Bulletin 1 (22) 2017

by

Issue 1 (22) 2017

I. Khozyainov S. A. Text classification using methods of pattern recognition

Text

This paper illustrates the text classification process using methods of pattern recognition. The problem of authorship of social and political essays attributed to A. S. Puskin is considered as an example. Means of increasing the reliability of the recognition system are suggested.

Keywords: text classification, methods of pattern recognition, authorship attribution, A. S. Puskin.

References

  1. Bongard M. M. Problema uznavaniya (Recognition Problem), Moscow: Nauka, 1967, 320 p.
  2. Marusenko M. A., Bessonov B. L., Bogdanova L. M., Anikin M. A., Miasojedova N. E. V poiskakh poteryannogo avtora: Etyudy atributsii (In search of the lost author. Studies in attribution), St. Petersburg: Faculty of Philology, Saint Petersburg University, 2001, 216 p.
  3. Marusenko M. A. Atributsiya anonimnykh i psevdonimnykh literaturnykh proizvedenii metodami raspoznavaniya obrazov (Attribution of anonymous and pseudonymous literary works using methods of pattern recognition), Leningrad: Leningrad University, 1990, 168 p.
  4. Rodionova E., Khozyainov S., Mitrofanova O. Text corpora in attribution of literary works, Proceedings of the International Conference «Corpus Linguistics — 2008», St. Petersburg: St. Petersburg State University, Faculty of Philology and Arts, 2008, pp. 338—349.
  5. Khozyainov S. A. Atributsiya publitsistiki, pripisyvaemoi A. S. Pushkinu (Attribution of social and political essays attributed to A. S. Puskin), Prikladnaya i matematicheskaya lingvistika: Materialysektsii XXXVII Mezhdunarodnoi filologicheskoi konferentsii, 11—15 marta 2008 g., Sankt-Peterburg (Applied and mathematical Linguistics: Materials of the section XXXVII International philological conference, March, 11—15, St. Petersburg), St. Petersburg, 2008, pp. 20—30.
  6. Khozyainov S. A. Atributsiya publitsistiki, pripisyvaemoi A. S. Pushkinu. Reshenie problemy avtorstva metodami raspoznavaniya obrazov (Attribution of social and political essays attributed to A. S. Puskin. Autorship attribution using methods of pattern recognition), LAP LAMBERT Academic Publishing, Saarbr¨ucken, 2012, 252 p.
  7. Khozyainov S. Some problems and methods of quantitative and structural research of authors’ styles, Izvestiya RGPU im. A. I. Gertsena, № 28 (63), St. Petersburg, 2008, pp. 378—383.
  8. Yakubaitis T. A., Sklyarevich A. N. Veroyatnostnaya atributsiyatipa teksta po neskol’kim morfologicheskim priznakam (Probability attribution of text type on the several morphological markings), Riga, 1982, 53 p.

For citation:Khozyainov S. A. Text classification using methods of pattern recognition, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №1 (22), pp. 3–20.

II. Vechtomov E. M., Lubyagina E. N. Definability of T1-spaces by the lattice of subalgebras of semirings of continuous partial real-valuedfunctions on them

Text

The article refers to the general theory of semirings of continuous functions. We consider subalgebras of semirings CP(X) of continuous partial functions on topological spaces X with values in the topological field R of real numbers. We study the minimal and maximal subalgebras of the R-algebra CP(X). We prove a definability theorem of an arbitrary T1-space X by the lattice A(X) of all subalgebras of the semiring CP(X).

Keywords: semiring, field of real numbers, partial real-valued function, subalgebra.

References

  1. Vechtomov E. M. Lattice of subalgebras of the ring of continuous functions and Hewitt spaces, Mat. Zametki, vol. 62, issue. 5, 1997, pp. 687–693.
  2. Vechtomov E. M., Lubyagina E. N. On semirings of partial functions, Vestnik of Syktyvkar University. Series 1: Mathematics. Mechanics. Computer science, 2014, issue. 19, pp. 3–11.
  3. Vechtomov E. M., Lubyagina E. N., Sidorov V. V., Chuprakov D. V. Elements of functional algebra: a monograph: in 2 volumes, vol. 1 / ed. E. M. Vechtomov, Kirov: Publishing House «Raduga-Press», 2016, 384 p.
  4. Vechtomov E. M., Lubyagina E. N., Sidorov V. V., Chuprakov D. V. Elements of functional algebra: a monograph: in 2 vol, vol. 2 / ed. E. M. Vechtomov, Kirov: Publishing House «Raduga-Press», 2016, 316 p.
  5. Grettser G. The theory of lattices, Moscow: Mir, 1982, 456 p.
  6. Engelking R. General topology, Moscow: Mir, 1986, 752 p.
  7. Gillman L., Jerison M. Rings of continuous functions, N. Y.: Springer-Verlang, 1976, 300 p.

