, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 3 (28), pp. 65–75.

VII. Odyniec W. P. The Immigration to the USSR: Profiles of Mathematicians. Part II

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The life and work of three mathematician who emigrated from Germany to the USSR in the 1920s/1920’s by ideological motives. They are the only woman mathematician Stefanie Bauer (neo Szilard) (1898–1938), born Scilard in old town of Gyor; Celestin Burstin (1888–1938), native of Tarnopol (both the towns of the Austria–Hungarian Empire); and Jacob Grommer (1881–1933), born in Brest–Litovsk of the Russian Empire.Keywords: Schwarz differential invariant, double relation, Stefanie Bauer (Szil´ard), Riemann spaces (the problems of embedding and immersion), Pfaff equations, hypersurface bending, Celestin Burstin, transcendental functions, general relativity theory, classes of complex numbers, Jacob Grommer, Albert Einstein.

References

1. Bauer M. E. Reminiscences of an ordinary man. SPb: ASSPIN Peterhof, 2003, 87 p.
2. Bauer S. Upon the Schwarz differential invariant, Mat. sbornik, V. 41, No. 1, 1934, p. 104–106.
3. Bibliografiyaizdanii Akademiinauk Belorusskoi SSR. Knigi i stat’iza 1929-1939 gg. (Bibliography of publications of the Academy of Science of Belorussian SSR. Books and articles for 1929–1939. Minsk: Izd-vo Acad. Nauk BSSR, 1961. 134 p.).
4. Burstin C. Beitragezum Problem von Pfaff und zurTheorie der Pfaffschen Aggregate. I. Beitrag // Матем. сборник. Т. 37, № 1–2. 1930. C. 13–22.
5. Burstyn C. Mathematical Works, Minsk: Institute for Physics and Mathematics of the Belorussian Academy of Sciences, 1932, 76 p.
6. Burstyn C. A. Course of differential geometry, Mensk: State publishes of Belorussia. Scientific and Educations Sector, 1933, 338 p.
7. Burstyn C. Physical methods of mathematics, Minsk:Institute for Physics and Technics of the Belorussian Academy of Sciences, 1933, 34 p.
8. Grommer J. Ganzetranszendente Funktionenmitlauterreelen Nulstelen // J. fur reineundangew. Math., Bd. 144. 1914. S. 114–165.
9. Grommer J. Betragzum Energiesatz in der allgemeinen Relativit¨atstheorie // Sitzungberichte der Prussschen Akademie der Wissenschaft, Kl. 1919. S. 860–862.
10. Grommer J., Einstein A. A General Relativity Theory and the Principle of Motion, Sitzungberichte der Prus. Akademie der Wissenschaft, KI., 1927, p. 2–13. (Einstein A. Collection of Scientific Works., V. 2, Works on Relativity Theory ,pp. 198–210. Moscow: Nauka, 1966. 689 p.).
11. Grommer J. Elementary consideration of the formation of complex numbers and their interpretation, Notes of the Belorussian Academy of Sciences, No. 5, 1936, p. 59–63.
12. Elbert A., Garay G. M.  Differential equations, Hungary, the extended first haf of the 20th century. pp. 245-294 // in: A panorama of Hungarian Mathematics in Twentieth Century. I. (ed. J. Horvath) — Berlin–NewYork: Springer Science & Business Media, Janos Bolyai Math. Soc. 14. 2010. 639 p.
13. Joffe A. F. Vstrechi s fizikami. Moivospominaniya o zarubezhnykhfizikakh (Encounters with physicists. My recollection of foreign physicists). Leningrad: Nauka, 1983, 262 p.
14. Matematika v SSSR za 40 let 1917–1957 (Mathematics in the USSR duringthe Forty Years 1917–1957), V. 2, Bibliography, Moskow: Fizmatgiz, 1959, 819 p.
15. Luca F., Odyniec W. P. The characterization of Van KampenFlores complexes by means of system of Diophantine equations, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, V. 5, 2003, pp. 5–10.
16. Pervaya Mezhdunarodnaya Konferenciya po tensornoidifferecialnoi geometrii i eeprilozheniya. (The First International Conference on tensor differential geometry and its applications. (Moscow, 17/V – 23/V, 1934), Moscow: Moscow Pokrovsky State University, 1934. 7 p.
17. Trudy PervogoVsesoyuznogos’yezdamatematikov (Kharkov, 1930). (Proceedings of the 1st All-Union Congress of Mathematicians (Kharkov, 1930), Moscow-Leningrad: ONTI NKTPof the USSR, 1936. 376 p.)
18. Trudy Vtorogo Vsesoyuznogo Matematicheskogos’ yezda (Leningrad 24/VI–30/VI, 1934). ( Proceedings of the 2nd All-Union Mathematician Congress (Leningrad, 24–30 June 1934), V. 1, Moscow-Leningrad: Academy of ScienceoftheUSSR Press, 1935, 371 p.
19. Zusmanovich P. Mathematicians Going East. arXiv: 18.05. 00242

For citation: Odyniec W. P. The Immigration to the USSR: Profiles of Mathematicians. Part II, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 3 (28), pp. 76–90.  

Issue 2 (27) 2018

I. Belyaeva N. A. The velocity of a stationary pressure flow of a structured liquid

Text

The pressure flow of a structured liquid with variable viscosity is analyzed. An analytical formula for determining the steady-state flow velocity is obtained from the equation of motion.

Keywords: mathematical modeling, flow, liquid, structured, pressure, stationary, variable viscosity.

References

1. Belyaeva N. A. Neodnorodnoye techeniye strukturirovannoy zhidkosti (The inhomogeneous flow of a structured liquid), Mathematical modeling, 2006, vol. 18, No. 6, pp. 3–14.
2. Belyaeva N. A., Stolin A. M., Pugachov D. V., Stelmakh L. S. Neustoychivyye rezhimy deformirovaniya pri tverdofaznoy ekstruzii vyazkouprugikh strukturirovannykh sistem (Unstable modes of deformation during solid-phase extrusion of viscoelastic structured systems), DAN, 2008, vol. 420, No. 6, pp. 777–780.
3. Belyaeva N. A., Stolin A. M., Stelmakh L. S. Dynamic of Solid-State Extrusion of Viscoelastic Cross-Linked polymeric Materials, Theoretical Foundations of Chemical Engineering, 2008, vol. 42, No. 5, pp. 549–556.
4. Belyaeva N. A. Osnovy gidrodinamiki v modelyakh : uchebnoye posobiye (Fundamentals of hydrodynamics in models: a manual), Syktyvkar: Publishing house of Syktyvkar State University, 2011, 147 p.
5. Belyaeva N. A., Yakovleva A.F. Frontal’naya volna napornogo techeniya (Frontal wave of pressure flow), Bulletin of Syktyvkar University. Ser. 1: Mathematics. Mechanics. Informatics, 2017, 2 (23), 2017, pp. 4–12.

