Андрей Ермоленко – Page 4 – Bulletin of Syktyvkar University

Bulletin 1 (20) 2015

by

Issue 1 (20) 2015

I. A. Grytczuk Sufficient and necessary condition for thesolution of the beal conjecture

In this paper we prove some sufficient and necessary conditionconnected with the Beal conjecture. In 1993 year Beal formulatedthe following conjecture: if the diophantine equation (∗) a^x + b^y=c^zhas a solution in positive integers a, b, c, x, y, z such that x > 2,y > 2, z > 2 then the numbers a, b, c have a prime common factor.

The following result is proved in this paper: The equation (∗) has a solution in positive integers a, b, c, x, y, z such that x > 2, y > 2,z > 2 and a, b, c are pairwise relative primes with b^y> a^xif and onlyif there is some integer r₁; 1 ≤ r₁< a^xsuch that (∗∗) b^y = a^x + r₁,c^z = 2 · a^x + r₁. In the proof of this result we use some properties ofthe divisibility relation.

Keywords: Diophantine equations, Beal’s conjecture.

References

Redmond D. Number Theory, Mercel Dekker, Inc. New York. Basel. Hong–Kong, 1996.
Sierpinski W. Elementary Number Theory, PWN Warszawa, 1987.

II. Bestuzhev A. S., Vechtomov E. M. Cyclic semirings with commutative addition

In the article we explore a semiring with cyclic multiplication in whichevery element (maybe with the exception of 0) is an entire non-negativepower of some generating element a. At first we consider particular cases ofsemirings where 0 or 1 is a natural power of the element a. Further we findout how a semiring isconstructed in general and we learn semirings withnonidempotent addition.

Keywords: semiring, cyclic semiring, generating element, absorbing element,cyclic semigroup, nonidempotent addition.

References

BestugevA. S., VechtomovE. M. Mulitiplicativelycyclicsemirings // XIII Международная научная конференцияим. академикаМ. Кравчука. Киев: Национальный технический университет Украины, 2010. Т. 2. С. 39.
Golan J. S. Semirings and their applications. Dordrecht: Kluwer Academie Publishers. 1999. 381 p.
Бестужев А. С. Конечные идемпотентные циклические полукольца //Математический вестник педвузов и университетов Волго–Вятского региона. 2011. Вып. 13. С. 71–78.
Бестужев А. С. О строении конечных мультипликативно–циклических полуколец // Ярославский педагогический вестник.2013. Т. III. № 2. С. 14–18.
Бестужев А. С., Вечтомов Е. М., Лубягина И. В. Полукольцас циклическим умножением // Алгебра и математическая логика: Международная конференция посвященная 100-летию В. В. Морозова. Казань: КФУ, 2011. С. 51–52.
Вечтомов Е. М. Введение в полукольца: пособие для студентов иаспирантов. Киров: Изд-во Вятского гос. пед. ун-та, 2000. 44 с.
Вечтомов Е. М., Лубягина И. В. Циклические полукольца сидемпотентным некоммутативным сложением // Фундаментальнаяи прикладная математика. 2012. Т. 17. Вып. 1. С. 33—52.

III. Kalinin S. I. Refinements of Ki Fang inequality by the improper integral method

Keywords: Ki Fang inequality , improper integral method.

References

Калинин С. И. Средние величины степенного типа. Неравенства Коши и Ки Фана : учебное пособие по спецкурсу. Киров: Изд-во ВГГУ, 2002. 368 с
Калинин С. И., Шалыгина М. Ю. Несобственный интеграл помогает уточнить весовые неравенства Коши и Ки Фана // Информатика. Математика. Язык : науч. журнал. Киров: Изд-во ВятГГУ,2013. Вып. 7. С. 70–72.

IV. Pimenov R. R.– Analogue of differentiation in the theory of numbersand its application for the special cases of Dirichlet’s theorem

Keywords: theory of numbers, Fermat’s little theorem, Dirichlet’s theorem

References

Бухштаб A. A. Теория чисел. М.: Просвещение, 1966. 384 с.
Пименов Р. Р. О нестандартном применении методов математического анализа к теории чисел // Математический вестникпедвузов и университетов Волго-Вятского региона: периодический межвузовский сборник научно-методических работ. Киров: Научн. изд-во ВятГУ, 2016. Вып. 18. С. 198–201.

V. Popov V. A. Design, development and implementation of complex automated car fleet management system

In the article we justify the impossibility of the deduction of differentialanalogues of the mean value theorems of Rolle, Lagrange and Cauchy forcertain classes of analytic functions, even if the differential mean value(point C) is sought in a much wider set than a segment. A class of fullydifferentiable functions for which the point С of Lagrange’s equality belongsto some circle, containing originally given points, is determined. The simpleproof of Lagrange’s mean value inequality and the traditional criterion ofstationarity of functions of a complex variable is given.

Keywords: Lagrange’s formula of finite increments, the condition for theexistence of a shortened harmonized chords, the full derivative of a functionat a point, Lagrange’s mean value inequality.

References

Popov V. А. П-derivative and analytical functions // Mathematics and Science Education in the North-East of Europe: History, Traditions Contemporary Issues. Proceedings of the Sixth Inter Karelian Conferen ce Sortavala, Russia. 11–14 September, 2003. Pp. 59–62.
Боярчук А. К. Справочное пособие по высшей математике. Т. 4:Функции комплексного переменного: теория и практика. М.: Едиториал УРСС, 2001. 352 с.
Ловягин Ю. Н., Праздникова Е. В. Элементарные функциина множестве комплексных гиперрациональных чисел // Вестник Сыктывкарского университета. Сер. 1. Вып. 9. 2009. С. 30–42.
Пименов Р. Р. О нестандартном применении методов математического анализа к теории чисел // Математический вестник педвузов и университетов Волго-Вятского региона : периодический межвузовский сборник научно-методических работ. Киров: Науч.изд-во ВятГУ, 2016. Вып. 18. С. 198–201.
Полиа Г., Сеге Г. Задачи и теоремы из анализа. Часть вторая: Теория функций (специальная часть). Распределение нулей. Полиномы. Определители. Теория чисел. М.: Наука, 1978. 432 с.
Попов В. А. Новые основы дифференциального исчисления : учебное пособие для спецкурсов. Сыктывкар: Изд-во КГПИ, 2002. 64 с.
Попов В. А. Изложение ТФКП на основе понятия полной производной // Проблемы теории и практики обучения математике : cб.науч. работ, представленных на Международную науч. конф. <58Герценовские чтения>. СПб.: Изд-во РГПУ им. А. И. Герцена, 2005.С. 270–276.
Попов В. А. Преднепрерывность. Производные. П-аналитичность.Сыктывкар: Коми пединститут, 2011. 228 с.
Праздникова Е. В. Моделирование вещественного анализа в рамках аксиоматики для гипернатуральных чисел // Вестник Сыктывкарского университета. Сер. 1. Вып. 7. 2007. С. 41–66.
Рудин У. Основы математического анализа. М.: Мир, 1976. 320 с.

VI. Asadullin F. F., Kotov L. N., Ustyugov V. A. Stream encryption based on FPGA

Mathematical model of the ferromagnetic granular films is described.The model allows to calculate demagnetization field and the frequencyof ferromagnetic resonance (FMR). The films are presented as ensemblesof ellipsoidal shape particles. For possible variants of particle orientationrelative to the external magnetic field FMR frequency is calculated.

Keywords: thin composite films, ferromagnetism, demagnetizing field.

References

Dubowik J. Shape anisotropy of magnetic heterostructures // Phys. Rev. B. 1996. Vol. 54, no. 2. Pp. 1088–1091.
Ishii Y., Okamoto T., Nishina H. Particle length and orientation distributions in magnetic recording media // JMMM. 1991. Vol. 98. Pp.210–214.
Мейлихов Е. З., Фарзетдинова Р. М. Ультратонкие плёнкиCo/Cu(110) как решётки ферромагнитных гранул с дипольным взаимодействием // Письма в ЖЭТФ. 2002. Т. 75. №3. С. 170–174.

VII. Muzhikova A. V. Interactive teaching of mathematics in higher school

Keywords : interactive forms of teaching, group teaching, higher mathematics.

References

Белозерцев Е. П., Гонеев А. Д., Пашков А. Г. и др. Педагогика профессионального образования : учебное пособие / под ред.В. А. Сластенина. М.: Академия, 2004. 368 с.
Гузеев В. В. Методы и организационные формы обучения. М. :Народное образование. 2001. С. 54–55.
Лебединцев В. Б. Модифицированные программы для разновозрастных коллективов на ступени основного общего образования. Биология. Химия. География : методическое пособие. Красноярск,2009. 84 с.
Лебединцев В. Б., Горленко Н. М. Позиции педагогов при обучении по индивидуальным образовательным программам // Народное образование. 2011. №9. С. 224–231.
Лебединцев В. Б., Горленко Н. М., Запятая О. В.,Клепец Г. В. Новые модели обучения в малочисленных сельских школах: институциональные системы обучения на основе индивидуальных учебных маршрутов и индивидуальных образовательных программ учащихся : методическое пособие / под ред. В. Б. Лебединцева. Красноярск, 2010. 152 с.
Литвинская И. Г. Коллективные учебные занятия: принципы, фазы, технология // Экспресс-опыт: приложение к журналу «Директор школы». 2000. №1. С. 21–26.
Мкртчян М. А. Методики коллективных учебных занятий //Справочник заместителя директора школы. 2010. №12. С. 50–63.
Мкртчян М. А. Концепция коллективных учебных занятий //Школьные технологии. 2011. №2. С. 65–72.
Сорокопуд Ю. В. Педагогика высшей школы : учебное пособие.Ростов н/Д: Феникс, 2011. 541 с
Шамова Т. И., Давыденко Т. М., Шибанова Г. Н. Управление образовательными системами : учебное пособие. М.: Издательский центр «Академия», 2002. 384 с.

