I. Dubatovskaya M., Primachuk L., Rogosin S. On factorization of triangle matrix functions
The paper is devoted to an analysis of the efficient factorization method for triangular matrix-functions of arbitrary order, which generalizes G. N. Chebotarev’s method. Results are illustrated by examples.
Keywords: matrix-functions factorization, triangular matrices, continuous fractions.
References:
1. Adukov V. M. Wiener-Hopf factorization of meromorphicmatrixfunctions, St. Petersburg Math. J., 1993, vol. 4 (1), pp. 51–69.
2. Bolibruch A. A. Monodromy Problems in the Analytic Theory of Differential Equations, Moscow: MTsNMO, 2009 (in Russian).
3. Chebotarev G. N. Partial indices of the Riemann boundary value problem with a triangular matrix of the second order, Uspekhi Mat. Nauk, 1956, vol. XI (3(69)), pp. 192–202 (in Russian).
4. Gakhov F. D. Boundary Value Problems, 3rd ed., Moscow: Nauka. 1977, 544 p. (in Russian).
5. Khrapkov A.A. Wiener-Hopf method in mixed elasticity problems, Sankt Petersburg, 2001.
6. Lawrie J. B., Abrahams, I. D. A brief historical perspective of the Wiener-Hopf technique, J. Engrg. Math., 2007, vol. 59 (4), pp. 351–358.
7. Litvinchuk G. S., Spitkovsky I. M. Factorization of measurable matrix functions, Basel-Boston: Birkha¨user, 1987, 371 p.
8. Muskhelishvili N. I. Singular Integral Equation, 3rd ed., Moscow: Nauka, 1968, 600 p. (in Russian).
9. Primachuk L., Rogosin S. Factorization of Triangular MatrixFunctions of an Arbitrary Order, Lobachevsky J. of Math., 2018, vol. 39 (1), pp. 129–137.
10. Rogosin S., Mishuris G. Constructive methods for factorization of matrix-functions, IMA J. Appl. Math., 2016, vol. 81 (2), pp. 365–391.
For citation:Dubatovskaya M., Primachuk L., Rogosin S. On factorization of triangle matrix functions, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №4 (25), pp. 5–14.
II. Pevnyi A. B., Sitnik S. M. Modified discrete Fourier transform and its spectral properties
Modified discrete Fourier transform of the order n is suggested. For n = 4m the matrix of this transform has 4 eigenvalues with multiplicities m.
Keywords: discrete Fourier transform, eigenvalues.
References:
1. Schur I. ¨Uber die GaussschenSummen, Nach. Gessel. G¨ottingen. Math.-Phys. Klasse, 1921, pp. 147–153.
2. Sitnik S. M. ObobshhjonnyediskretnyepreobrazovanijaFur’eiihspektral’nyesvojstva (Generalized discrete Fourier transform and its spectral properties), New information technologies in automized systems, M., MIET, 2014.
For citation:Pevnyi A. B., Sitnik S. M. Modified discrete Fourier transform and its spectral properties, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, №4 (25), pp. 15–19.
III. Cheredov V. N., Kuratova L. A. Dynamics of a network of intermolecular bonds and phase transitions in condensed media
A new approach to the investigation of the molecular structure of the liquid and solid phases of matter — the model of flickering bonds — is proposed. This approach is based on the development of the model of thermal vibrations of atoms (molecules) of a matter and their effect on the dynamics of the molecular structure and the structure of the intermolecular bond network of the solid and liquid phases of matter. The temperature dependence of the dynamics of the properties of the network of intermolecular bonds of the solid and liquid phases of matter, as well as the dynamics of the properties of this bond network in the first-order phase transitions «solid-liquid» and «liquid-gas» is revealed. On the basis of the constructed model, the dynamics of the structure of H2O and its phase transitions is studied.
Keywords: intermolecular bonds, phase transitions, crystallization, lattice structure.
References:
1. Kaplan I. G. Mezhmolekuljarnyevzaimodejstvija. Fizicheskajainterpretacija, komp’juternyeraschjotyimodel’nyepotencial (Intermolecular interactions. Physical interpretation, computer calculations and model potentials), Moscow: BINOM, Laboratory of Knowledge, 2012, 400 p.