For citation: Belyaeva N. A. The velocity of a stationary pressure flow of a structured liquid, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 2 (27), pp. 3–9.

II. Gromov N. А., Kuratov V. V. Harmonic oscillator on Minkowski plane

Text

The problem of quantum harmonic oscillator on Minkowski plane is discussed. The corresponding Schr¨odinger equation for eigenstates is obtained with the help of Beltrami-Laplas operator of pseudoeuclidean plane. The infifinitely high potential barriers are placed on isotropic lines. The discrete energy eigenvalues of oscillator are obtained.

Keywords:Minkowski plane, Schr¨odinger equation, harmonic oscillator.

References

1. Gromov N. A., Kuratov V. V. Garmonicheskiy ostsillyator na ploskostyakh Keli-Kleyna s rimanovoy i vyrozhdennoy metrikami (A harmonic oscillator on the Cayley-Klein planes with Riemannian and degenerate metrics), Proceedings of Int. Seminar «Group theoretical methods for studying physical systems» Syktyvkar, 2018, (Bulletin of the Komi Scientifific Center of the Ural Branch of the Russian Academy of Sciences, Issue 33), pp. 21–36.
2. Gromov N. A., Kuratov V. V. Kvantovaya chastitsa na ploskosti Minkovskogo (Quantum particle on the Minkowski plane), Proceedings of the Komi Scientifific Center of the UrB RAS, 2018, Issue 3 (35), pp. 5–7.
3. Remnev M. A., Klimov V. A. Metapoverkhnosti: novyy vzglyad na uravneniya Maksvella i novyye metody upravleniya svetom (Metasurfaces: a new view of Maxwell’s equations and new methods of light control), Progress in physical sciences, 2018, vol. 188, No. 2, pp. 169–205.
4. Smolyaninov I. I. Hyperbolic metamaterials; arXiv: 1510.07137.
5. Green M. B., Schwartz J., Witten E. Teoriya superstrun (Theory of superstrings), Moscow: Mir, 1990.
6. Kaku M. Vvedeniye v teoriyu superstrun (Introduction to the theory of superstrings), Moscow: Mir, 1999, 624 p.
7. Bars I. Relativistic Harmonic Oscillator Revisited, Phys. Rev. D, v. 79, Iss. 4. 045009. 2009, arXiv: 0810.2075.
8. 8. Betemmen G., Erdei A. Vysshiye transtsendentnyye funktsii (Higher transcendental functions), M.: Mir, 1973, vol. 1.
9. Shabad A. E. Singulyarnyy tsentr kak negravitatsionnaya chernaya dyra (The singular center as a non-gravitational black hole), Theoretical and Mathematical Physics, 2014, vol. 181, No. 3, pp. 603–613.
10. Perelomov A. M., Popov V. S. «Padeniye na tsentr» v kvantovoy mekhanike («Falling to the center» in quantum mechanics), Theoretical and Mathematical Physics, 1970, vol. 4, No. 1, pp. 48–65.
11. Gitman D. M., Tyutin I. V., Voronov B. L. Self-Adjoint Extensions in Quantum Mechanics: General Theory and Applications to Schr¨odinger and Dirac Equations with Singular Potentials, Progress in Mathematical Physics, vol. 62, Birkh¨auser: New York, 2012, 511 p.

For citation:Gromov N. А., Kuratov V. V. Harmonic oscillator on Minkowski plane, Bulletin of Syktyvkar University. Series 1:Mathematics. Mechanics. Informatics, 2018, 2 (27), pp. 10–23.

III. Kazakov A. Yu. Exact solution of the heat equation under symmetry conditions

Text

The paper considers the application of operational calculus to solve two initial-boundary value problems with the equation T_t= a²∆T in areas with cylindrical and spherical symmetry. The solutions are obtained in the form of the traditional Fourier functional series problems for this class.

Keywords: Laplace transformation, heat conduction equation, residues.

References

1. Aramanovich I. G., Luntz G. L., Elsholz L. E. Funktsii kompleksnogo peremennogo. Operatsyonnoye ischislenie. Teoriya ustoychivosti (Functions of a complex va-riable. Operational calculus. Stability theory). M.: Nauka, 1968. Ed. 2nd, 416 p.
2. Belyaeva N. A. Matematicheskoe modelirovanie: uchebnoe posobie (Mathematical modeling: tutorial). Syktyvkar: Publishing house of Syktyvkar state University, 2014. 116 p.
3. Boyarchuk A. K., Golovach G. P. Spravochnoe posobie povysshey matematike. Tom 5. Difffferentsyalnye uravneniya v primerakh I zadachakh. (Handbook on higher mathematics. Volume 5. Difffferential equations in examples and problems). M.: URSS, 1999. 384 p.
4. Koshlyakov N. S. and others. Uravneniya v chastnykh proizvodnykh matemati-cheskoy fifiziki. Uchebnoe posobie dlya mech.-mat. fak. un-tov (Partial difffferential equations of mathematical physics. Tutorial for mechanics and mathematics faculties of universities). M.: Vysshaya shkola, 1970. 712 p.
5. Bogolyubov A. N., Kravtsov V. V. Zadachi po matematicheskoy fifizike: Ucheb. posobie (Tasks in mathematical physics: tutorial). M.: Publishing house of Mos-cow state University, 1998. 350 p.
6. Carslaw H. S., Jaeger J. S. Operatsionnyye metody v prikladnoy matematike (Operational methods in applied mathematics. M.: IL, 1948. 294 p.
7. Doetsch G. Rukovodstvo k prakticheskomu primeneniyu preobrazovaniya Laplasa i Z-preobrazovaniya (A guide to the practical application of Laplace transform and Z-transform). M.: Nauka, 1971. 288 p.

