Bulletin 3 (28) 2018

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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 2εpo-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

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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

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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

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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.  

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