VIII. Yermolenko A. V., Gintner A. N. Influence of transverse shears on decrease of strain state of plates

In the Karman–Timoshenko–Nagdi theory the moments consist of two components: the moments, related to the curvature of the middle surface, and the moments, related to the changes in transverse shears. It is shown, the maximum values of these components are in opposition in contact problems.Keywords: refined theory of plates, contact problem, antiphase.

References

Ермоленко А.В. О контактном взаимодействии цилиндрически изгибаемой пластины с абсолютно жестким основанием //Нелинейные проблемы механики и физики деформируемого тела :тр. научной школы акад. В.В.Новожилова. СПб.: СПбГУ, 2000.Вып. 2. С. 79–95.
Ермоленко А.В. Теория плоских пластин типа Кармана – Тимошенко – Нагди относительно произвольной базовой плоскости //В мире научных открытий. Красноярск: НИЦ, 2011. № 8.1 (20).C. 336–347.
Михайловский Е.И., Бадокин К.В., Ермоленко А.В. Теория изгиба пластин типа Кармана без гипотез Кирхгофа // Вестник Сыктывкарского университета. Серия 1. Мат. Мех. Инф. 1999. Вып. 3. С. 181–202.
Михайловский Е.И., Ермоленко А.В., Миронов В.В., Тулубенская Е.В. Уточненные нелинейные уравнения в неклассических задачах механики оболочек. Сыктывкар: Изд-во Сыктывкарского университета, 2009. 141 с.
Михайловский Е.И., Тарасов В.Н. О сходимости метода обобщенной реакции в контактных задачах со свободной границей //РАН. ПММ. 1993. Т. 57. Вып. 1. С. 128–136.

Bulletin 1 (21) 2016

by

Issue 1 (21) 2016

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

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

Piegl L., Tiller W. The NURBS book. 2nd Edition. New York: Springer-Verlag, 1995–1997. 327 p.
Golovanov N. N. Geometricheskoe modelirovanie (Geometric modeling). Moscow: Izd. Fiz.-Mat. Lit., 2002. 472 p.
Zavyalov Y. S. , Kvasov B. I. , Miroshnichenko V. L. Metody splayn-funkcij (Methods of spline functions). Moscow: Nauka, 1980. 350 p.
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

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

Cochran J.F., Kambersky V. Ferromagnetic resonance in very thin films // JMMM. Vol. 302. 2006. Pp. 348–361.
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.
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.
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.
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.
M. Born, E. Wolf Principles of optics. M.: Science, 1973. 720 p.
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.
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.
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.
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.
Kurin V.V. Resonance scattering of light in nanostructured metallic and ferromagnetic films // PHYSICS-USPEKHI. 2009. Vol. 179. № 9. Pp. 1012–1018.
L.D. Landau, E.M. Lifshitz Course of Theoretical Physics. Volume 8. Second Edition: Electrodynamics of Continuous Media. M.: Fizmatlit, 2005. 656 p.
G.S. Landsberg Optics. M.: Fizmatlit, 2010. 848 p.
Perevalov T.V., Gritsenko V.A. Application and electronic structure of high-permittivity dielectrics // PHYSICS-USPEKHI. 2010. Vol. 180. № 6. Pp. 587–603.
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.
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

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

Kodokostas D. Proving and Generalizing Desargues’ Two-Triangle Theorem in 3-Dimensional Projective Space. Hindawi Publishing Corporation, Geometry. Volume 2014, Article ID 276108.
Bachmann F. Aufbau der Geometrie aus dem Spiegelungsbegriff, Die Grundlehren der mathematischen Wissenschaften Volume 96. 1973.
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.
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

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

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).
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).
Friedrich Bachmann. Aufbau der Geometrie aus dem Spiegelungsbegriff. Die Grundlehren der mathematischen Wissenschaften Volume 96, 1973.
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

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

Backgraund. Vol. 7, No. 2 (Aug., 1963). Pp.109–110. Oxford, New Jersey: Blackwell Publishing. The International Studies Association, 1963.
Hopper G. The education of a computer /Proceeding of 1952 ACM Meeting (Pittsburg). Pp. 243–249. New York: ACM, 1952.
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.
Naur P. The Science of Datalogy. Letter to the editor Comm. ACM, Vol. 9, No. 7, 1966, p. 485.
Steinbuch K. Informatik: Automatische Informationsverarbeitung. Berlin: SEG–Nachrichten, 1957.
Sveinsdottir E., Frokjaer E. Datalogy — the Copenhagen Tradition of Computer Science. BIT(Nordisk Tidskrift for Informationsbehandling), Vol. 28(3), 1988. 22 p.
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.
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.
Ignatyev M.B. The cybernetic pictures of the universe. The complex cyberphysics systems. Saint-Petersburg: GUAP, 2014. 673 p.
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.
Mihailov A.I. and others. The scientific information. Moscow: Izd-vo VINITI Akademii Nauk SSSR, 1961. 27 p.
Mihailov A.I., Cherniy A.I., Gilyarovsky R.S. The basis of scientific information. Moscow: «Nauka», 1965. 655 p.
Odyniec W.P. Sketches in the history of computer sciences. Syktyvkar: Izd-vo KGPI, 2013. 420 p.
Fradkov A.L. Cybernetic physic: principles and examples. Saint-Petersburg: «Nauka», 2003. 208 p.
Harkevich A.A. Selected topics in 3 Volumes. V.3. The Information Theory. The Identification of form. Moscow: «Nauka», 1973. 524 p.
Bol’shaya Rossiisrkaya Encyklopedia (The Grand Russian Encyclopedia). Vol. XI., p. 481 (Computer sciences). Moscow:«Rossiiskaya Encyclopedia», 2008.
Ivanov I.I. Harkevich A.A. // Bolshaya Sovetskaya encyclopedia (The Grand Soviet Encyclopedia) (The 3th ed.), V. 28, p. 590 (). Moskow: «Sovetskaya encyclopedia», 1978.
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

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

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.
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.
Odyniec V.P. On the 10 th anniversary of the Bologna process in Russia // Vestnik MGU, Ser. 20. № 1 (2014). Pp. 3–10.
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

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

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

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

James W. Cooley, John W. Tukey An Algorithm for the Machine Calculation of Complex Fourier Series // Mathematics of Computation, 1965. Pp. 297–301.
Yukito Sato Illustrated Introduction to Mechatronics. Introduction to Signal Management (Revised 2nd Edition). Tokyo: Ohmsha, 1999. 176 p.
PulseAudio Documentation // http://freedesktop.org: Software development management system. URL: http://freedesktop.org/software/pulseaudio/doxygen/ (date of the application: 17.07.2016).
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).
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)

References

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).
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.
Zhdanov L. A. Isakov Valerian Nikolaevich // Syktyvkar: Encyclopedia. Syktyvkar: Komi scientific center, UB RAS, 2010.
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).
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.
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.

Bulletin 1 (22) 2017

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Issue 1 (22) 2017

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

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

Bongard M. M. Problema uznavaniya (Recognition Problem), Moscow: Nauka, 1967, 320 p.
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.
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.
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.
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.
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.
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.
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

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

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.
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.
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.
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.
Grettser G. The theory of lattices, Moscow: Mir, 1982, 456 p.
Engelking R. General topology, Moscow: Mir, 1986, 752 p.
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

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

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.
Vechtomov E. M. Introduction to Semirings, Kirov: VGPU, 2000, 44 p.
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.
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.
Vechtomov E. M., Orlova I. V. Cyclic Semirings with Nonidempotent Noncommutative Addition, Fundamentalnaya i Prikladnaya Matematika, 2015, t. 20, vyp. 6, pp. 17–41.
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.
Skornyakov L. A. Elements of Algebra, M.: Nauka, 1986, 240 p.
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

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

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.
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

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

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

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

Giordano N. J., Nakanishi H. Computational physics, Pearson/ Prentice Hall, 2006, 544 p.
Coey, J. Magnetism and Magnetic Materials, Cambridge University Press, 2010, 633 p.
Binder K., Heermann D. W. Monte Carlo methods in Statistical Physics, M.: FIZMATLIT, 1995, 144 p.
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

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

References

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).
Pompeiu D. Sur une proposition analogue au th´eor`eme des accroissements finis. Mathematica. Cluj, Romania, 22, 1946, pp. 143–146.
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

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

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

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.

Bulletin 2 (23) 2017

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Issue 2 (23) 2017

I. Belyaeva N. A., Yakovleva A. F. Frontal wave of pressure ﬂow

The model of a pressure ﬂow of a structured liquid is analyzed. An inhomogeneous solution of the diﬀusion-kinetic equation is constructed in the region of nonmonotonicity of the discharge-pressure characteristic. This solution corresponds to a heteroclinic trajectory connecting two stable homogeneous states.

Keywords: pressure ﬂow, homogeneous equilibrium states, heteroclinic trajectory, traveling wave.

References:

1. Belyaeva N. A., Sazhina A. N. Analizusrednennogonapornogotecheniya (Analysis of the averaged pressure ﬂow), Twenty-third annual session of the Academic Council of Syktyvkar State University named after Pitirim Sorokin (February readings): a collection of materials / Otv.red. N. S. Sergiev, Syktyvkar: Publishing House of SSU named after Pitirim Sorokin, 2016, pp. 60–69.