For citation:Kazakov A. Yu. Exact solution of the heat equation under symmetry conditions, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 2 (27), pp. 24–31.

IV. Kostyakov I. V., Kuratov V. V. Quantum computations and contractions of Lie algebras

Text

The connection between the nonunitary Kraus transformations of the qubit density matrix with contraction theory of the su(2) Lie algebra is pointed. The use of contraction constructions is demonstrated.

Keywords: contractions of Lie algebras, quantum channels, qubit.

References

1. Nielsen M. A., Chuang I. L. Kvantovyye vychisleniya i kvantovaya informatsiya (Quantum Computation and Quantum Information), Cambridge University Press, 2010, 676 p.
2. Preskill J. Kvantovaya informatsiya i kvantovyye vychisleniya (Lecture Notes for Physics 229:Quantum Information and Computation), Izhevsk: RKHD, 2008, 2011, t. 1–2, 464+312 p.
3. Ruskai M. B., Szarek S., Werner E. An Analysis of CompletelyPositive Trace-Preserving Maps on 2×2 Matrices, Lin. Alg. Appl., vol. 347, 2002, pp. 159–187. ArXiv:quant-ph/0101003.
4. Gromov N. A. Kontraktsii klassicheskih i kvantovyh grupp (Contractions of classical and quantum groups), M.: Fizmatlit, 2012, 318 p.
5. In¨on¨u E., Wigner E. P. On the Contraction of Groups and Their Representations, Proc. Nat. Acad. Sci., vol. 39, iss. 6, pp. 510–524, 1953.
6. Saletan E. J. Contraction of Lie groups, J. Math. Phys., vol. 2, iss. 1, 1961, pp. 1–21.

For citation:Kostyakov I. V., Kuratov V. V. Quantum computations and contractions of Lie algebras, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 2 (27), pp. 32–39.

V. Pimenov R. R. The geometry of perpendicularity: the axiomatic multidimensional space and de Morgan’s laws

 Text

We propose the short axiomatic for fifinite dimensional geometrical structure, using only perpendicularity relation. This structure appear projective space in which hold De Morgan’s laws. We show the connection work with the Veblen’s axiom and with partition four elements to pairs various modes. The research is connected with ortholattice, matroids, Galois connections and quantum logic.

Keywords: the foundation of geometry, perpendicularity, ortholattice,Galois connections, logic, projective space.

References

1. Cameron P. J. Projective and Polar Spaces, second edition, Sep 2000. http://www.maths.qmul.ac.uk/ pjc/pps/
2. Birkhoffff G. Teoriya reshetok (Lattice Theory), М.: Nauka, 1984, 565 p. Aigner M. Kombinatornaya teoriya (Combinatorial Theory), M .: Mir, 1982, 556 p.
3. Bachmann F. Postroenie geometrii na osnove ponyatiya simmetrii (Aufbau der Geometrie aus dem Spiegelungsbegriffff), М.: Nauka, 1969, 380 p.
4. Pimenov R. I. Yedinaya aksiomatika prostranstv s maksimal’noy gruppoy dvizheniy (Unifified axiomatics of spaces with the maximum group of motions), Litovsk. Mat. Sb., vol. 5, No. 3, 1965, pp. 457–486.
5. Maclaren M. D. Atomic orthocomlemented lattices, Pacifific Journal of Mathematics, vol. 14, June 1964, pp. 697–612 (site https://msp.org/pjm/1964/14-2/pjm-v14-n2-p18-p.pdf)
6. Norman D. Megill and Mladen Pavicˆ´i, Hilbert Lattice Equations, Ann. Henri Poincare 99 (9999), 1–24 1424-0637/99000-0, DOI 10.1007/ s00023-003-0000 ©2009 Birkhauser Verlag Basel/Switzerland (site https: //bib.irb.hr/datoteka/413891.megill-pavicic-a-henri-p-09r.pdf)
7. Odyniec W. P. Ob istorii nekotorykh matematicheskikh metodov, ispol’zuyemykh pri prinyatii upravlencheskikh resheniy (Upon the history of some mathematical methods, which use for the taking a steering decision), Syktywkar: SGU, 2015, 107 p.
8. Vasukov V. L. Kvantovaya logika (Quantum logic), M.: Per Se, 2005, 191 p.
9. Tabachnikov S. Skewers, Arnold Mathematical Journal, 2, 2016, pp. 171–193.
10. Pimenov R. R. Obobshcheniya teoremy Dezarga: geometriya perpendikulyarnogo (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.
11. Pimenov R. R. Traktovki teorem Pappa: perpendikulyarnost’ i involyutivnost’ (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.
12. Pimenov R. R. Geometriya perpendikulyarnogo: tupyye i ostryye ugly v izvestnykh teoremakh (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.

For citation:Pimenov R. R. The geometry of perpendicularity: the axiomatic multidimensional space and de Morgan’s laws, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics,2018, 2 (27), pp. 40–70.

VI. Odyniec W. P. About a Wien-born Mathematician Who Immigrated to the USSR for the Development of a «New Society»

Text

The life and work of Felix Frankl (1905–1961), a prominent mathematician from Wien, who immigrated to the USSR in 1929 for the development of a «new society» is presented.

Keywords: the border of oriented manifold, prime end, L. Pontryagin, Zhukovsky’s propeller, M. V. Keldysh, Frankl’s problem, Frankl-Laval nozzle, L. Euler, model of bora.