For citation:Vechtomov E. M., Lubyagina E. N. Defiinability of T1-spaces by the lattice of subalgebras of semirings of continuous partial real-valued functions on them, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №1 (22), pp. 21–28.

III. Vechtomov E. M., Orlova I. V. Ideals and congruences of cyclic semirings

Text

In this paper we study ideals and congruences of cyclic semirings with commutative and non-commutative addition.

Keywords: semiring, semifield, cyclic semiring, ideal, equivalence relation, congruence.

References

  1. Bestuzev A. S., Vechtomov E. M. Cyclic Semirings with Commutative Addition, Bulletin of Syktyvkar State University. Series 1: Mathematics. Mechanics. Informatics, edition 1 (20), 2015, pp. 8–39.
  2. Vechtomov E. M. Introduction to Semirings, Kirov: VGPU, 2000, 44 p.
  3. Vechtomov E. M., Bestuzev A. S., Orlova I. V. The Structure of Cyclic Semirings, IX Vserossiiskaya nauchnaya conferenciya «Matematicheskoe modelirovanie razvivausheysya ekonomoki, ekologii i tehnologii», EKOMOD – 2016: Sbornik materialov conferencii, Kirov: Izdatelstvo VyatGU, 2016, pp. 21–30.
  4. Vechtomov E. M., Lubyagina (Orlova) I. V. Cyclic Semirings with Idempotent Noncommutative Addition, Fundamentalnaya i Prikladnaya Matematika, 2011/2012, t. 17, vyp. 1, pp. 33–52.
  5. Vechtomov E. M., Orlova I. V. Cyclic Semirings with Nonidempotent Noncommutative Addition, Fundamentalnaya i Prikladnaya Matematika, 2015, t. 20, vyp. 6, pp. 17–41.
  6. Orlova I. V. Ideals and Congruences of Cyclic Semirings with Noncommutative Addition, Trudi Matematiteskogo Centra imeni N. I. Lobachevskogo, Kazan: Kazanskoe matematicheskoe obshestvo, 2015, t. 52, pp. 118–120.
  7. Skornyakov L. A. Elements of Algebra, M.: Nauka, 1986, 240 p.
  8. Brown T. Lazerson E. On Finitely Generated Idempotent Semi-groups, Semigroup Forum, 2009, vol. 78, iss. 1, pp. 183–186.

For citation:Vechtomov E. M., Orlova I. V. Ideals and congruences of cyclic semirings, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №1 (22), pp. 29–40.

IV. Belykh E. A. Teaching Haar cascade

Text

This article describes Haar cascades and based on article by Paul Viola and Michael Jones. Here is described some features, that weren’tdecsribed in the original article. In particular, this is a weak classififier’s threshold choosing and also optimized method of building the cascade of classififiers.

Keywords: pattern recognition, machine learning, classifification, image processing.

References

  1. 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. 01, 511 p.
  2. Freund Y., Schapire R. E. Decision-Theoretic Generalization of On-Line Learning and an Application to Boosting, Journal of computer and system sciences 55, 1997, №SS971504, pp. 119–139.

For citation:Belykh E. A. Teaching Haar cascade, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №1 (22), pp. 41–53.

V. Odyniec W. P. On the history of the mathematical Olympiads in Leningrad — St. Petersburg

Text

Article is devoted to the history of a solution of the problem of competitiveness in school education, one of form which are the mathematical Olympiads, which appeared in Russia in 1934 year in St. Petersburg (thenLeningrad). The statement is finished to the last decade.

Keywords: mathematical Olympiads, specialized professional school.