2. Kolmogorov A. N, Petrovsky I. G, Piskunov N. S. Issledovanieuravneniya diﬀuzii, soedinennoj s vozrastaniemkolichestvaveshchestva, i ego primenenie k odnojbiologicheskoj problem (An investigation of the diﬀusion equation, coupled with the increase in the amount of matter, and its application to a single biological problem), Bul. Moscow State University. Section A, 1937, 633 p.

3. Kholodnik M., Klich A., Kubichek M., Marek M. Metodyanalizanelinejnyhdinamicheskihmodelej (Methods of analysis of nonlinear dynamic models), Moscow: Peace, 1991, 368 p.

4. Khudyaev S. I. Porogovyeyavleniya v nelinejnyhuravneniyah (Threshold phenomena in nonlinear equations), M.: Fizmatlit, 2003, 272 p.

For citation:Belyaeva N. A., Yakovleva A. F. Frontal wave of pressure ﬂow, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, 2 (23), pp. 3–12.

II. Mikhailov A. V. The ﬂuctuations of the ring supported with threads

Problems of ﬂuctuations of the elastic rings supported with elastic threads; problems of the stability of elastic rings under the action of a pulsating load are considered.

Keywords: ring, ﬂuctuation, stability, natural frequency, Euler-Ostrogradsky equation, monodromy matrix, Mathieu equation.

References:

1. Abramowitz M., Stegun I. A. Spravochnikpospecial’nymfunkciyam (Handbook of mathimatical functions with formulas, graphs and mathematical tables, National bureau of standards, applied mathematics series„ 1964, 1046 p.

2. Vol’mir A. S. Ustojchivost’ deformiruemyhsistem (Stability of deformable systems), Moscow: Nauka, 1967, 984 p.

3. Gelfand I. M., Fomin S. V. Variacionnoeischislenie (Calculus of Variations), Moscow: Gos. izd-voﬁz.-matem. literatury, 1961, 228 p.

4. Lerman L. M. Linejnye diﬀerencial’nye uravneniyaisistemy (The linear diﬀerential equations and systems), Nizhny Novgorod: Nizhegorodsliyuniversitet, 2012, 89 p.

5. Mathews J., Walker R. L. Matematicheskiemetody v ﬁzike (Mathematical methods of physics), New York – Amsterdam: W. A. Benjamin INC., 1964, 475 p.

6. PanovkoYa. G. Osnovyprikladnojteoriiuprugihkolebanij (Basics of applied theory of elastic vibrations), Moscow: Mashinostroenie, 1967, 318 p.

7. Tarasov V. N. Metodyoptimizacii v issledovaniikonstruktivnonelinejnyhzadachmekhanikiuprugihsistem (Optimization methods in a research of constructively nonlinear problems of mechanics of elastic systems), Syktyvkar: KNC UrO RAN, 2013, 238 p.

8. Ulam S. M. Nereshennyematematicheskiezadachi (A Collection of mathematical problems), New York: 1960, 150 p.

9. Faddeev L. D., Yakubovskii O. A. Lekciipokvantovojmekhanikedlyastudentov-matematikov (Lectures on Quantum Mechanics for Mathematics Students), Leningrad: Izd-voLeningradskogouniversiteta, 1980, 200 p.

For citation:Mikhailov A. V. The ﬂuctuations of the ring supported with threads, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, 2 (23), pp. 13–28.

III. Pimenov R. R. The interpretation and generalizations of the Pappus’s theorems: involutions and perpendicularity

If we draw the arrows on the picture of projection we can see involutive transformation. Geometric picture now is a diagram of involutions and their compositions. It gives useful interpretation for theorems of projective geometry.We generalize these arrows to multidimensional spaces that connect geometry of spheres with projective space and non-euclidian geometries. We study perpendicularity also. We change the word incidence for the word perpendicularity in the Pappus’s theorem and get true and meaningful propositions.

Keywords: theory of numbers, Fermat’s little theorem, Dirichlet’s theorem.

References:

1. Bachmann F. Postroeniegeometriinaosnoveponyatiyasimmetrii (Aufbau der GeometrieausdemSpiegelungsbegriﬀ), М.: Nauka, 1969, 380 p.

2. Pimenov R. R. ObobshcheniyateoremyDezarga: geometriyaperpendikulyarnogo (The generalization of the Desargues’s theorem and geometry of perpendicularity), Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2016, №1 (21), pp. 28–43.

3. Pimenov R. R. ObobshcheniyateoremyDezarga: skrytyeprostranstva (The generalization of the Desargues’s theorem and hidden subspaces), Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2016, №1 (21), pp. 44–57.

4. Pimenov R. R. Otobrazheniyasferyineevklidovygeometrii (Mapping the sphere and non-euclidian geometries), Mathematical Education, 1999, ser. 3, № 3, pp. 158–166.

5. Pimenov R. R. Ehsteticheskayageometriyailiteoriyasimmetrij (Aesthetic geometry or theory of symmetries). SPb: School league, 2014, 288 p.

6. Hartshorne R. Osnovyproektivnojgeometrii (Foundations of Projective Geometry). Lecture notes at Harvard University. W. A. Benjamin 1nc, New York, 1967.

7. Tabachnikov S. Skewers, Arnold Mathematical Journal, 2, 2016, pp. 171–193.

For citation:Pimenov R. R. 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.

IV. Makarov P. A. On the variational principles of the mechanics of conservative and non-conservative systems

On the basis of the Hamilton—Ostrogradsky principle, applied to the motion of conservative and non-conservative systems, homogeneous and inhomogeneous Euler—Lagrange equations are compiled. An example of a plane motion of a material point is considered. The inﬂuence of dissipative forces on the characteristics of motion is determined.

Keywords: Hamilton’s mechanical action, variational principles of motion, the Euler—Lagrange equation, straight and circuitous paths, energy dissipation.

References:

1. Veretennikov V. G., Sinitsin V. A. Metodperemennogodejstviya (Method of variable action), 2 ed, M.: FIZMATLIT, 2005, 272 p.

2. Veretennikov V. G., Sinitsin V. A. Teoreticheskayamekhanika (Theoretical mechanics (additions to the general sections)), M.: FIZMATLIT, 2006, 416 p.

3. Gantmacher F. R. Lekciipoanaliticheskojmekhanike (Lectures on analytical mechanics), 2 ed, M.: Science, 1966, 300 p.

4. Goldstein G. Klassicheskayamekhanika (Classical mechanics), M.: Science, 1975, 416 p.

5. Landau L. D., Lifshitz E. M. Teoreticheskayaﬁzika (Theoretical physics: V.I, Mechanics), 5 ed, M.: FIZMATLIT, 2007, 224 p.

6. Sludsky F. A. Zametka o nachalenaimen’shegodejstviya (A note on the principle of least action), Varational principles of mechanics, M.: FIZMATGIZ, 1959, pp. 388–391.

For citation: Makarov P. A. On the variational principles of the mechanics of conservative and non-conservative systems, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, 2 (23), pp. 46–59.

V. Odyniec W. P. Zenon IvanovichBorewicz (1922–1995) (To the 95th anniversary)

The article is devoted to the biography of the famous algebraist professor ZenonIvanovichBorewicz (to pronounce Borevich), the dean of Mathematics and Mechanics faculty of the Leningrad state university in 1973–83 years, seen by Polish mathematicians, and also to Z.I. Borewicz contacts with Poland, with detailed comments of the author.

Keywords: Z.I. Borewicz, the Siege of Leningrad, homologous algebra, linear groups theory, society of «Polonia».

References:

1. Narkiewicz W., Wie¸s law W. ZenonBorewicz (1922–1995), Wiadomo´sciMatematyczne, 36, 2000, pp. 65–72.

2. Odyniec W. P. About mathematicians of Leningrad, Wiadomo´sciMatematyczne, 27, 1987, pp. 279–292.

3. Odyniec W. P. About mathematicians of Leningrad – (St. Petersburg) – and not only of them, Wiadomo´sciMatematyczne, 34, 1998, pp. 149–158.

4. Jakovlev A. V. ZenonIvanovichBorevich. Questions of the theory of representations of algebras and groups. 5, Zapiskinauchnyhseminarov POMI, t. 236, 1997, pp. 9–12.

For citation:Odyniec W. P. ZenonIvanovichBorevich (1922–1995) (To the 95th anniversary), Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, 2 (23), pp. 60–69.

VI. Lubyagina E. N., Timshina L. V. Experience in the organization of students’ educational and research activities in the study of second-order curves

In the article, we oﬀer materials that can be used to organize students’ educational and research activities in studying second-order curves. We give examples of the use of the GeoGebra environment.

Keywords: research activity, second-order curves, GeoGebra.

References:

1. Akopyan A. V., Zaslavsky A. A. Geometricheskiesvojstvakrivyhvtorogoporyadka (Geometric properties of second-order curves), М ., 2007, 136 p.

2. Atanasyan L. S., Atanasyan V. A. Sbornikzadachpogeometrii (Collection of problems on geometry), Textbook for students of physical and mathematical sciences, I. M.: Enlightenment, 1973, 480 p.

3. Bezumova O. L., Ovchinnikova R. P., Troitskaya O. N., Troitsky A. G., Vorkunova L. V., Shabanova M. V., Shirokova T. S., Tomilova O. M. Obucheniegeometrii s ispol’zovaniemvozmozhnostejGeoGebra (Geometry training using GeoGebra capabilities), Arkhangelsk: Kira, 2011, 140 p.

4. Boltyanskii V. G. Ogibayushchaya (Envelope), Kvant, N. 3, 1987, pp. 2–7.

5. Vechtomov E. M. ,Lubyagina E. N. Geometricheskieosnovykomp’yuternojgraﬁki (Geometric Foundations of Computer Graphics: A Training Manual), Kirov. Publishing house: «Rainbow-Press», 2015, 164 p.