References

1. Gutman L. N., Frankl F. Termo-gidrodinamicheskaya model’ bory (Thermo-hydrodynamic Model of Bora), Doklady AN USSR, vol. 130, No. 3, 1960, pp. 533–536.
2. Kazakov A. In Commemoration of the Late Professor Lev N.Gutman, Ukrainskii gidrometeorologichnyi zhurnal, No. 4, 2009, pp. 11–12.
3. Keldysh M. V., Frankl F. Vneshnyaya zadacha Neymana dlya nelineynykh ellipticheskikh uravneniy v szhimayemom gaze (Neuman’s Exterior Problem for Nonlinear Elliptic Equation of Compressed Gas), Izvestiya AN USSR, VII Ser, 1934, No. 4, pp. 561–601.
4. Keldysh M. V., Frankl F. Strogoye obosnovaniye teorii vinta Zhukovskogo (Strict Foundating the Theory of Zhukovsky Propeller), Mat. Sbornik, 42, No. 2, 1935, pp. 241–273.
5. Matematika v SSSR za 40 let 1917–1957 (Mathematics in the USSR during the Forty Years 1917–1957), vl. 2, Biobibliography, Moscow: Fizmatgiz, 1959, 819 p.
6. Frankl F. Upon the theory of prime ends (Doctorate Thesis), Wien, University, 1927, 25 Bl, Verbund-ID-Nr.AC06513142.
7. Frankl F., Pontryagin L. A Knoth Theorem with the application to the dimension theory, Mathem. Annalen, v. 102, No.1, 1930, pp. 785–789.
8. Frankl F. Characterizing of (n-1)-dimension closed set of Rⁿ, Mathem. Annalen, vol. 103, No. 1, 1930, pp. 784–787.
9. Frankl F. Upon the theory of prime ends, Mat. Sbornik, 38, No. 3–4, 1931, pp. 66–69.
10. Frankl F. Upon the topology of the three-dimensional space, Monats-hefte f¨ur Mathem. und Physik, 38, 1931, p. 357–364.
11. Frankl F. O ploskoparallel’nykh vozdushnykh techeniyakh cherez kanaly pri okolozvuchnykh skorostyakh (Upon the plane-parallel air flow through the cannels by near sound speed), Mat. Sbornik, 40, No. 1, 1933, pp. 59–72.
12. Frankl F., Alekseeva R. Dve krayevyye zadachi iz teorii giperbolicheskikh uravneniy v chastnykh proizvodnykh s prilozheniyem k sverkhzvukovym gazovym techeniyam (Two boundary-value problem from the theory of hyperbolic partial differential equations with the application to the supersonic gas flow), Mat. Sbornik, 41, No. 3, 1934, pp. 483–502.
13. Frankl F. O zadache Koshi dlya lineynykh i nelineynykh uravneniy v chastnykh proizvodnykh vtorogo poryadka giperbolicheskogo tipa (Upon the Cauchy problem for the hyperbolic-type linear and nonlinearpartial differential equations of the second order), Mat. Sbornik, v. 2, 44, No. 5, 1937, pp. 793–814.
14. Frankl F. I., Khristianovich S. N., Alekseeva R. N. Osnovy gazovoy dinamiki (Foundation of Gas Dynamics), Issue 364, Moscow: CAGI, 1938, 111 p.
15. Frankl F. I., Karpovich E. A. Gazodinamika tonkikh tel (Gas dynamics of thin bodies), Moscow-Leningrad: GTTL, 1948, 175 p.
16. Frankl F. I., Il’ina A. A., Karpovich E. A. Kurs aerodinamiki v primenenii k artilleriyskim snaryadam (The course of air dynamics with application to artillery projectiles) (ed. by L.I. Sedov), Moscow: Oborongiz, 1952, 684 p.
17. Frankl F. I., Sukhomlinov G. A. Vvedeniye v mekhaniku deformiruyemykh tel (Introduction to the mechanics of deformed bodies), Frunze: 1954, 204 p.
18. Frankl F. I. O pryamoy zadache teorii sopla Lavalya (On the direct problem of the Laval nozzle), Uchenyezapiski Kabardino-Balkarskogo universiteta, Issue 3, 1959, pp. 35–61.
19. Frankl F. I. Izbrannyye trudy po gazovoy dinamike (Selected works of gas dynamics), Moscow: Nauka, 1973,711 p.
20. Frankl F. I. O sisteme uravneniy dvizheniya vzveshennykh potokov (On a system of equations of the motion of suspended flow), Issledovanie maksimalnogo stoka, volnovogo vozdeistviya i dwizheniya nanosov, Moscow: AN USSR, 1960, pp. 85–91.
21. Euler L. Integral’noye ischisleniye (Integral Calculus), vol. III (Transl. and comment. by F. Frankl), Moscow: Fizmatgiz, 1958, 447 p.

For citation:Odyniec W. P. About a Wien-born Mathematician Who Immigrated to the USSR for the Development of a «New Society», Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 2 (27), pp. 71–85.

VII. Yermolenko A. V., Melnikov V. A. Calculation of the contact interaction of a rectangular plate and a base by the Karman theory

Text

This article is about contact interaction of rectangular plate with base by Karman theory with usage of fifinite difffference method under the constant normal load. Wanted functions were discovered with method of generalized reactions developed in Syktyvkar state university. The obtained graphs arequalitatively consistent with the calculations of a cylindrically bent plate.

Keywords: plate, method of generalized reaction, contact problem, the Karman theory.

References

1. Mikhailovskii E. I., Toropov A. V. Matematicheskie modeli teorii uprugosti (Mathematical models of the theory of elasticity). Syktyvkar: Syltyvkar University, 1995. 251 p.
2. Yermolenko A.V. Chislennye metody v reshenii kontaktnyh zadach so svobodnoj granicej (Numerical methods in solving contact problems with a free boundary), Problems of the development of the transport
3. infrastructure of the northern territories: Proceedings of the All-Russian Scientifific and Practical Conference on April 25–26, 2014. SPb.: Publishing House GUMRF them. adm. S.O. Makarova, 2015, pp. 29–35.
4. Mikhailovskii E. I., Tarasov V. N. O sxodimosti metoda obobshhennoj reakcii v kontaktny’x zadachax so svobodnoj granicej (On the convergence of the generalized reaction method in contact problems with a free boundary), Journal of Applied Mathematics and Mechanics, 1993, v. 57, No. 1, pp. 128–136.
5. Yermolenko A. V. Utochnennye sootnosheniya teorii plastin, orientirovannye na reshenie kontaktnyh zadach (Refifined relations of the theory of plates, oriented to the solution of contact problems), Bulletin of Syktyvkar University. Ser. 1. Mathematics. Mechanics. Informatics, 2014, 19, pp. 25–32.

For citation:Yermolenko A. V., Melnikov V. A. Calculation of the contact interaction of a rectangular plate and a base by the Karman theory, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 2 (27), pp. 86–92.

