Bulletin 1 (21) 2016

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Issue 1 (21) 2016

I. Kotelina N. O. Interpolation with B-spline curves

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This article deals with the problem of interpolation with polynomial Bspline curves. It examines methods of global interpolation when systems of linear equations are set up and solved.

Keywords: NURBS, B-spline curves, interpolation.

References

  1. Piegl L., Tiller W. The NURBS book. 2nd Edition. New York: Springer-Verlag, 1995–1997. 327 p.
  2. Golovanov N. N. Geometricheskoe modelirovanie (Geometric modeling). Moscow: Izd. Fiz.-Mat. Lit., 2002. 472 p.
  3. Zavyalov Y. S. , Kvasov B. I. , Miroshnichenko V. L. Metody splayn-funkcij (Methods of spline functions). Moscow: Nauka, 1980. 350 p.
  4. Hill F. OpenGL. Programmirovanie komputernoy grafiki (Computer Graphics Programming). Dlya professionalov. SPb.: Piter, 2002. 1088 p.

For citation:Kotelina N. O. Interpolation with B-spline curves // Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics. 2016. №1 (21). Pp. 3–8.

II. Makarov P. A. The recursive method for determining the reflective properties of multilayer film coatings

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An algorithm for calculating the coefficients of reflection, transmission and absorption of electromagnetic energy plane-polarized monochromatic electromagnetic waves propagating in multilayer systems of film was developed. The limits of applicability of the method were determined.

Keywords: multilayer film coatings, boundary conditions, reflection and transmission of electromagnetic waves.

References

  1. Cochran J.F., Kambersky V. Ferromagnetic resonance in very thin films // JMMM. Vol. 302. 2006. Pp. 348–361.
  2. D. de Cos, Garcia-Arriabas A., Barandiaran J.M. Ferromagnetic resonance in gigahertz magneto-impedance of multilayer systems // JMMM. Vol. 304. 2006. Pp. 218–221.
  3. Diaz M. de Sihues, Durante-Rincon C.A., Fermin J.R. A ferromagnetic resonance study of NiFe alloy thin films // JMMM. Vol. 316. 2007. Pp. 462–465.
  4. Antonets I.V., Kotov L.N., Makarov P.A., Golubev Y.A. Nanostructure, conductivity, and reflectivity of thin iron and (Fe)x(BaF2)yfilms // Technical physics. The Russian Journal of Applied Physics. 2010. Vol. 80. №9. Pp. 134–140.
  5. Antonets I.V., Kotov L.N., Nekipelov S.V., Karpushov E.N. Conducting and reflecting properties of thin metal films // Technical physics. The Russian Journal of Applied Physics. 2004. Vol. 74. № 11. Pp. 102–106.
  6. M. Born, E. Wolf Principles of optics. M.: Science, 1973. 720 p.
  7. Buznikov N.A., Antonov A.S., D’yachkov A.L., Rakhmanov A.A. Frequency spectrum of the nonlinear magnetoimpedance of multilayer film structures // Technical physics. The Russian Journal of Applied Physics. 2004. Vol. 74. № 5. Pp. 56–61.
  8. Buchel’nikov V.D., Babushkin A.V., Bychkov I.V. Electromagnetic-wave reflectivity of the surface of a cubic-ferrite plate // Physics of the Solid State. 2003. Vol. 45. № 4. Pp. 663–672.
  9. Goncharov A.A., Ignatenko P.I., Petukhov V.V. et al. Composition, structure, and properties of tantalum boride nanostructured films // Technical physics. The Russian Journal of Applied Physics. 2006. Vol. 76. № 10. Pp. 87–90.
  10. Kotov L.N., Antonets I.V., Korolev R.I., Makarov P.A. Resistance and oxidation films of iron and influence upper layer from dielectric and metal // Journal of the Chelyabinsk State University. Physics. Vol. 39 (254). № 12. 2011. Pp. 57–62.
  11. Kurin V.V. Resonance scattering of light in nanostructured metallic and ferromagnetic films // PHYSICS-USPEKHI. 2009. Vol. 179. № 9. Pp. 1012–1018.
  12. L.D. Landau, E.M. Lifshitz Course of Theoretical Physics. Volume 8. Second Edition: Electrodynamics of Continuous Media. M.: Fizmatlit, 2005. 656 p.
  13. G.S. Landsberg Optics. M.: Fizmatlit, 2010. 848 p.
  14. Perevalov T.V., Gritsenko V.A. Application and electronic structure of high-permittivity dielectrics // PHYSICS-USPEKHI. 2010. Vol. 180. № 6. Pp. 587–603.
  15. Usanov D.A., Skripal A.V., Abramov A.V., Bogolyubov A.S. Determination of the metal nanometer layer thickness and semiconductor conductivity in metal-semiconductor structures from electromagnetic reflection and transmission spectra // Technical physics. The Russian Journal of Applied Physics. 2006. Vol. 76. № 5. Pp. 112–117.
  16. Usanov D.A., Skripal A.V., Abramov A.V., Bogolyubov A.S. Changing the type of resonant reflection of electromagnetic radiation in the structures of nanometer metal film — dielectric // Letters in Technical Physics Journal. 2007. Vol. 33. № 2. Pp. 13–22.