6. Gurov A. E. Zamechatel’nyekrivyevokrugnas (Wonderful curves around us), M., 1989, 112 p.

7. Zabelina C. B. Formirovanieissledovatel’skojkompetentnostimagistrantovmatematicheskogoobrazovaniya (Formation of research competence of undergraduates of mathematical education (direction pedagogical education)). Dis. … cand. ped. sciences, M., 2015.

8. Kachalova L. P. Issledovatel’skayakompetenciyamagistrantov: strukturno-soderzhatel’nyjanaliz (Research competence of undergraduates: structurally-substantial analysis), Political journal of scientiﬁc publications «Discussion», 3 (55), 2015.

9. Ruinsky A. Inversnyepreobrazovaniyagiperboly (Inverted hyperbola transformations), Mathematical education, s. 3, 4 (2000), pp. 120–126.

10. Smirnov V. I. Kursvysshejmatematiki (Course of Higher Mathematics), t. 2, M.: «Science», 1974, 479 p.

11. Timshina L. V. Seminarskiezanyatiyapogeometrii v vuze (Seminars on Geometry in the University), Teaching Mathematics, Physics, Informatics in Universities and Schools: Content Problems, Technologies and Techniques: Proceedings of the V All-Russian Scientiﬁc Conference. Conf. Glazov: «Glazov printing house», 2015, p. 131–133.

12. Chebotareva E. V. Komp’yuternyjehksperiment s GeoGebra (Computer experiment with GeoGebra), Kazan: Kazan University, 2015, 61 p.

13. Shabanova M. V., Ovchinnikova R. P., Yastrebov A. V., Pavlova M. A., Tomilova A. E., Forkunova L. V., Udovenko L. N., Novoselova N. N., Fomina N. I., Artemieva M. V., Shirikova T. S., Bezumova O. L., Kotova S. N., Parsheva V. V., Patronova N. N., Belorukova M. V., Teplyakov V. V., Rogushina T. P., Tarkhov E. A., Troitskaya O. N., Chirkova L. N. Ehksperimental’nayamatematika v shkole. Issledovatel’skoeobuchenie (Experimental mathematics in the school. Research training. Monograph on research activities), M.: Publishing house Academy of Natural History, 2016, 300 p.

14. Shirikova T. S. Metodikaobucheniyauchashchihsyaosnovnojshkolydokazatel’stvuteorempriizucheniigeometrii s ispol’zovaniem Geo Gebra (Method of teaching students of the basic school the proof of theorems in the study of geometry using GeoGebra). Diss. … cand. ped. sciences. Arkhangelsk, 2014.

15. Jaglom I. M., Ashkinuz V. G. Ideiimetodyaﬃnnojiproektivnojgeometrii: CH. I (Ideas and methods of aﬃne and projective geometry, I). M: 1962, 247 p.

For citation:Lubyagina E. N., Timshina L. V. Experience in the organization of students’ educational and research activities in the study of second-order curves, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, 2 (23), pp. 70–84.

VII. Yermolenko A. V., Osipov K. S. Parallel programming in contact problems with a free boundary

The method of generalized reaction requires a large number of iterations, on each of which a large number of calculations is carried out. To accelerate calculations, the article considers parallelizing a contact problem using the OpenMP technology in C ++.

Keywords: plate, method of generalized reaction, contact problem, parallel computing.

References:

1. Antonov A. S. Parallel’noeprogrammirovanie s ispol’zovaniemtexnologiiOpenMP (Parallel Programming Using OpenMP Technology), Moscow.: Publishing house of MSU, 2009, 77 p.

2. Yermolenko A. V., Gintner A. N. Vliyaniepoperechny’xsdvigovnaponizhenienapryazhennogosostoyaniyaplastiny (The eﬀect of transverse shear on the lowering of the stressed state of the plate), Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2015, №1 (20), pp. 91–96.

3. Yermolenko A. V. TeoriyaploskixplastintipaKarmana–Timoshenko–Nagdiotnositel’noproizvol’nojbazovojploskosti (The Karman– Timoshenko–Naghdi theory of plane plates relative to arbitrary base surface), In the world of scientiﬁc discoveries, Krasnoyarsk: SIS, 2011, № 8.1 (20), pp. 336–347.

4. Mikhailovskii E. I., Yermolenko A. V., Mironov V. V., Tulubenskaya E. V. Utochnenny’enelinejny’euravneniya v neklassicheskixzadachaxmexanikiobolochek (Reﬁned nonlinear equations in nonclassical problems of shell mechanics), Syktyvkar: Publishing house of the Syktyvkar university, 2009, 141 p.

5. Mikhailovskii E. I., Tarasov V. N. O sxodimostimetodaobobshhennojreakcii v kontaktny’xzadachax so svobodnojgranicej (On the convergence of the generalized reaction method in contact problems with a free boundary, Journal of Applied Mathematics and Mechanics, 1993, v. 57, №. 1, pp. 128–136.

For citation:Yermolenko A. V., Osipov K. S. Parallel programming in contact problems with a free boundary, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, 2 (23), pp. 85–91.

VIII. Chuprakov D. V., Vedernikova A. V. About structure of ﬁnite cyclic semirings with idempotent commutative addition

The paper deals with ﬁnite idempotent cyclic semirings with commutative addition. Authors present a criterion for existence of ﬁnite idempotent cyclic semirings with commutative addition, associated with ideal of nonnegative integers. They derive estimates of the cardinality of FIC-semiring. The article oﬀers algorithms for calculation of cardinality of FIC-semiring by basis of associated ideal of nonnegative integers.

Keywords:semiring, cyclic semiring, monogenoussemiring, idempotent, ideal, positive integer.

References:

1. Bestujev A.S. Konechnyeidempotentnyeciklicheskiepolukol’ca (Finite Idempotent Cyclic Semirings), MatekaticheskiyVestnikPedvuzov I UniversitetovVolgo-VyatskogoRegiona, 2011, n. 13, pp. 71–78.

2. Bestuzev A.S., Vechtomov E.M. Ciklicheskiepolukol’ca s kommutativnymslozheniem (Cyclic SemiringsWith Commutative Addition), Bulletin of Syktyvkar State University. Series 1: Mathematics. Mechanics. Informatics, vol. 1 (20), 2015, pp. 8–39.

3. Vedernikova A.V., Chuprakov D.V. O predstavleniikonechnyhidempotentnyhciklicheskihpolukoleckortezhamicelyh chisel (About Representation of Finite Idempotent Cyclic Semirings by Tuples of Integers), Mathematical Bulletin of Universities and Pedagogical Unyversities of Volgo-Vyatskiy Region, 2017, n. 19, pp. 70–76.

4. Vechtomov E.M. Vvedenie v polukol’ca (Introduction to Semirings), Kirov: VGPU, 2000, 44 p.

5. Vechtomov E.M., Lubyagina (Orlova) I. V. Ciklicheskiepolukol’ca s idempotentnymnekommutativnymslozheniem (Cyclic SemiringsWith Idempotent Noncommutative Addition), Fundamentalnaya I PrikladnayaMatematika, 2011/2012, vol. 17, n. 1, pp. 33–52.

6. Vechtomov E.M., Orlova I.V. Ciklicheskiepolukol’ca s neidempotentnymnekommutativnymslozheniem (Cyclic SemiringsWithNonidempotent Noncommutative Addition), Fundamentalnaya I PrikladnayaMatematika, 2015, vol. 20, n. 6, pp. 17–41.

7. Vechtomov E.M. Mul’tiplikativnociklicheskiepolukol’ca (Multiplicative Cyclic Semirings), Technologies of Productive Learning of Mathematics: Traditions And Innovations, Arzamas, 2016, pp. 130–140.

8. Vechtomov E.M., Orlova I.V. Idealyikongruehnciiciklicheskihpolukolec (Ideals and Congruences of Cyclic Semirings), Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, n. 1 (22), pp. 29–40.

9. Lubyagina I.V. O ciklicheskihpolukol’cah s nekommutativnymslozheniem (About Cyclic SemiringsWith Noncommutative Addition), Trudy MatematicheskogoChentraIm. N.I. lobachevskogo, Kazan, 2010, vol. 40, pp. 212–215.

10. Naudin P., Quitt`e C. Algebraicheskayaalgoritmika s uprazhneniyamiiresheniyami (AlgorithmiqueAlg`ebrique Avec ExercicesCorrig`es), M.: Mir, 1999, 720 p.

11. Chermnyh V.V., Nikolaeva O.V. Ob idealahpolukol’canatural’nyh chisel (Amout Ideals of Semiring of Posivive Integers), Mathematical Bulletin of Universities and Pedagogical Unyversities of Volgo-Vyatskiy Region, 2009, n. 11, pp. 118–121.

12. Bestugev A.S., Vechtomov E.M. Multiplicatively Cyclic Semirings, International Scientiﬁc Conference Named After Academician M. Kravchuk, Kiev: National Technical University of Ukraine, 2010, p. 39.

For citation:Chuprakov D. V., Vedernikova A. V. About structure of ﬁnite cyclic semirings with idempotent commutative addition, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, 2 (23), pp. 92–109.

Bulletin 3 (24) 2017

by

Issue 3 (24) 2017

I. Yermolenko A. V. Scientiﬁc work with Yevgeny Ilyich

The article is devoted to the description of scientiﬁc work with the wellknown mathematician and mechanic, the honored worker of the Russian Federation, the doctor of physical and mathematical sciences, professor EvgenyIlyichMikhailovskii (1937–2013).