VIII. Uvarovskaya O. V., Mikhailov A. V. Use of modern pedagogical technologies in high school (on the example of linear and vector algebras)

Text

The processes taking place in the higher school now, predetermine the new requirements for the teaching of disciplines. To implement the competency approach in higher education, a transition from a one-way interaction process — monologue (in the broadcast mode), to an active process of two-way communication — is necessary for dialogue (fifirst in communication and then communication) to facilitate more effffective student learning. The application of interactive forms of teaching in teaching, which are realized through modern pedagogical technologies, allow to form the competences defifined in GEF. The article presents and substantiates theproject of the lesson on the topic «Complex numbers» using the integration of technologies for developing critical thinking and learning in cooperation.

Keywords: modern pedagogical technologies, complex numbers.

References

1. Zagashev I. O., Zair-Bek S. I. Kriticheskoye myshleniye: tekhnologii razvitiya (Critical thinking: development technologies), St. Petersburg, 2003. 284 p.
2. Pedagogika vysshey shkoly (Pedagogy of Higher School), Textbook. allowance, under the general ed. O. B. Uvarovskaya, Syktyvkar: Publishing House of Syktyvkar State University, 2013.
3. Polat E. S. Novyye pedagogicheskiye i informatsionnyye tekhnologii v sisteme obrazovaniya (New pedagogical and information technologies in the education system), Moscow: Academy, 2000.
4. Uvarovskaya O. V. Pedagogika professional’nogo obrazovaniya (Pedagogy of Vocational Education) [Electronic resource]: textbook: text of the manual Electronic book on CD-ROM. Feder. state. budget. a higher education institution is established. education Syktyv. Gos. University of. Pitirima Sorokina: Izd-vo SSU im. Pitirima Sorokina, 2017.
5. Kurosh A. G. Kurs vysshey algebry, devyatoye izdaniye (Course of Higher Algebra. Ninth edition), Moscow: Nauka, 1968.
6. Entsiklopediya dlya detey (Encyclopedia for Children). Vol. 11. Mathematics. Ed. M. D. Aksenova; method. and otv. Ed. V. A. Volodin. M.: Avanta+. 2003, 688 p.: Ill.
7. Bergelson M. Yazykovyye aspekty virtual’noy kommunikatsii (Language aspects of virtual communication), Vestn. Moscow State University, 2002, S. 19, No. 1, 54 p.

For citation:Uvarovskaya O. V., Mikhailov A. V. Use of modern pedagogical technologies in high school (on the example of linear and vector algebras), Bulletin of Syktyvkar University. Series 1:Mathematics. Mechanics. Informatics, 2018, 2 (27), pp. 93–106.

Issue 4 (29) 2018

I. Andryukova V. Yu., Tarasov V. N. Constructive-nonlinear problems stability of rods and rings

Text

Analytical solutions of the stability problem of rods of compressible longitudinal force in an elastic medium, the deflections of which on the one hand are limited by a rigid obstacle, are obtained. The problem of the stability of a circular ring compressed by uniformly distributed central forces with one-sided constraints on displacements is considered.

Keywords: stability, circular ring, rod, one-sided restrictions.

References

1. Andryukova V. Yu. Nekotorye konstruktivno-nelineynye zadachi ustoychivosti uprugikh sistem pri odnostoronnikh ogranicheniyakh na peremeshcheniya (Some constructive non-linear problems of stability of elastic systems with one-sided constraints on displacements), Computational mechanics of continuous media, Institute of Continuous Media Mechanics UB RAS, 2014, No. 4, pp. 412–422.
2. Tarasov V. N. Metody optimizatsii v issledovanii konstruktivno-nelineynykh zadach mekhaniki uprugikh sistem (Optimization Methods in the Study of Structurally Nonlinear problems of mechanics of elastic systems), Syktyvkar: Komi Scientific Center UB RAS, 2013, 238 p.

For citation:Andryukova V. Yu., Tarasov V. N. Constructive-nonlinear problems stability of rods and rings, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 4 (29), pp. 4–11.

II. Golovataya O. S., Petrakov A. P., Shilov S. V. The calculation of hazardous areas explosion of tanks with liquefied gas

Text

In the work the simulation of the damaging effect of shock wave in the explosion of liquefied gaswas carried out. Amendments to the normative method of calculationare made. Cases of transportation ofgases in automobile tanks and their stationary placement are considered. The method of estimation of hazardous zones of industrial buildings is given.

Keywords: shock wave, defeat, liquefied gas.

References

1. Gazovozy. Avtotsisterny SUG (Gas carrier. Tankers), Liquefied petroleum gas. URL: https://rodisgroup.ru (date of the application: 28.11.2018).
2. Zashchita ob’yektov narodnogo khozyaystva ot oruzhiya massovogo porazheniya (Protection of objects of national economy from weapons of mass destruction), a Handbook, G. P. Demidenko, 2nd ed. Kiev, HighSchoolPubl., 1989, 287 p.
3. Ivkina M. A. Analiz «Metodiki otsenki posledstviy avariynykh vzryvov toplivno-vozdushnykh smesey» («Methods of estimation of consequences of emergency fuel-air mixtures explosions»), Safety in emergency situations. Proc. of the VIII all-Russian scientific-practical conference, Saint-Petersburg, Polytechnical University Publ., 2017, pp. 380–382.
4. Rachevsky B. S. Szhizhennyye uglevodorodnyye gazy (Liquefied petroleum gases), Moscow, Oil and gas Publ, 2009, 164p.
5. Rukovodstvo po bezopasnosti «Metodika otsenki posledstviy avariynykh vzryvov toplivno-vozdushnykh smesey» (Safety Guide «Methods for assessing the effects of emergency explosions of fuel-air mixtures»), series 27, issue 15, Moscow, Closed Joint Stock Company «Scientific and Technical Center for the Study of Industrial Safety Problems», 2015, 44 p.
6. Staskevich N. L, Sevyarynets G. N., Vigdorchik D. Ya. Spravochnik po gazosnabzheniyu i ispol’zovaniyu gaza (Handbook of gas supply and use of gas), Leningrad, NedraPubl, 1990, 762 p.
7. Hramov G. N. Goreniye i vzryv (Burning and explosion), Saint-Petersburg, St. Petersburg State Technical UniversityPubl, 2007, 278 p.