2. Cheredov V. N. Statikaidinamikadefektov v sinteticheskihkristallahfljuorita (Statics and dynamics of defects in synthetic fluorite crystals), Saint-Petersburg: Nauka, 1993, 112 p.
3. Landau L. D., Lifshitz E. M. Statisticheskajafizika (Statistical physics), part 1, Moscow: Fizmatlit, 2010, 616 p.
4. Enochovich A. S. Spravochnikpofizikeitehnike (Reference book on physics and techniques), Moscow: Prosveshenie, 1989, 224 p.
5. Zatsepina G. N. Fizicheskiesvojstvaistrukturavody (Physical properties and structure of water), Moscow: Moscow State University, 1998, 184 p.
6. Eisenberg D., Kautsman V. Strukturaisvojstvavody (Structure and properties of water), Moscow: Direct-Media, 2012, 284 p.
For citation:Cheredov V. N., Kuratova L. A. Dynamics of a network of intermolecular bonds and phase transitions in condensed media, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №4 (25), pp. 20–32.
IV. Korolev I. F. Efficient implementation of ChaCha20 stream cipher
The article is about efficient implementation of ChaCha20 stream cipher for ARM architecture. This algorithm has the ability to parallel computations. The article describes the use of the ability to accelerate the operation of the encryption algorithm using ARM NEON which has SIMD vector instructions.
Keywords: theory of plates, contact problem, antiphase.
References:
1. ARM Architecture Reference Manual ARMv7-A and ARMv7-R edition. 2012. 2734 p.
2. Bernstein D. J. ChaCha, a variant of Salsa20. 2008. URL: https://cr.yp.to/chacha/chacha-20080128.pdf (date of the application: 20.05.2017)
3. Bernstein D. J. The Salsa20 family of stream ciphers. 2007. URL: https://cr.yp.to/snuffle/salsafamily-20071225.pdf (date of the application: 20.05.2017)
4. Bernstein D. J., Schwabe P. NEON crypto. 2012. URL: https:// cryptojedi.org/papers/neoncrypto-20120320.pdf (date of the application: 20.05.2017)
5. Internet Engineering Task Force (IETF), Google, Inc. ChaCha20Poly1305 Cipher Suites for Transport Layer Security (TLS). 2016. URL: https://tools.ietf.org/html/rfc7905 (date of the application: 20.05.2017)
6. OpenBSD: PROTOCOL.chacha20poly1305, v 1.3 2016/05/03. URL: http://bxr.su/OpenBSD/usr.bin/ssh/PROTOCOL.chacha20poly1305 (date of the application: 20.05.2017)
7. Speeding up and strengthening HTTPS connections for Chrome on Android. URL: https://security.googleblog.com/2014/04/speeding-upand-strengthening-https.html (date of the application: 20.05.2017)
For citation: Korolev I. F. Efficient implementation of ChaCha20 stream cipher, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №4 (25), pp. 33–43.
V. Kotelina N. O. The application of FFT in problems of competitive programming
In this paper the use of FFT in problems of competitive programming is considered.
Keywords: discrete Fourier transform, competitive programming.
References:
1. Codeforces (c). Copyright 2010–2017. MihailMirzayanov. Sorevnovaniyapoprogrammirovaniyu 2.0: URL: http://codeforces.com. (date of the application: 12.09.2017).
2. MAXimal. URL: http://e-maxx.ru. (date of the application: 12.09.2017). 3. Kormen T., Leiserson Ch., R. RivestAlgoritmy: postroeniyeianaliz (Algorithms: construction and analysis), M.: MCNMO, 2001, 960 p. 4. Malozyomov V. N., Masharsky S. M. Osnovydiskretnogogarmonicheskogoanaliza (Fundamentals of discrete harmonic analysis), SPb.: Lan, 2012, 302 p.
For citation:Kotelina N. O. The application of FFT in problems of competitive programming, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, №4 (25), pp. 44–49.
VI. Makarov P. A. Methodical of the using struct type in C/C++ programs
Some features of the methodology of teaching C/C++ programming languages to students of physical and mathematical specialties of higher educational institutions are considered. The application of the structural data type in programs as a means of logical organization of the solution of the problem is discussed. The features of the transition from procedural programming paradigm to object-oriented programming are described.