Keywords: reﬁned theory of plates, contact problem.

References:

1. Vavilina N. N., Yermolenko A. V., Mihajlovskii E. I. Ustojchivost’ podkreplennojshpangoutamicilindricheskojobolochki (Stability of a cylindrical shell reinforced by frames), In the world of scientiﬁc discoveries, Krasnoyarsk: SIS, 2013, № 2.1 (38), pp. 43–55.

2. Yermolenko A. V. O poludeformacionnomvariantegranichnyhvelichin v teoriigibkihplastinKarmana (On the semi-deformational variant of boundary values in the theory of the ﬂexible Karman plates), Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 1996, №2, pp. 235–242.

3. Yermolenko A. V. TeoriyaploskixplastintipaKarmana–Timoshenko–Nagdiotnositel’noproizvol’nojbazovojploskosti (The Karman– Timoshenko–Naghdi theory of plane plates relative to arbitrary base surface), In the world of scientiﬁc discoveries, Krasnoyarsk: SIS, 2011, № 8.1 (20), pp. 336–347.

4. Yermolenko A. V., Mihajlovskii E. I. Granichnyeuslovijadljapodkreplennogokraja v teoriiizgibaploskihplastinKarmana (Boundary conditions for the reinforced edge in the Karman theory of bending of ﬂat plates), IOO, 1998, № 3, pp .73–85.

5. Mihajlovskii E. I., Badokin K. V., Yermolenko A. V. TeorijaizgibaplastintipaKarmana bez gipotezKirhgofa (The theory of bending of Karman-type plates without the Kirchhoﬀ’s hypotheses), Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 1999, №3, pp. 181–202.

For citation:Yermolenko A. V. Scientiﬁc work with Yevgeny Ilyich, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 4–10.

II. Melnikov V. A. Methods for representing ﬁgures of general kind for a two-dimensional cutting problem

This article introduces representation of ﬁgures as rastr matrixes. Also the algorithm of additional data processing for reducing future computations diﬃculty is given. The last part describes principles of positioning ﬁgures on the workpiece.

Keywords: ﬁgures of general kind, cutting, two-dimensional space, bottomleft principle.

References:

1. Dyckhoﬀ H. A typology of cutting and packing problems, European Journal of Operational Research, № 44, pp. 150—152.

2. Zalgaller V. A., Kantorovich L. V. Ratsionalnyi raskroi promyshlennyh materialov (Rational cutting of industrial materials), Novosibirks: Nauka, 1971, 300 p.

3. Nikitenkov V. L., Holopov A. A. Zadachi lineynogo programmiriovaniya i metody ih resesheniya (Linear programming problems and methods for their solution), Syktyvkar: Izdatelstvo Syktyvkarskogo universiteta, 2008, 143 p.

4. Prasolov V. V. Zadachi po planimetrii (Planning problems), 4th ed., dopolnennoe, M.: MCNMO, 2001, 584 p.

5. Shabat B. V. Vvedenie v kompleksnyi analiz (Introduction to complex analysis), M.: Nauka, 1969, 91 p.

6. Benell A. J., Olivera F. J. The geometry of nesting problems: A tutorial, European Journal of Operational Research, 2008, № 184, pp. 399—402.

7. Coordinate Systems, Transformations and Units // https:// www.w3.org: W3C. 6 мая 2017. URL: https://www.w3.org/TR/ SVG/coords.html.W3C (date of the application: 05.10.2017)

For citation: Melnikov V. A. 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.

III. Kalinin S. I. GA-convex functions

The paper is devoted to the class of socalled GA-convex functions on the interval. A geometric characterization of such functions is given, their properties are studied, in particular, the Jensen inequality and its analogue are established. Suﬃcient conditions for the GA-convexity and GA-concavity of a function in terms of derivatives are formulated.

Keywords: GA-convex function, GA-concave function, Jensen’s inequality, analogue of Jensen’s inequality.

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. and Applics., Vol. 2010, Article ID 507560, 11 pages, doi:10.1155/2010/507560.

3. Kalinin S. I. (α,β)-vypuklye funkcii, ix svojstva i nekotorye primeneniya ((α,β)-convex functions, their properties and some applications), Ufa international mathematical conference. Abstracts / Executive editor R. N. Garifullin. Ufa: RITS Bashgu, 2016, pp. 75–76.

4. Abramovich S., Klariˇci´c Bakula M., Mati´c M. and Peˇcari´c J. A variant of Jensen–Steﬀensen’s inequality and quasi-arithmetic means, J. Math. Anal. Applics., 307 (2005), pp. 370–385.

5. Mercer A. McD. A variant of Jensen’s inequality, J. Inequal. In Pure and Appl. Math., Vol. 4, Issue 4, Article 73, 2003, pp. 1–2.

For citation: Kalinin S. I. GA-convex functions, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 25–42.

IV. Lovyagin Yu. N. Some remarks on the problem of the normability of Boolean algebras

We study the connection between the property of normability of a Boolean algebra and the existence on it of a semi-additive (o) -continuous essentially positive function. Criteria are given, under which the seminormalized Boolean algebra has no measure.

Keywords: Boolean algebra, measure, problem D. Magaram.

References:

1. Poroshkin A. G. Teoriyameryiintegrala (Theory of measure and integral), Moscow: KomKniga, 2006, 184 p.

2. Poroshkin A. G. Uporyadochennyemnozhestva. Bulevyalgebry (Ordered sets. Boolean algebras), Syktyvkar: Syktu State University, 1987, 85 p.

3. Halmos P. Measure theory, Berlin-Haidelberg-New York: Springer, 1950, 304 p.

4. Kelley J. General topology, Toronto-London-New York: D van Nostard company, 1957, 432 p.

5. Vladimirov D. A. Bulevyalgebry (Boolean algebras), Moscow: Nauka, 1969, 318 p.

6. Vladimirov D. A. Teoriyabulevyhalgebr (The theory of Boolean algebras), St. Petersburg: Publishing house of the St. Petersburg University, 2000, 616 p.

7. Halmos P. Lectures on Boolean algebras, Prinston, New-Jersey. D. vanNostardcompany, 1963, 96 p.

8. Mayaram D. An algebraic characterization of measure algebras, Ann. Math., 1947, v. 48, № 1, pp. 154–167.

9. Popov V. A. Additivnyeipoluadditivnyefunkciinabulevyhalgebrah (Additive and semiadditive functions on Boolean algebras), Sibirsk. mat., 1976, vol. 17, No 2, pp. 331–339.

10. Alexyuk V. N. Teorema o minorante. Schetnost’ problemyMagaram (The Minorant Theorem. The countability of the problem of Magaramz), Mathematics, 1977, t. 21, No. 5, pp. 597–604.

11. Lovyagin Yu. N. Bulevyalgebry s dostatochnymchislomnepreryvnyhkvazimer (Boolean algebras with a suﬃcient number of continuous quasimers), Syktyvkar: Dep. in VINITI, № 3111-В97, 1997, 24 p.

12. Lovyagin Yu. N. O nekotoryhsvojstvahbulevyhalgebr (On some properties of Boolean algebras), Some actual problems of modern mathematics and mathematical education: Proceedings of the scientiﬁc conference «Herzen readings — 2009», SPb: RSPU them. A. I. Herzen, 2009, pp. 131–135.

13. Lovyagin Yu. N. Regulyarnyeipolunormirovannyebulevyalgebry (Regular and semi-normalized Boolean algebras), Some actual problems of modern mathematics and mathematical education: Proceedings of the scientiﬁc conference «Herzen readings — 2011», SPb: RSPU them. A. I. Herzen, 2011, pp. 146–148.

14. Lovyagin Yu. N. Primer regulyarnoj, no nenormirovannojbulevyalgebry (An example of a regular but not normalized Boolean algebra), Some actual problems of modern mathematics and mathematical education: Proceedings of the scientiﬁc conference «Herzen Readings — 2012», SPb: RSPU them. A. I. Herzen, 2012,pp. 129–130.

15. Lovyagin Yu. N. O problemenormiruemostibulevyhalgebr (On the problem of normability of Boolean algebras), Proceedings of the Russian Pedagogical University. A. I. Herzen, 2013, № 154, pp. 23–33.

16. Gaifman H. Cjncerning measure on Boolean algebras, Pacif. J. Math., 1964, v. 14, № 1, pp. 61–73.

For citation:Lovyagin Yu. N. Some remarks on the problem of the normability of Boolean algebras, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 43–55.

V. Pimenov R. R. The geometry of perpendicularity: obtuse and acutes angles in known theorems

In the article we introduce and research the conception of «the impossible conﬁguration of obtuse and acute angles» and its relation to theorems about perpendicularity in the plane and Rn. We study two theorems, about intersection altitudes in triangle and about projections, the last we named as «the domino theorem». We generalise both theorems for arbitrary numbers of lines and discover related with them impossible conﬁguration of angles. We show as using continuity and method of «small moving» we can derive theorems about perpendicular lines from impossible conﬁgurations of angles. We view at the right angle as the boundary between acute and obtuse angles for this. We consider the using of these methods in non-Euclidean geometry, in Rn and express them in terms of vector algebra.

Keywords: perpendicularity, continuity, projection, orientation, altitude of triangle.

References:

1. Bachmann F. Postroeniegeometriinaosnoveponyatiyasimmetrii (Aufbau der GeometrieausdemSpiegelungsbegriﬀ), М.: Nauka, 1969, 380 p. 2. Tabachnikov S. Skewers, Arnold Mathematical Journal,

2, 2016, pp. 171–193.