For citation:Golovataya O. S., Petrakov A. P., Shilov S. V. The calculation of hazardous areas explosion of tanks with liquefied gas, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 4 (29), pp. 12–23.

III. Kholopov A. A. Suboptimal parameters in the method of additive splitting

Text

An equation in a Banach space with continuous linear operator is solved by splitting A to some parts and using an appropriate iteration procedure. The suboptimal parameters of the splitting extend the spectral domain of convergence along the real axis as much as possible up to a small parameter.

Keywords: operator equation, spectral domain of convergence, suboptimal parameters.

References

1. Nikitenkov V. L., Kholopov A. A. Optimal’nyye oblasti skhodimosti lineynykh mnogosloynykh iteratsionnykh protsedur (Optimal areas of convergence of linear multilayer iterative procedures), Voprosy funktsional’nogo analiza (teoriya mer, uporyadochennyye prostranstva, operatornyye uravneniya): mezhvuz. sb. nauch. tr. (Questions of functional analysis (measure theory, ordered spaces, operator equations): Interst. Sat scientific tr.), Syktyvkar: Sykt. un-t 1991, pp. 134–142.
2. Nikitenkov V. L., Kholopov A. A. Optimal’nyye parametry metoda additivnogo rasshchepleniya (MAR) (The optimal parameters of the method of additive splitting (MAP)), Bulletin of the Syktyvkar University, ser. 1, 2010, no. 12, pp. 53–70.
3. Nikitenkov V. L., Kholopov A. A. Tochnyye formuly dlya optimal’nykh parametrov MAR (Exact formulas for optimal MAR parameters), Bulletin of Syktyvkar University, ser. 1, 2011, no. 14, pp. 67–94.

For citation:Kholopov A. A. Suboptimal parameters in the method of additive splitting, Bulletin of Syktyvkar University. Series 1:Mathematics. Mechanics. Informatics, 2018, 4 (29), pp. 24–33.

IV. Isayeva S. E. The initial boundary value problem for one system with acoustic transmission conditions

Text

In this work we consider the initial-boundary value problem for one system of hyperbolic equations with acoustic transmission conditions. We prove the existence of weak solutions for this problem. Faedo-Galerkin method is used.

Keywords: acoustic transmission conditions, Dirichlet boundary condition, initial-boundary value problem, weak solution, Faedo-Galerkin method.

References

1. Beale J. T., Rosencrans I. Acoustic boundary conditions, Bull. Amer. Math.Soc., 1974, 80, pp. 1276–1278.
2. Beale J. T. Spectral properties of an acoustic boundary condition, Indiana Univ. Math. J., 1976, 25, pp. 895–917.
3. Beale J. T. Acoustic scattering from locally reating surfaces, Indiana Univ. Math. J., 1977, 26, pp. 199–222.
4. Cousin A. T., Frota C. L., Larkin N. A. On a system of Klein-Gordon type equations with acoustic boundary conditions, J. Math. Appl., 2004, 293, pp. 293–309.
5. Frota C. L., Cousin A. T., Larkin N. A. Global solvability and asymptotic behaviour of a hyperbolic problem with acoustic boundary conditions, Funkcial. Ekvac., 2001, vol. 44, no. 3, pp. 471–485.
6. Jeong J. M., Park J. Y., Kang Y. H. Global nonexistence of solutions for a quasilinear wave equation with acoustic boundary conditions, Jeong et al. Boundary Value Problems, 2017, 42, pp. 1–10.
7. Lions J. L., Magenes E. Neodnorodnyye granichnyye zadachi i ikh prilozheniya (Inhomogeneous boundary value problems and their applications). Moscow, World Publ., 1971, 357 p.

For citation:Isayeva S. E. The initial boundary value problem for one system with acoustic transmission conditions, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 4 (29), pp. 34–42.

V. Chernov V. G. Multi-criteria alternative choice based on fuzzy conditional inference rules

Text

The solution of the problem of multi-criteria alternative choice in the conditions of non-statistical uncertainty based on the rules of fuzzy conditional inference, when the evaluation of alternatives by criteria are in the form of fuzzy linguistic statements, and the solution is not based on the convolution of criteria in the conditional part of the rules, and on the convolution of particular implications for the criteria.

Keywords: multicriteria alternative choice, fuzzy set, membership function, fuzzy conditional inference, implication.

References

1. Borisov A. N., Krumberg O. A., Fedorov I. P. Prinyatie reshenij na osnove nechetkih modelej: primery ispol’zovaniya (Fuzzy model-based decision making: examples of use), Riga: Zinatne Publ., 1990, 184 p.
2. Babuska R., Verbruggen H. B. A new’ identification method for linguistic fuzzy models, Proceedings of the International Conference FUZZ-IEEE/IFES’95, Yokohama, Japan, 1995, pp. 905–912.
3. Chernov V. G. Modifikaciya algoritmov upravleniya, ispol’zuyushchih pravila nechetkogo uslovnogo vyvoda (Modifification of control algorithms using rules of fuzzy conditional conclusion), Information management systems, 2013, no. 3(64), pp. 23–29.

For citation:Chernov V. G. Multi-criteria alternative choice based on fuzzy conditional inference rules, Bulletin of Syktyvkar University.Series 1: Mathematics. Mechanics. Informatics, 2018, 4 (29), pp. 43–49.

VI. Shuchalina A. V. Development of a voluntary collection system of user’s data by means of messengers on the example of a task on determining places of the hogweed’s growing

Text

The article describes the current phenomenon of Citizen Science, discusses the rationale for the use of instant messengers in data collection for the existing civil science project DIPS (Distribution of Invasive Plant Species), as well as the creation and use of chat bots using the Telegram example.

Keywords: citizen science, messengers, bot, data collection, hogweed.