For citation: Makarov P. A. The recursive method for determining the reflective properties of multilayer film coatings // Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics. 2016. №1 (21). Pp. 9–27.

III. Pimenov R. R. The generalization the Desargues’s theorem and geometry of perpendicularity

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This article studies the generalization the Desargues’s theorem with using perpendicularity and the new concept of connector. We research application this generalization in planimetry and stereometry. We discovery connection between this generalization and the theorem about altitudes triangle and the theorem Hjelmslev-Morley.

Keywords: the Desargues’s theorem, foundation of geometry, perpendicularity, geometry of lines, stereometry

References

  1. Kodokostas D. Proving and Generalizing Desargues’ Two-Triangle Theorem in 3-Dimensional Projective Space. Hindawi Publishing Corporation, Geometry. Volume 2014, Article ID 276108.
  2. Bachmann F. Aufbau der Geometrie aus dem Spiegelungsbegriff, Die Grundlehren der mathematischen Wissenschaften Volume 96. 1973.
  3. Odyniec W., S’le’zak W. Selected topics in graph theory. Translated. from pol. by W. Odyniec- M.-Izhevsk: Institute Computer’s Research, SRC: “RHD“, 2009. 504 с.
  4. Skopenkov M. Visual geometry and topology // http://skopenkov.ru: Mikhail Skopenkov’s homepage. URL: http://skopenkov.ru/courses/ geometry-16.html (date of the application: 20.02.2016).

For citation:Pimenov R. R. 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.

IV. Pimenov R. R. The generalization of the Desargues’s theorem and hidden subspaces

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This article studies the generalization of the Desargues’s theorem in 7-dimensional space. We consider lines as points and 3-dimensional spaces as lines. It provides us with the conception of the hidden spaces. The result is generalized for multidimensional spaces of arbitrary dimension. The article continues the research, started in the work. The generalization of the Desargues’s theorem and geometry of perpendicularity.

Keywords: The Desargues’s theorem, projective stereometry,many-dimensional space.

References

  1. Cameron Peter J. Projective and Polar Spaces // www.maths.-qmul.ac.uk: School of Mathematical Sciences. 2000. URL: http: //www.maths.qmul.ac.uk/pjc/pps/ (date of the application: 01.04.2016).
  2. Tabachnikov S. Skewers // https://arxiv.org/archive/math: Cornell University Library. Mathematics. [math.MG] 19 Sep 2015. URL: https://arxiv.org/pdf/1509.05903.pdf (date of the application: 01.04.2016).
  3. Friedrich Bachmann. Aufbau der Geometrie aus dem Spiegelungsbegriff. Die Grundlehren der mathematischen Wissenschaften Volume 96, 1973.
  4. Pimenov R. The generalization the Desargues’s theorem and geometry of perpendicularity // Bulletin of Syktyvkar State University. Series 1: Mathematics. Mechanics. Informatics. Edition 1 (21). 2016. Pp. 28–43.

For citation:Pimenov R. R. The generalization the Desargues’s theorem and hidden supspace // Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics. 2016. №1 (21). Pp. 44–57.

V. Odyniec W. P.  Emergence of the name of discipline «Computer Sciences» — time command

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The short history of emergence in the continental Europe (except of Denmark and Sweden) and also in the USSR, of name of new scientific discipline (and actually a number of sciences) «informatics», and in the rest of the world – «Computer Sciences» (in Denmark and Sweden – «datalogy»)— is presented. As by definition of the Great Russian Encyclopaedia (GRE) (2008) informatics formally is not bound to computer, it is more logical to call new discipline – «computer sciences».

Keywords: computer sciences, informatics, information value, G. Hopper, K. Steinbuch, L. Fein, G. Forsythe, Ph. Dreyfus, A.I. Mikhaylov, A.A. Harkevich, M.M. Bongard, A.P. Ershov, P. Naur.