3. Pimenov R. R. K logicheskiminaglyadno-geometricheskimsvojstvamorientacii 1 (About logic and visual-geometric properties of orientation 1), MatematicheskyvestnikpedvuzoviyniversitetovVolgoViatskogoregiona: periodicheskymejvuzovskysborniknauchno-metodicheskyhrabot, Kirov: Naucn. izd-voViatGU, 2016, vyp. 18, pp. 99–114.

4. Pimenov R. R. K logicheskiminaglyadno-geometricheskimsvojstvamorientacii 2 (About logic and visual-geometric properties of orientation 2), MatematicheskyvestnikpedvuzoviyniversitetovVolgoViatskogoregiona: periodicheskymejvuzovskysborniknauchno-metodicheskyhrabot, Kirov: Naucn. izd-voViatGU, 2016, vyp. 18, pp. 115–126.

5. Pimenov R. R. ObobshcheniyateoremyDezarga: geometriyaperpendikulyarnogo (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.

6. Pimenov R. R. TraktovkiteoremPappa: perpendikulyarnost’ iinvolyutivnost’ (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.

7. Pogorelov A. V. Osnovaniyageometrii (The foundation of geometry), 3-e izdanie, Moskva: Nauka, 1968, 208 p.

8. Pimenov R. I. Edinayaaksiomatikaprostranstv s maksimal’nojgruppojdvizhenij (Uniﬁedaxiomatics of spaces with the maximum group of motions), Litovsk. Mat. Sb., 5, 1965, pp. 457–486.

9. SkopenkovMichail. Naglyadnayageometriyaitopologiya (Visual geometry and topology), URL: http://skopenkov.ru/courses/geometry16.html.

For citation:Pimenov R. R. 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.

VI. Gulyaeva S. T., Kabanova S. L., Mironov V. V. To a problem of increase in eﬀectiveness of educational process when using the modern systems of the organization of videoconferences

In work topical issue of increase in eﬀectiveness of educational process when using the modern systems of the organization of videoconferences is considered. The chart of business process of use of videoconferences is provided and technologies and most the videoconferences popular systems are considered.

Keywords: education, videoconference, eﬀectiveness, business process, videoconferencing.

References:

1. Videokonferencsvjaz’. Avtor: KompanijaTrueConf // https:// trueconf.ru/: TrueConf 7.2 для Windows. URL: https:// trueconf.ru/ videokonferentssvyaz/070 (date of the application: 10.07.2017).

2. Chtotakoe VoIP? // http://aver.ru/: Vsyo o novinkaxtexniki. URL: http://aver.ru/all/chto-takoe-voip/ (date of the application: 10.07.2017).

3. Oborudovaniedljaprovedenijavideokonferencij // https:// www.insotel.ru/: Insotel. URL: http:// www.insotel.ru/article. php?id=31 (date of the application: 10.07.2017).

4. Obzorstandartovperedachidannyhispol’zuemyh v videokonferencsvjazi // http:// www.ipvs.ru/: IP Video Systems. URL: http:// www.ipvs.ru/information/videoconferencing/113-protocols-videoconferencing-data.html (date of the application: 10.07.2017).

5. Skype // https:// ru.wikipedia.org/wiki: Wikipedia. URL: https:// ru.wikipedia.org/wiki/Skype (date of the application: 10.07.2017).

6. Sistemy VKS Polycom // https:// www.nav-it.ru/: Gruppakompanij navigator. URL: http://www.nav-it.ru/services/system-integration /videokonferentssvyaz/sistemy-vks-polycom/ (date of the application: 10.07.2017).

7. O kompanii Life size // http:// av-pro.com.ua/: Kompaniyaavpro. URL: http://av-pro.com.ua/taxonomy/term/15/0 (date of the application: 10.07.2017).

8. Videokonferencsvjaz’. Chast’ 1: Vvedenie v predmet // http://networklab.ru/: Setevayaakademiya CISCO. URL: http:// network-lab.ru/ videokonferentssvyaz-chast-1-vvedenie/ (date of the application: 10.07.2017).

9. Prodazhaoborudovanija Polycom // http:// www.polycom-spb.ru: Polycom. URL: http://www.polycom-spb.ru/Polycom_HDX_70001080 (date of the application: 10.07.2017).

For citation:Gulyaeva S. T., Kabanova S. L., Mironov V. V. To a problem of increase in eﬀectiveness of educational process when using the modern systems of the organization of videoconferences, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 74–87.

VII. Odyniec W. P. On a history of some mathematical models in ecology

The prehistory of the appearance of some mathematical models and methods in ecology is brieﬂy reviewed. History the ﬁve mathematical models reviewed in detail: the model, which based on multifractal analysis, the model of absorption by rain of pollution of atmosphere, the Lotka–Volterramodelsand their development, the model of the population stability by the genetic level.

Keywords:Margalef index, Hedervari estimation, multifractal analysis, the Lotka–Volterra models, repressilator.

References:

1. Abdurakhmanov A. I., Firstov P. P., Shirokov V. A. Vozmozhnayasvyaz’ vulkanicheskihizverzhenij s ciklichnost’yusolnechnojaktivnosti (A possible connection of volcanic eruption and the cyclicity of the sun activity), Bul. vulcanol. stancii, № 52, 1976, pp. 3–11.

2. Bagotskii S. V., Bazykin A. D., Monastyrskaya N. P. Matematicheskiemodeli v ehkologii (Mathematical models in ecology), Bibliographicheskiiukazatel’ otechestvennyhrabot, Moscow: VINITI, 1981, 224 p.

3. Bo¨ckman C. Hybrid regularization method for the ill-possed inversion of multiwave length lidar data to determine aerosol size distribution, Applied Optics, 40 (2001), pp. 1329–1342.

4. Borisenkov E. P., Paseckii V. M. Ekstremal’nyeprirodnyeyavleniya v russkihletopisyah XI–XVII vv (Extremal natural phenomena in the Russian chronicles), Leningrad: Gidrometeoizdat, 1983, 241 p.

5. Bullard F. M. Volcanoes in history, in theory, in eruption, Austin: Univ. Texas Press, 1962, 441 p.

6. Vlodavets V. I. VulkanyZemli (Volcanoes of the Earth), Moscow: Nauka, 1973, 169 p.

7. Volterra V. The changes and variations in the number of a coexisting animal species, Mem. R. Accad. Naz. deiLincei, Ser. 2., 1926, pp. 31–113.

8. Gelashvili D. B., Yakimov V. N., Iudin D. I., Dmitriev A. I., Rosenberg G. S., Solncev L. A. Mul’tifraktal’nyjanalizvidovojstrukturysoobshchestvamelkihmlekopitayushchihNizhegorodskogoPovolzh’ya (Multifractal analysis of species structure of company of the small mammal situated on Volga around from Nizhny Novgorod), Ecologiya, № 6, 2008, p. 456–461.

9. Georgi I. About the self-in ﬂammableend of city dump of Revel, In: The selection of economical work’s which support for German language the Free Economical Society of St. Petersburg, vol. 3, St. Petersburg, 1791, pp. 330–331.

10. Glyzin S. D., Kolesov A. Yu., Rozov N. Kh. Sushchestvovanieiustojchivost’ relaksacionnogociklaimatematicheskojmodelirepressilyatora (The existence and stability ofa relaxation cycle and mathematical model of a repressilator), Matemat. Zametki, vol. 101, № 1, 2017, pp. 58–76.

11. Gulamov M. I. Teoretiko-gruppovojpodhod k issledovaniyuvzaimodejstviyaehkologicheskihfaktorov (A Group – The oretic Approach towards the Study in Interaction of Environmental Factors), Ecologicheskayachimiya, 21 (1), 2012, pp. 1–9.

12. Kolmogorov A. N. The Theory by Volterra of survival struggle for existence, G. Inst. Ital. Attuari, 7, № 1, 1936, pp. 74–80.

13. Kolmogorov A. N. Kachestvennoeizucheniematematicheskihmodelejdinamikipopulyacij (Qualitative research of mathematical models of dynamics of population), Problemycybernetiki, № 25, Moscow: Nauka, 1972, pp. 100–106.

14. Krasheninnikov S. P. OpisanieZemliKamchatki (A Description of the Land of Kamchatka), St. Petersburg: 1755, vol. 1 and vol. 2 (Reprint. Reproduction, St. Petersburg: Nauka, 1994, vol. 1, 440 p.; vol. 2, 320 p.).

15. Lotka A. To towards the Theory of Periodical Reactions, Z. Physics. Chem., 72, (1910), pp. 508–511.

16. Mandelbrot B. Fractals: Form, Chance and Dimension, San-Francisco: W. H. Freeman and Co., 1977, 365 p.

17. Margalef R. Oblikbiosfery (Our biosphere), (Transl. from Spanisz.), Moscow: Nauka, 1992, 254 p.

18. Moiseev N. N. Ekologiyachelovechestvaglazamimatematika (The ecology of mankind through the eyes of a mathematician), Moscow: Molodayagvardiya, 1988, 255 p.

19. Nikonenko V. A., Tyantova E. N. Model’ pogloshcheniyadozhdyomzagryaznyayushchihveshchestvizatmosfery (Model of absorption of pollutants from atmosphere by a rain), Ekologicheskayachimiya, 2010, 19 (2), pp. 98–104.

20. Odyniec W. P. Zarisovkipoistoriikomp’yuternyhnauk (Sketches in the history of computer sciences), Syktyvkar: Izdatelstvo Komi GPI, 2013, 421 p.