References

1. 10 Principles of Citizen Science. URL: https://ecsa.citizen-science.net/engage-us/10-principles-citizenscience (date of the application 06.12.2018).
2. List of citizen science projects. URL: https://en.wikipedia.org/wiki/List_of_citizen_science_projects (date of the application 07.12.2018).
3. Schroterab M., Kraemerab R., Mantelab M., Kabischabc N., Heckerab S., Richterab A., Neumeierab V., Bonnabd A. Citizen science for assessing ecosystem services: Status, challenges and opportunities, Ecosystem Services, 2010, v. 28, pp. 80–94. URL: https://www.sciencedirect.com/science/article/pii/S2212041617302462 (date of the application 06.12.2018).
4. Grazhdanskaya nauka v pomoshch’ specialistam (Civil science in the help of the experts ). URL: https://newtonew.com/science/citizen-science (date of the application 06.12.2018).
5. Dal’keh I. V., CHadin I. F., Zahozhij I. G., Madi E. G., Kirillov D. V. Podhody v modelirovanii geograficheskih predelov rasprostraneniya invazivnyh vidov na primere Heracleum Sosnowskyi Manden v taezhnoj zone evropejskojchasti Rossii (Approaches to modeling geographical limits of invasive species distribution on the example of HeracleumSosnowskyiManden in the taiga zone of the European part of Russia ), The study of adventive and synanthropic flora of Russia and CIS countries: results, problems of prospects: materials of the International scientific conference, Izhevsk, 2017, pp. 48–51. URL: http://proborshevik.ru/wpcontent/uploads/2016/11/ Dalke_e_a_Izevsk_2017.pdf (date of the application 07.12.2018).
6. Dal’keh I. V., CHadin I. F., Zahozhij I. G. Sbor i analiz dannyh o rasprostranenii borshchevika Sosnovskogo na territorii Respubliki Komi (Collection and analysis of data on the distribution of Sosnovsky cow parsnip in the Republic of Komi), Biodiagnostics of the state of natural and man-made systems: Proceedings of the XIV all-Russian scientific and practical conference with international participation, Kirov, 2016, vol. 1, pp. 11–14. URL: http://proborshevik.ru/wpcontent/uploads/ 2017/12/Dalke_IV_e_a_Kirov_2016.pdf (date of the application 07.12.2018).
7. Nuzhna li razrabotkamobil’nogoprilozheniya internet-magazina (Do you need to develop a mobile application for the online store?) URL: https:// www.insales.ru/blogs/university/prilozhenie (date of the application 09.12.2018).
8. Roboty (Robots), Documentation of Telegram. URL: https:// tjournal.ru/tech/56573-svyaznoy-bot-quest (date of the application 16.12.2018).
9. «Svyaznoj» zapustil v Telegram kvest pro lyubov’ nakanune Hehllouina («Svyaznoj» launched a telegram quest about love on the eve of Halloween). URL: https://tjournal. ru/tech/56573- svyaznoy-bot-quest (date of the application 16.12.2018).

For citation:Shuchalina A. V. Development of a voluntary collection system of user’s data by means of messengers on the example of a task on determining places of the hogweed’s growing, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 4 (29), pp. 50–59.

VII. Voevodin V. A., Zabolotni A. S., Nastinovn E. O. Training complex to prepare for the practical security audit

Text

The features of master’s training in the program «Audit of information security of automated systems», the relevance of the implementation of educational and methodical complex for the organization of business games and the acquired advantages, the approach to the formalization of the object of audit. The results are reported.

Keywords: audit, information security, business game.

References

1. Federal’nyy zakon ot 30.12.2008 N 307-FZ (red. ot 23.04.2018) «Obauditorskoy deyatel’nosti» (Federal law of 30.12.2008 N 307-FZ (asamended on 04.23.2018) «On Auditing »), Art. 1, p. 2
2. GOST R ISO/MEK 27006-2006. Informatsionnaya tekhnologiya. Metody i sredstva obespecheniya bezopasnosti. Trebovaniya k organam, osushchestvlyayushchim audit i sertifikatsiyu sistem menedzhmenta informatsionnoy bezopasnosti (GOST R ISO / IEC 27006-2006. Information technology. Methods and means of security. Requirements for bodies performing the audit and certification of information security management systems), Enter 2008-18-12, No. 524-st, Moscow: Standardinform Publ., 2010, 35 p.
3. GOST R ISO/MEK 27004-2012. Informatsionnaya tekhnologiya. Metody i sredstva obespecheniya bezopasnosti. Menedzhment informatsionnoy bezopasnosti (GOST R ISO / IEC 27004-2012. Informationtechnology. Methods and means of security. Information Security Management. Measurements), Enter 2011-01-12 № 681-ст, Moscow: Standardinform Publ., 2012, 55 p.
4. Abramova G. S., Stepanovich V. A. Delovyye igry: teoriya i organizatsiya (Business games: theory and organization), Ekaterinburg: Business book Publ., 1999, 192 p.
5. Aylamazyan A. M. Aktual’nyye metody vospitaniya i obucheniya: delovaya igra (Actual methods of education and training: a business game), Moscow: Vlados – press Publ., 2000, 332 p.
6. Dewey J. Obrazovaniye konservativnoye i progressivnoye / Demokratiya i obrazovaniye (Conservative and progressive education /Democracy and education), Moscow: Pedagogy Press Publ., 2000, 384 p.
7. Corneli D., Danoff Ch. Paragogika: sinergiya samostoyatel’noy i organizovannoy uchebnoy deyatel’nosti (Paragogik: Synergy of Independent and Organized Learning Activities), Per. I, Travkina, Management problems in social systems, 2014, t. 7, vol. 11, pp. 84–97.
8. Clear J. Sistemologiya. Avtomatizatsiya resheniya sistemnykh zadach (Systematology. Automation of solving system problems), Moscow: Radio and communication Publ., 1990, 544 p.
9. Panfilova A. P. Igrotekhnicheskiy menedzhment. Interaktivnyye tekhnologii dlya obucheniya i organizatsionnogo razvitiya personala (Igrotechnical management. Interactive technologies for staff training and organizational development), Tutorial, SPb IVESEP, 2003, 536 p.
10. Patarakin E. Sotsial’nyye vzaimodeystviya i setevoye obucheniye 2.0 (Social Interactions and Networked Learning 2.0), Moscow: NP «Modern technologies in education and culture», 2009, 176 p.
11. Platov V. Ya. Delovyye igry: razrabotka, organizatsiya i provedeniye (Business games: development, organization and implementation: Textbook), Moscow: Profizdat Publ., 1991, 156 p.