References

  1. Backgraund. Vol. 7, No. 2 (Aug., 1963). Pp.109–110. Oxford, New Jersey: Blackwell Publishing. The International Studies Association, 1963.
  2. Hopper G. The education of a computer /Proceeding of 1952 ACM Meeting (Pittsburg). Pp. 243–249. New York: ACM, 1952.
  3. McCorduck P. An Interview with Louis Fein. (9 May 1979). Palo Alto, California: Ch. Babbage Institute. The Center for the History of Information Processing University of Minnesota, 1979. 27 p.
  4. Naur P. The Science of Datalogy. Letter to the editor Comm. ACM, Vol. 9, No. 7, 1966, p. 485.
  5. Steinbuch K. Informatik: Automatische Informationsverarbeitung. Berlin: SEG–Nachrichten, 1957.
  6. Sveinsdottir E., Frokjaer E. Datalogy — the Copenhagen Tradition of Computer Science. BIT(Nordisk Tidskrift for Informationsbehandling), Vol. 28(3), 1988. 22 p.
  7. Wiener N. Cybernetics: Or Control and Communication in the Animal and the Machine. Paris: (Hermann&Сie) & Camb. Mass. (MIT Press), 1948. 2nd revised ed 1961. New York-London: Wiley, 1961. 212 p.
  8. Ershov A.P., Monakhov V.M., Beshenkov S.A. and others. The basis of Computers Sciences and the Calculations. The Parts 1,2. Moscow: «Prosveshchenie», 1985. 96 p.
  9. Ignatyev M.B. The cybernetic pictures of the universe. The complex cyberphysics systems. Saint-Petersburg: GUAP, 2014. 673 p.
  10. Kraineva I.A. The pages of the biography academician A.P. Ershov // The papers of International Conferences to memory academician A.P. Ershov. Novosibirsk: Izd-vo Institute of System of Computer Sciences SO RAN, 2009.
  11. Mihailov A.I. and others. The scientific information. Moscow: Izd-vo VINITI Akademii Nauk SSSR, 1961. 27 p.
  12. Mihailov A.I., Cherniy A.I., Gilyarovsky R.S. The basis of scientific information. Moscow: «Nauka», 1965. 655 p.
  13. Odyniec W.P. Sketches in the history of computer sciences. Syktyvkar: Izd-vo KGPI, 2013. 420 p.
  14. Fradkov A.L. Cybernetic physic: principles and examples. Saint-Petersburg: «Nauka», 2003. 208 p.
  15. Harkevich A.A. Selected topics in 3 Volumes. V.3. The Information Theory. The Identification of form. Moscow: «Nauka», 1973. 524 p.
  16. Bol’shaya Rossiisrkaya Encyklopedia (The Grand Russian Encyclopedia). Vol. XI., p. 481 (Computer sciences). Moscow:«Rossiiskaya Encyclopedia», 2008.
  17. Ivanov I.I. Harkevich A.A. // Bolshaya Sovetskaya encyclopedia (The Grand Soviet Encyclopedia) (The 3th ed.), V. 28, p. 590 (). Moskow: «Sovetskaya encyclopedia», 1978.
  18. The mathematical encyclopedic Dictionary. (Computer sciences), p. 244. Moscow: «Sovetskaya encyclopedia», 1988. 847 p.

For citation:Odyniec W. P. Emergence of the name of discipline «Computer Sciences» — time command // Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics. 2016. №1 (21). Pp. 58–68.

VI. Odyniec W. P. Some comments to comparison of Unified State Examination in mathematics (expanded level, May, 2016) in Poland and in Russia

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In work comparison of final works on mathematics (USE of expanded level) in form and in content in Poland and in Russia is carried out.

Keywords:final work on mathematics (USE), Mathematics Olympiads, experts.

References

  1. Leontieva N.V. On the problem of the system of criteria for evaluating of the achievement the students of the school in the mathematic // Matematicheskii vestnik pedagog. institutes and university from Volga- Vyatsk. region; Vyp. 18. Pp. 271–276. Kirov: Nauch. Izd-vo Vyat GU, 2016. 400 p.
  2. Odyniec V.P. Some problems of the training of the past-graduate students for the theory and principles of teaching mathematics // Vestnik MGU, Ser. 20, № 4 (2012) Pp.3–8.
  3. Odyniec V.P. On the 10 th anniversary of the Bologna process in Russia // Vestnik MGU, Ser. 20. № 1 (2014). Pp. 3–10.
  4. Testov V.A. The problem of the going over mathematical education to the new paradigm in information society // Trudy X mezhdunarodnyh Kolmogorovskih chtenii, pp. 94–97. Yaroslavl’: Izd-vo YaGPU, 2012. 248 p.

For citation:Odyniec W. P. Some comments to comparison of Unified State Examination in mathematics (expanded level, May, 2016) in Poland and in Russia // Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics. 2016. №1 (21). Pp. 69–76.

VII. Ustyugov V. A. Smith – Beljers formula

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The article gives a brief historical overview of ferromagnetic resonance studies and describes a derivation of the Smith – Beljers formula. An example of the calculation of the resonance frequency of single-domain ellipsoidal particles is given.

Keywords: ferromagnetism, resonance frequency.