Keywords: procedural and object-oriented programming paradigms, structured data type, methods, constructors, operators overloading.
References:
1. Eckel B. Filosofija C++. Vvedenie v standartnyj C++ (Philosophy of C++. Introduction to C++), 2-е ed, SPb.: Piter, 2004, 572 p.
2. Kernighan B., Ritchie D. Jazykprogrammirovanija (C programming language), 2-е ed., M.: Williams, 2015, 289 p.
3. Stolyarov A. V. Vvedenie v jazyk Si++ (Introduction in C++ language), 3-е ed, M.: Max Press, 2012, 128 p.
4. Salimov F. B., Bukharaev N. R. Izopytaprepodavanijakursa «Algoritmyistrukturydannyh» v Kazanskomfederal’nomuniversitete (From the experience of teaching the course «Algorithms and Data Structures» at the Kazan Federal University), Kazan Pedagogical Journal, № 4 (99), 2013, pp. 46–54.
5. Abrahamyan M. E. Primeneniejelektronnogozadachnikapriprovedeniipraktikumapodinamicheskimstrukturamdannyh (The use of an electronic task book in a workshop on dynamic data structures), Computer tools in education, № 3, 2013, pp. 45–56.
For citation:Makarov P. A. Methodical of the using struct type in C/C++ programs, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №4 (25), pp. 50–58.
VII. Chirkova L. N. Regarding the solution of optimization problems linear programming in learning the basics of system analysis
This article is devoted to the solution of optimization problems linear programming in learning the basics of system analysis students of the university.
Keywords: system analysis, economic system, the optimization problems of linear programming.
References:
1. Vdovin V. М. Teorija sistemisistemnyjanaliz (Systems theory and systems analysis): Textbook/ V. М. Vdovin, L. Е. Syrkov, V. А. Valentinov, Moscow: Publishing and trading corporation «Dashkov and C», 2016, 644 p.
2. Kremer N. Sh., Pytko B. А., Trishin I. М., Fridman M. N. Issledovanieoperacij v jekonomike (Research of operations in economy): textbook for university/under the editorship of prof. N. Sh. Kremer. Moscow: Publisher Urait, 2013, 438 p.
3. Berman N. D., Shadrina N. I. Resheniezadachlinejnogoprogrammirovanija v Microsoft Excel 2010 (The decision problems of linear programming in Microsoft Excel 2010): methodical instructions to performance of laboratory works on computer science for bachelors and specialists, Chabarovsk: Publisher University of the Pacific, 2015, 27 p.
For citation:Chirkova L. N. Regarding the solution of optimization problems linear programming in learning the basics of system analysis, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №4 (25), pp. 59–67.
VIII. Popov N. I., Gabova E. P. Euclidean and non-Euclidean geometry: a mathematical excursion for schoolchildren
The paper describes elements of Euclidean and non-Euclidean geometry in a mathematical language accessible to schoolchildren. Examples of models of geometry N.I. Lobachevsky are given. The work is aimed at expanding the scientific outlook and the mathematical outlook of students in secondary general education institutions.
Keywords: Euclidean geometry, non-Euclidean geometry, models of the Lobachevsky.
References:
1. Gabova E. P. Izuchenietvorcheskojdejatel’nostidvuhvelichajshihmatematikovEvklidaAleksandrijskogoi N. I. Lobachevskogo (A study of the creative activities of the two greatest mathematicians Euclid of Alexandria and N. Lobachevsky), Lobachevsky and the XXI century: materials of the IV educational scientific student conference dedicated to the Year of Lobachevsky’s in Kazan Federal University, ed. by L. R. Shakirova. Kazan: University, 2017, pp. 50–67.
2. Galimkhanova Z. T., Guzyalova A. N. Jelementygeometrii N. I. Lobachevskogo v arhitekture A. Gaudi (Geometry of N. Lobachevsky in the Architecture of A. Gaudi), Lobachevsky and the XXI century: materials of the IV educational scientific student conference dedicated to the Year of Lobachevsky’sin Kazan Federal University, ed. by L. R. Shakirova, Kazan: University, 2017, pp. 67–82.