For citation: Voevodin V. A., Zabolotni A. S., Nastinovn E. O. Training complex to prepare for the practical security audit, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 4 (29), pp. 60–71.

VIII. Voevodin V. A., Zabolotni A. S., Nastinovn E. O. The object model for audit information security

Text

It is reported about the relevance of information security audit in solving the problem of information security. Models of a problem situation are given, its philosophical description, formal model of object of audit is given. A General statement of the task of evaluating the effectiveness of the allocated forces and funds is carried out, the concept of a monitoring channel is introduced, the results of research and the promising direction of research will be reported.

Keywords: audit, information security, the model of the object of the audit, audit evidence, channel monitoring.

References

1. Anfilatov V. S., Emelyanov A., Kukushkin A. A. Sistemnyy analiz v upravlenii (System analysis in management), Moscow, Finance and statistics Publ., 2002, 368 p.
2. GOST R ISO/MEK 27004-2012. Informatsionnaya tekhnologiya. Metody i sredstva obespecheniya bezopasnosti. Menedzhment informatsionnoy bezopasnosti. Izmereniya (GOST R ISO/IEC 27004-2012.Information technology. Methods and means of security. Information security management), Measurements-Enter. 2011-01-12 №681-St. Moscow: Standrtinform Publ., 2012, 55 p.
3. Clear J. Sistemologiya. Avtomatizatsiya resheniya sistemnykh zadach (Systemology. Automation of solving system problems), Moscow: Radio and communication Publ., 1990, 544 p.
4. Matematicheskiy entsiklopedicheskiy slovar’ (Mathematical encyclopedic dictionary / Prokhorov), Moscow, Big Russian encyclopedia Publ., 1995, 847 p.
5. Materialy VI Konferentsii «Informatsionnaya bezopasnost’ ASU TP KVO» (Proceedings of the VI Conference «information security of APCS»), [Electronic resource]: publications in the media, access Mode: http://www.ибкво.рф/publikatsii, free (date of the application: 10.01.2019).
6. Nadezhnost’ i effektivnost’ v tekhnike: Spravochnik (Reliability and efficiency in engineering: a Handbook), vol. 3 the Effectiveness oftechnical systems, Under. Edition of V. F. Utkin, Y. V. Kryuchkova, Moscow, Mashinostroenie Publ., 1988, 328 p.
7. Osnovnyye napravleniya gosudarstvennoy politiki v oblasti obespecheniya bezopasnosti avtomatizirovannykh sistem upravleniya proizvodstvennymi i tekhnologicheskimi protsessami kriticheski vazhnykhobyektov infrastruktury Rossiyskoy Federatsii: [utv. Prezidentom Rossiyskoy Federatsii D. Medvedevym 3 fevralya 2012 g (The Main directions of the state policy in the field of safety of the automated control systems of production and technological processes of critically important objects of infrastructure of the Russian Federation: [UTV. President of the Russian Federation Dmitry Medvedev February 3, 2012), № 803 mode of access: http://www.scrf.gov.ru/security/information/document113/ (date of the application: 10.01.2019).
8. Pegat A. Nechetkoye modelirovaniye i upravleniye (Fuzzy modeling and control), translated from English, Moscow, BINOM. Laboratory of knowledge, 2009, 798 p.
9. Sovetov B. Y., Yakovlev S. A. Modelirovaniye sistem (Modeling of systems), Moscow, Higher school Publ., 1985, 271 p.
10. Uemov A. I. Logicheskiye osnovy metoda modelirovaniya (Logical foundations of the modeling method), Moscow, Thought Publ., 1971, 311 p.

For citation:Voevodin V. A., Zabolotni A. S., Nastinovn E. O. The object model for audit information security, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 4 (29), pp. 72–82.

IX. Isakov V. N., Odyniec W. P. Popov Vyacheslav Aleksandrovich (on his seventieth birthday)

Text

References

1. Shchedrin S. Eta uskol’zayushchaya granitsa nepoznannogo (This elusive border of the unknown), The right to be ahead, Syktyvkar: Komi Prince. publishing house, 1982, pp. 94–100.
2. Arteev A. Most cherez propast’ Lagranzha (Bridge across the Lagrange chasm), Youth of the North, 2003, No. 38, September 18, p. 12.
3. Zhuravlev S. Gost’ nomera Vyacheslav Popov: «Ne byt’ sukharemzanudoy» (Guest of the room Vyacheslav Popov: «Do not be a cracker»), Red flag, 2004, No. 170, September 24, p. 5.
4. Isakov V. N. Popov Vyacheslav Aleksandrovich. Gorod Syktyvkar: entsiklopediya. (Popov Vyacheslav Aleksandrovich. Syktyvkar City: Encyclopedia), Syktyvkar: Komi Scientific Center, Ural Branch of the Russian Academy of Sciences, 2010.
5. Popov Vyacheslav Aleksandrovich. Kafedra matematiki Komi pedinstituta: istoriya stanovleniya i razvitiya (Vyacheslav Aleksandrovich Popov. Department of Mathematics, Komi Pedagogical Institute: History of Formation and Development), Syktyvkar: Komi Pedagogical Institute, 2012, pp. 175–177.
6. Vyacheslav Aleksandrovich Popov. Vysshaya shkola Respubliki Komi v litsakh (Vyacheslav Aleksandrovich Popov. High School of the Republic of Komi in persons), Syktyvkar: SSU them. Pitirim Sorokin, 2017, part 1, pp. 258–259.
7. Burlykina M. I. Syktyvkarskiy gosudarstvennyy universitet imeni Pitirima Sorokina : entsiklopediya (Syktyvkar Pitirim Sorokin State University: Encyclopedia), Syktyvkar: SSU them. Pitirima Sorokina, 2018, 156 p.

For citation:Isakov V. N., Odyniec W. P. Popov Vyacheslav Aleksandrovich (on his seventieth birthday), Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 4 (29), pp. 83–94.

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 π_g ― rezonansa formy v NK ― spektre pogloshcheniya molekuly azota (The oscillator strength of the π_g― 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

Text

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

Text

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.

Issue 2 (31) 2019

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

Text

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

Text

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 S_φof 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 S_φ[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.

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

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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

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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

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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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15. ege20.html (accessed 11.15.19).

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.

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