References

  1. Atiyah M. Mathematics and the Computer Revolution, Izvestiya of Russian Academy of Science, Ser. Math, t. 80, № 4, 2016, pp. 5–16.
  2. Salgaller V. F. The convex polyhedrons with the regular face, Notes of sciences seminars LOMI, t. 2, Leningrad: «Nauka», 1967, 211 p.
  3. Morosova E. A., Petrakov I. S. International mathematical Olympiads, Moskcow: Prosveshchenie, 1971, 254 p.
  4. Odyniec W. P. From the memory about mathematical Olympiad of the beginning of 60th years, Matematika v shkole, 1998, № 2, pp. 94–96.
  5. Rukhshin S. E. Mathematicals contests in Leningrad–St.-Petersburg, The first 50 years, Rostov-on-Don: Press centre «MarT», 2000, 320 p.
  6. Fomin D.V. St.-Petersburg mathematical Olympiad, St. Petersburg: Polytechnic, 1994, 309 p.
  7. Memoirs of I All-Russian congress of teachers and lecturers of mathematic, St.-Petersburg: Press «Sever», 1913, t. I, 609 p.; t. II, 363 p.; t. III, 113 p.

For citation:Odyniec W. P. On the history of the mathematical Olympiads in Leningrad — St. Petersburg, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №1 (22), pp. 54–60.

VI. Ustyugov V. A The Ising model

Text

The article provides an overview of the mathematical method of the Ising model and average field theory. We compared the values of the critical temperature, analytically derived based on the mean field theory and by numerical simulation. The causes differences of these values are discussed.

Keywords: ferromagnetism, Ising model, thermodynamics.

References

  1. Giordano N. J., Nakanishi H. Computational physics, Pearson/ Prentice Hall, 2006, 544 p.
  2. Coey, J. Magnetism and Magnetic Materials, Cambridge University Press, 2010, 633 p.
  3. Binder K., Heermann D. W. Monte Carlo methods in Statistical Physics, M.: FIZMATLIT, 1995, 144 p.
  4. Gould H., Tobochnik J. Computer modelling in physics, M.: Mir, 1990, 400 p.

For citation:Ustyugov V. A. The Ising model, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №1 (22), pp. 61–71.

VII. Kalinin S. I., Dozmorov A. V. Pompeiu theorem and its generalizations

Text

Keywords: Pompeiu’s theorem, Lagrange’s theorem, differentiable function.

References

  1. Dragomir S. S. An inequality of Ostrowski type via Pompeiu’s mean value theorem // http://www.emis.de/journals/JIPAM/index-4.html: Journal of Inequalities in Pure and Applied Mathematics. 6(3) Art. 83, 2005. URL: http://www.emis.de/journals/JIPAM/article556.html?sid=556 (date of the application: 09.03.2017).
  2. Pompeiu D. Sur une proposition analogue au th´eor`eme des accroissements finis. Mathematica. Cluj, Romania, 22, 1946, pp. 143–146.
  3. Finta B. A generalization of the Lagrange mean value theorem. Octogon. 4. № 2, 1996, pp. 38–40.

For citation:Kalinin S. I., Dozmorov A. V. Pompeiu theorem and its generalizations, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №1 (22), pp. 72–78.

VIII. Pevnyi A. B., Yurkina M. N. Inequalities for the sum of three quadratic trinomials

Text

For f(x) = ax2+ bx + c, a >0 the autors prove inequality f(x) + f(y) +

+f(z) ≥ 3f(1), where numbers x, y, z are positive and satisfy the conditions x + y + z = 1 or xyz = 1.

Keywords: quadratic trinomial, optimization problem, minimum, inequality

References

  1. Dannan F.M., Sitnik S.M. The Damascus inequality, Probl. Anal. Issues Anal, vol. 5 (23), №2, 2016, pp. 3–19.

For citation:Pevnyi A. B., Yurkina M. N. Inequalities for the sum of three quadratic trinomials, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №1 (22), pp. 79–84.

IX. OdyniecV. P. On the seventieth of professor alexander borisovich pevny

Text

The interview in connection with the 70th anniversary of the professor, doctor of physical and mathematical sciences Alexander Borisovich Pevny, who was celebrated on March 1, 2017.

For citation: OdyniecV. P.On the seventieth of professor Alexander Borisovich Pevny, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №1 (22), pp. 85–86.

Leave a Comment