3. Euclid. NachalaEvklida (The Beginning). Books I-VI. Translation from Greek and comments ofA.D. Mordukhai-Boltovskiy, Moscow — Leningrad: Gostekhizdat, 1950, 447 p.
4. Pidou D. Geometrijaiiskusstvo (Geometry and art), Moscow: Mir, 1979, 332 p.
5. Prasolov V. V. GeometrijaLobachevskogo (Geometry of Lobachevsky), Moscow: Eksmo, 2004, 89 p.
6. Hensbergen G. Gaudi-toreador iskusstva (Gaudi-toreador of art), Moscow: Eksmo, 2004, 352 p.
For citation: Popov N. I., Gabova E. P. Euclidean and non-Euclidean geometry: a mathematical excursion for schoolchildren, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №4 (25), pp. 68–74.
IX. Aleksyuk V. N. Measure on Boolean algebras
If measures exist on all regular Boolean algebras with a countable system of generators, then on complete Boolean algebras with continuous external (outer) measure there are measures (in the set theory ZFC+CH).
Keywords: Boolean algebras, the external (outer) measure, measure.
References:
1. Vladimirov D. A. Bulevyalgebry (Boolean algebras), M.: Izdatel’stvo «NAUKA», 1969, 320 p.
2. Magaram D. An algebraic characterisation of measure algebras, Annals of Mathematics, 1947, v. 48, №1, pp. 154-167.
3. Aleksjuk V. N. Teorema o minorante. Schetnost’ problemyMagaram (The Minorant Theorem. The countability of the Magaram problem), Matematicheskiezametki, 1977, t. 21, №5, pp. 597–604.
4. Vladimirov D. A. Teorijabulevyhalgebr (The theory of Boolean algebras), SPb.: Izdatel’stvo S.-Peterburgskogouniversiteta, 2000, 616 p.
5. Sikorskij R. Bulevyalgebry (Boolean algebras), M.: Izdatel’stvo «MIR», 1969, 376 p.
For citation:Aleksyuk V. N. Measure on Boolean algebras, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №4 (25), pp. 75–77.
X. Vechtomov E. M. Vladimir LeonidovichNikitenkov would be 65 years old
The article is dedicated to the honored worker of the Higher School of the Russian Federation, Doctor of Physical and Mathematical Sciences, Professor Vladimir LeonidovichNikitenkov (1952–2015).
References:
1. Personalii. Nashi jubiljary: Nikitenkov Vladimir Leonidovich (k 60letiju) (People. Our heroes: Nikitenkov Vladimir Leonidovich (to the 60th anniversary)), MatematicheskijvestnikpedvuzoviuniversitetovVolgo-Vjatskogoregiona, gl. red. E. M. Vechtomov, 2013, vyp. 15, pp. 465–466.
2. EvgenijIl’ichMihajlovskiji ego Uchenik Vladimir LeonidovichNikitenkov: sbornikvospominanijidokumentov (annotirovannyjkataloglichnyhfondov) (EvgenyIlyichMikhailovsky and his pupil Vladimir LeonidovichNikitenkov: a collection of memoirs and documents (annotated catalog of personal funds)) ,sost. M. I. Burlykina, M. A. Lodygina, Syktyvkar: Izd-vo SGU im. PitirimaSorokina, 2017, 236 p.
3. Vechtomov E. M. K vos’midesjatiletijuprofessoraEvgenijaIl’ichaMihajlovskogo (On the occasion of the eightieth birthday of Professor Yevgeny Mikhailovsky), Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, Vyp. 3 (24), pp. 116–119.
4. Matematicheskoemodelirovanieiinformacionnyetehnologii: sbornikstatejMezhdunarodnojnauchnojkonferencii, posvjashhennoj 80-letiju E. M. Mihajlovskogo (Mathematical modeling and information technologies: a collection of articles of the International Scientific Conference dedicated to the 80th anniversary of EM Mikhailovsky) Syktyvkar: Izd-vo SGU im. PitirimaSorokina, 2017, 156 p.
For citation:Vechtomov E. M. Vladimir LeonidovichNikitenkov would be 65 years old, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №4 (25), pp. 78–83.