21. Orlov K. G., Mingalev I. V., Mingalev V. S., Chechetkin V. M., Mingalev O. V. ChislennoemodelirovanieobshchejcirkulyaciiatmosferyZemlidlyauslovijzimyileta (Numerical Modelling of the global circulation for of the Earth atmosphere by winter and summer conditions), Trudy Kolskogonauchnogocentra, Geliogeophisika, Vyp. 1-6/2015, Apatity: Polyarnyigeophisicheskii institute, 2015, p. 140-145.

22. Pallas R. S. A travel through various Provinces of the Russian Empire, part 2, the book 2, St. Petersburg: 1773, pp. 54–57.

23. Pannikov V. D., Mineev V. G. Pochva, klimat, udobreniyaiurozhaj (Soil, climate, fertilizere and harvest), Moscow: Kolos, 1977, 413 p.

24. Pegov S. A., Khomyakov P. M. Modelirovanierazvitiyaehkologicheskihsistem (The modelling of development of ecologic systems), St. Petersburg: Nauka, 1991, 218 p.

25. Petrosyan L. A., Zakharov V. V. Vvedenie v matematicheskuyuehkologiyu (Introduction to mathematical ecology), Leningrad: Leningrad State University Publishers, 1986, 222 p.

26. Pihlak A.-T. A. Zametkipoistoriiissledovaniyaprocessovsamovozgoraniyai problem kislorodaatmosfery v EHstonii (An overview on the history of self-ingition and air oxygen problem in Estonia), Ecologicheskayachimiya, 2009, 18 (1), pp. 31–40.

27. Romashev Yu. A., Skorobogatov G. A. Deterministskoeistohasticheskoemodelirovaniyaehkosistemy (zhertva–hishchnik), himicheskojsistemy (goryuchee–okislitel’), ehkonomicheskojsistemy (resursy–industriya) (Deterministic and stochastic modelling of the ecosystem (predator–pray), chemical system (fuel– oxidizer), economical system (resources–industry)), Ecologicheskayachimiya, 20 (3), 2011, 129–149 p.

28. Trifonova T. A., Il’ina M. E. Ekologicheskijmenedzhment: prakticheskieaspektyprimeneniya (Ecological management: some practical aspects of application), Vladimir: ARKAIM, 2015, 362 p.

29. Forrester J. Mirovayadinamika (World Dynamics), (Transl. from Wright-Allen Press, 1971), Moscow: AST, 2008, 384 p.

30. Harrington E. C., Jr. The Desirability Function, Industrial Quality Control, vol. 21, № 10, 1965, pp. 494–498.

31. Hedervari P. On the energy and magnitude of volcanic eruption, Bul. volcanologiq., XXV, 1963, pp. 373–379.

32. Shepherd E. S. The analysis of gases obtained from volcanoes and from rocks, J. Geol., vol. 33, № 3, 1925.

33. Elovitz M. B., Leibler S. A synthetic oscillatory network of transcriptional regulators, Nature, 403 (2000), pp. 335–338.

34. Yachmennikova N. Letimskvoz’ pepel (Flying through aches), Rosijskayagazeta, № 139 (7305) from 28.06.2017.

For citation:Odyniec W. P. On a history of some mathematical models in ecology, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 88–103.

VIII. Ustyugov V. A., Chufyrev A. E. The percolation problem

The article gives an overview of algorithms for solving the problem of ﬁnding a spanning cluster on a square lattice. A technique for determining the percolation threshold is described. The singular behavior of the last dependence in the vicinity of the critical concentration is explained. The solution of the problem in the form of a program in Python programming lagnuage is given.

Keywords: percolation, spanning cluster, Hoshen-Kopelman algorithm.

References:

1. Giordano N. J. Computational physics / N. J. Giordano, H. Nakanishi, Pearson/Prentice Hall, 2006, 544 p.

2. Gould H., Tobochnik J. Komp’yuternoemodelirovanie v ﬁzike (Computer modelling in physics), M.: Mir, 1990, 400 p.

3. Tarasevich Yu. Yu. Perkolyaciya: teoriya, prilozheniyaialgoritmy (Percolation: theory, application, algorithms), M.: Editorial URSS, 2002, 112 p.

For citation:Ustyugov V. A., Chufyrev A. E. The percolation problem, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 104–113.

IX. Vechtomov E. M. Yevgeny IlyichMikhailovsky (to the ﬁftieth anniversary from the birthday)

The article is devoted to the prominent scientist, the deserved ﬁgure of science of the Russian Federation, the head of the school of mechanics of the Komi Republic, the doctor of physics and mathematics, professor EvgenyMikhailovsky.

For citation:Vechtomov E. M. Yevgeny IlyichMikhailovsky (to the ﬁftieth anniversary from the birthday), Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 114– 117.

Bulletin 4 (25) 2017

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Issue 4 (25) 2017

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.

Bulletin 1 (26) 2018

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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

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

Shavrov V. G., Shcheglov V. I. Magnitostaticheskiye i elektromagnitnyye volny v slozhnykh strukturakh (Magnetostatic and electromagnetic waves incomplex structures), M.: FIZMATLIT, 2017, 360 p.
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.
Vinogradov A. P. Elektrodinamika kompozitnykh materialov (Electrodynamics of composite materials), M.: URSS, 2001, 207 p.
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).
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.
Barta O., et al. Magneto-optics in bi-gyrotropic garnet waveguide // Opto-electronics review. Vol. 9. № 3. 2001. Pp. 320–325.
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.
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.
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.
Rychly J. et al. Magnonic crystals — Prospective structures for shaping spin waves in nanoscale // Low Temperature Physics. Vol. 41. № 10. 2015. Pp. 745–759
Gurevich A. G., Melkov G. A. Magnitnyye kolebaniyai volny (Magneticoscillations and waves), M.: Nauka, 1994, 464 p.
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.
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.
Elsgolz L. E. Differentsialnyy euravneniya i variatsionnoye ischisleniye(Differential equations and the calculus of variations), M.: URSS,2002, 320p.
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

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

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.
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.
Malenkov G. G. Struktura i dinamika zhidkoyvody (Structure and dynamics of liquid water), Journal of Structural Chemistry, 2006, v. 47, pp. 5–35.
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.
Landau L. D., Lifshitz E. M. Statisticheskaya fizika (Statistical physics), Part 1, Moscow: Fizmatlit, 2010, 616 p.
Wang Kuo-Ting, Brewster M.Q. An Intermolecular Vibration Model for Lattice Ice //International Journal of Thermodynamics. 2010. V. 13. № 2. Pp. 51–57.
Eisenberg D., Kautsman V. Struktura i svoystvavody (Structure and properties of water), Moscow: Direct-Media, 2012, 284 p.
Enochovich A. S. Spravochnik po fizike i tekhnike (Reference book on physics and techniques), Moscow: Prosveshenie, 1989, 224 p.
Zatsepina G. N. Fizicheskiye svoystva i strukturavody (Physical properties and structure of water), Moscow: Moscow State University, 1998, 184 p.
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.
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

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

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.
Nikolai E. L. Trudi po mexanike (Works on mechanics), M.: Isdatelstvotexniko-teoretiteskoiliteraturi, 1955, 376 p.
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.
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

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

Pierrard V., Lazar M. Kappa distributions: theory and applications in space plasmas // Solar Physics. 2010. V. 267. Pp. 153–174.
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).
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

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

Keywords: two-dimensional ternary search, competitive programming.

References

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

Keywords: genetic algorithms, optimization, genom, individuals.

References

MacLeod C. An Introduction to Practical Neural Networks and Genetic Algorithms For Engineers and Scientists, p. 85.
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.
Panchenko T. V. Geneticheskie algotritmy (Genetic algorithms), pod red. U. U. Tarasevicha, Astrahan: Izdatelskiydom «Astrahanskiyuniversitet», 2007, p. 16.
Kudryavcev L. D. Matematicheskiyanaliz (Mathematical analysis), 2-e izd, M.: Vyshayashkola, 1973, v. 1, 687 p.
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).
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

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

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).
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).
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).
Sorevnovaniya po programmirovaniyu 2.0 (Programming competitions 2.0) URL: http://codeforces.com (date of usage: 19.02.2018).
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).
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.