References

  1. Coey, J. Magnetism and Magnetic Materials / J. Coey. Cambridge University Press, 2010. 633 p.
  2. Osborn, J. A. Demagnetizing factors of the general ellipsoid / J. A. Osborn // Phys. Rev. B. 1945. vol. 67. Pp. 352–357.
  3. Suhl H. Werromagnetic resonance in nickel ferrite / H. Suhl // Phys. Rev. 1954. Vol. 97. Pp. 555–557.
  4. Smith J., Beljers H. J. Ferromagnetic resonance absorbtion in BaFe12O19, a highly anisotropic crystall // Philips Res. Rep. 1955. Vol 10. Pp. 113-130.
  5. Ferromagnetic resonance / Ed. by S. V. Vonsovsky. Moscow: Gosudarstvennoe izdatelstvo fiziko-tekhnichskoi literatury, 1961. 344 p.
  6. Gurevich A. G. Magnetic oscillations and waves / A.G. Gurevich, G.A. Melkov. Moscow: Fizmatlit, 1994. 464 p.

For citation:Ustyugov V. A. Smith-Beljers formula // Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics.2016. №1 (21). Pp. 77–85.

VIII. Nosov L. S., Vecherskij V. V., Zudin V. S., Mozhajkin A. V. Encoding voice information in the IP-telephony

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In this article, the voice data protection for its transmission over an IP-telephony systems is considered, since this channel is potentially exposed to interference in order to violate the confifidentiality of negotiations. The challenge of protecting speech information from interception is relevant for ordinary users (daily use) and for various organizations, fifirms or companies in order to prevent the interception of commercial secrets by competitors.

In this paper we propose a method of encoding audio channels, create our own minimalist software that allows to encode / decode the speech information in the frequency domain.

Keywords: IP telephony, Protection of IP telephony, speech intelligibility.

References

  1. James W. Cooley, John W. Tukey An Algorithm for the Machine Calculation of Complex Fourier Series // Mathematics of Computation, 1965. Pp. 297–301.
  2. Yukito Sato Illustrated Introduction to Mechatronics. Introduction to Signal Management (Revised 2nd Edition). Tokyo: Ohmsha, 1999. 176 p.
  3. PulseAudio Documentation // http://freedesktop.org: Software development management system. URL: http://freedesktop.org/software/pulseaudio/doxygen/ (date of the application: 17.07.2016).
  4. ALSA project – the C library reference // http://www.alsa-project.org: Advanced Linux Sound Architecture (ALSA) project homepage. URL: http://www.alsa-project.org/alsa-doc/alsa-lib/ (date of the application: 17.07.2016).
  5. JACK Audio Connection Kit // URL: http://www.jackaudio.org/ (date of the application: 17.07.2016).

For citation:Nosov L. S., Vecherskij V. V., Zudin V. S., Mozhajkin A. V. Encoding voice information in the IP-telephony // Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics. 2016. №1 (21). Pp.86–99.

IX. Odyniec W. P., Popov V. A. Valerian Nikolayevich Isakov (to the seventieth anniversary from the birthday)

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References

  1. Valerian Isakov rector of the Komi state pedagogical Institute // http://ktovobrnauke.ru/: Federal specialized magazine ”who’s Who in science and education“. № 1(1), 2009. URL: http://ktovobrnauke.ru/ 2009/1/innovacii-severnogo-vuza.html (date of the application: 10.05.2016).
  2. Valerian Nikolayevich Isakov (to the 65-th anniversary from birthday) // Bulletin of Syktyvkar State University. Series 1: Mathematics. Mechanics. Informatics. Edition 13. 2011. Pp. 155–159.
  3. Zhdanov L. A. Isakov Valerian Nikolaevich // Syktyvkar: Encyclopedia. Syktyvkar: Komi scientific center, UB RAS, 2010.
  4. Natalia Kirillova. Innovation of the North high school // http:// ktovobrnauke.ru/: Federal specialized magazine ” who’s Who in science and education“. № 1(1), 2009. URL: http://ktovobrnauke.ru/2009/1/innovacii-severnogo-vuza.html (date of the application: 10.05.2016).
  5. Odinets V.P. (Odyniec W.P.), Popov V. A. Isakov Valerian Nikolaevich // Rectors (Directors) of the Komi pedagogical Institute / L. A. Zhdanov, V. A. Popov, N. I., Surkov, etc. Syktyvkar: Komi pedagogical Institute, 2012. P. 100–107.
  6. Popov V. A. Kafedra of mathematics Komi pedagogical Institute: history of formation and development / V. A. Popov. Komi pedagogical Institute. Syktyvkar, 2012. 216 p.

For citation:Odyniec W. P., Popov V. A. Valerian Nikolayevich Isakov (to the seventieth anniversary from the birthday) // Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics. 2016. №1 (21). Pp. 100–104.

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