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

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).
Arkhiv Sankt-Peterburgskogo gosudarstvennogo universiteta (St. Petersburg State University Archive), File 7240.14 № 191 (Order № 352а from 20/X–1932).
Bergmann S. Uberdie Kernfunktioneines Bereichs und ihrVerhalten am Rande. Teil 1 // J. furreine und angewandte Math. Bd. 169. Heft 1. 1932. S. 1–42.
Bergmann S. Uberdie Kernfunktioneines Bereichs und ihrVerhalten am Rande. Teil 2 // J. furreine und angewandte Math. Bd. 172. Heft 2. 1934. S. 89–128.
Bergmann S. Zur Theorie von pseudokon formen Abbildungen, Matem. Sbornik, t. 1 (43), No. 1, 1936, pp. 79–96.
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.
Bergmann S. Zur Theorie der linearen Integral — und Funktional gleichun genimcomplexen Gebiet, Izvestiya NIIMM TGU, Tomsk, vol. 1, issue 3, 1937, pp. 242–257.
Bergmann S. The Kernel Function and Conformal Mapping.- Cambridge (Massachusetts): Amer. Math. Society, 1950. 161 p.
Bergman S., Schiffer M. M. Kernel functions and elliptic differential equations in mathematical physics. New York: Academic Press, 1953. 432 p.
Bergmann S. Integral operators in the theory of linear partial differential equations. Berlin-New York: Springer, 1961, 2thed., 1969.
Brewer J. W., Smith M. K. (eds.) Emmy Noether: a tribute to her life and work. New York: Marcel Dekker, Inc., 1981. 237 p.
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.
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.
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.
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.
Muntz Ch. Zum Randwertproblem der partiellen Differential gleichung der Minimal flachen // J. fur Reineund Angew. Math. 139. 1911. S. 52–79.
Muntz Ch. Uber den Approximationssatz von Weierstrass / H. A. Schwarz–Festschrift. Berlin: 1914. S. 303–312.
Muntz Ch. Die Losung des Plateauschen Problems uberkonvexen Bereichen // Math. Ann., 94. No. 1–2. 1925. S. 53–96.
Gottfried Noether, 76: Educator in Statistics // New York Times. August 27, 1991. P. 22. (Obituary).
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.
Noether Fr. Asymptotische Darstellungen und Geometrische Optik, Izvestiya NIIMM TGU, Tomsk: 1937, t. 1, issue 3, p. 175–189.
NoetherFr. Zur Kinematik des starren Korpers in der Relativtheorie // Annalen der Physik. 336 (5). 1910. S. 914–944.
Noether Fr. Bemerkunguber die Losungszahlzueinan deradjungierten Randwertaufgaben beilinearen Differentialgleichungen // Sitzungsberichte der Heidelberger Akad. der Wissenschaft. Math. Nat. Klasse. 1920, I. Abhandlung. S. 37–52.
Noether Fr. Ubereine Klassesingularer Integralgleichungen // Math. Ann. Bd. 82. 1921. S. 42–63.
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.
Ortiz E. L., Pinkus A. Herman Muntz: A Mathematician’s Odyssey //Mathem. Intellig. Berlin. 27. 2005. S. 22–30.
Segal, Sanford L. Mathematicians under the Nazis. Princeton: Princeton University Press, 2003. 536 p.
Siegmund-Schulze R. Mathematiker auf der Fluchtvor Hitler.- Wiesbaden: Vieweg Verlag, 1998. 324 s.
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.

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

Guan Kaizhong. GA-convexity and its applications // Anal. Math. 2013. 39. № 3. Pp. 189–208.
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. 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.

Bulletin 3 (28) 2018

by

Issue 3 (28) 2018

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

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

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.
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).
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

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

Lamport L. LATEX: a document preparation system. 2 ed., AddisonWesley, 1994. 291 p.
Lvovski S. M. Nabor i verstka v sisteme LATEX (Typesetting in the LATEXsystem), 3rd ed, M.: MCNMO, 2003, 448 p.
Kotelnikov I. A., Chebotarev P. Z. LATEX 2_εpo-russki (LATEX 2ε in Russian), 3rd ed, Novosibirsk: Siberian chronograph, 2004, 496 p.
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.
Knut D. E. Vse pro TEX (All about TEX), M.: Williams, 2003, 560 p.
Hammerlindl A., Bowman J., Prince T. Asymptote: the Vector Graphics Language, 2016. 189 p.
KryachkovYu. G. Yevklidova geometriya na yazyke vektornoygra fiki ASYMPTOTE (Euclidean geometry with a symptote), Volgograd: VGSPU, 2015, 88 p.
Goossens M., Rahtz S., Mittelbach F. The LATEX graphics companion: illustrating documents with TEX and PostScript. Addison Wesley, 1997. 299 p.
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
KiryutenkoYu. A. TikZ&PGF. Sozdaniyegrafiki v LATEX 2εdokumentakh (TikZ& PGF. Creating graphics in LATEX 2ε-documents), Rostov-on-Don, 2014, 277 p.
Tantau T. The TikZand PGF Packages. Manual for version 2.10. Institutf¨ ur Theoretische Informatik Universit¨ atzuL¨ubeck, 2010. 880 p.
Taft E., Chernicoff S., Rose C. PostScript language reference manual. 3 ed. Adobe Systems Incorporated, 1999. 912 p.
Reid G. C. Thinking in PostScript. Addison-Wesley Publishing Company, 1990. 239 p.
PostScript language. Tutorial and cookbook. Addison-Wesley Publishing Company, 1985. 247 p.
Casselman B. Mathematical illustrations: a manual of geometry and PostScript. Cambridge University Press, 2004. 264 p.
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.
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).
Baldin E. M. Sozdaniye illyustratsiy v METAPOST (Creating illustrations in METAPOST), Linux Format, № 6–10, 2006.
Knut D. E. Vse pro METAFONT (All about METAFONT), M.: Williams, 2003, 376 p.
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).
Guibe O., Ivaldi P. geometry.asy. Euclidean geometry with asymptote. 2011. 95 p.
Belyaev Yu. N. Vektornyy i tenzornyyanaliz (Vector and tensor analysis), Syktyvkar: Syktyvkar State University, 2010, 298 p.
Kabardin O. F. Tranzistornaya elektronika. Spetspraktikum (Transistor electronics. Special Practice), M.: «Education», 1972, 207 p.
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

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

Polikarpova N. Avtomatnoye programmirovaniye (Automata programming), SPb: Piter, 2011, 176 p.
Morton J. Mikrokontrollery AVR. Vvodnykurs (AVR microcontrollers. Introductory course), M.: Dodeka, 2010, 271 p.
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

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

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
Smolyaninov I. I. Hyperbolic metamaterials, ArXiv:1510.07137 [physics. optics].
Katanaev M. O. Geometricheskie metody v matematicheskoj fizike (Geometric methods in mathematical physics), ArXiv:1311.0733[mathph].
Shabad A. E. Singulyarnyj centrkaknegravitacionnaya chernaya dyra (Singular center as a non-gravitational black hole), TMF, 2014, t. 181, N 3, pp. 603–613.
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.
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.
Case K. M. Singular potentials, Phys. Rev., 1950, vol.80, pp. 797–806.
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.
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

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

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.
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.
Vyaly M. N. Pfaffiany, iliiskusstvorasstavlyat’ znaki (Pfaffians, or the art to set signs), Matematich eskoeprosv eshchenie, 2005, vyp. 9, pp. 129–142.
Schwarz M. Efficiently computing the permanent and Hafnian of some banded Toeplitz matrices // Linear Algebra and its Applications. 2009. V. 430. Pp. 1364–1374.
Efimov D.B. The hafnian and a commutative analogue of the Grassmann algebra // Electronic Journal of Linear Algebra. 2018. V. 34. Pp. 54–60.
Sloane N. J. A., editor The On-Line Encyclopedia of Integer Sequences, published electronically at https://oeis.org.
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.
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

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

Gallica. http://gallica.bnf.fr (date of the application: 05.10.2018)
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).
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.
Depman I. Ya. S.-Peterburgskoye matematicheskoy eobshchestvo (S.-Petersburg Mathematical Society), Historical-mathemftical investigation, 13, 1960, pp. 11–106.
Protokoly S.-Peterburgskogom atematicheskogo obshchestva (S.-Petersburg Mathematical Society protocols), St.P., 1899.
Brockhaus F. A., Efron I. A. Enciclopedia, Ripol Classic, Moscow, 2013.
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.
Government of Saint-Petersburg, Law N 88/1-rp 11.07.2005.
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.
Kochina P. Ya. S. V. Kovalevskaya, Moscow, Nauka, 1981.
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

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

Bauer M. E. Reminiscences of an ordinary man. SPb: ASSPIN Peterhof, 2003, 87 p.
Bauer S. Upon the Schwarz differential invariant, Mat. sbornik, V. 41, No. 1, 1934, p. 104–106.
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.).
Burstin C. Beitragezum Problem von Pfaff und zurTheorie der Pfaffschen Aggregate. I. Beitrag // Матем. сборник. Т. 37, № 1–2. 1930. C. 13–22.
Burstyn C. Mathematical Works, Minsk: Institute for Physics and Mathematics of the Belorussian Academy of Sciences, 1932, 76 p.
Burstyn C. A. Course of differential geometry, Mensk: State publishes of Belorussia. Scientific and Educations Sector, 1933, 338 p.
Burstyn C. Physical methods of mathematics, Minsk:Institute for Physics and Technics of the Belorussian Academy of Sciences, 1933, 34 p.
Grommer J. Ganzetranszendente Funktionenmitlauterreelen Nulstelen // J. fur reineundangew. Math., Bd. 144. 1914. S. 114–165.
Grommer J. Betragzum Energiesatz in der allgemeinen Relativit¨atstheorie // Sitzungberichte der Prussschen Akademie der Wissenschaft, Kl. 1919. S. 860–862.
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.).
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.
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.
Joffe A. F. Vstrechi s fizikami. Moivospominaniya o zarubezhnykhfizikakh (Encounters with physicists. My recollection of foreign physicists). Leningrad: Nauka, 1983, 262 p.
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.
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.
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.
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.)
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.
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.

Bulletin 2 (27) 2018

by

Issue 2 (27) 2018

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

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

Belyaeva N. A. Neodnorodnoye techeniye strukturirovannoy zhidkosti (The inhomogeneous flow of a structured liquid), Mathematical modeling, 2006, vol. 18, No. 6, pp. 3–14.
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.
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.
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.
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

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

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.
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.
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.
Smolyaninov I. I. Hyperbolic metamaterials; arXiv: 1510.07137.
Green M. B., Schwartz J., Witten E. Teoriya superstrun (Theory of superstrings), Moscow: Mir, 1990.
Kaku M. Vvedeniye v teoriyu superstrun (Introduction to the theory of superstrings), Moscow: Mir, 1999, 624 p.
Bars I. Relativistic Harmonic Oscillator Revisited, Phys. Rev. D, v. 79, Iss. 4. 045009. 2009, arXiv: 0810.2075.
8. Betemmen G., Erdei A. Vysshiye transtsendentnyye funktsii (Higher transcendental functions), M.: Mir, 1973, vol. 1.
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.
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.
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

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

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.
Belyaeva N. A. Matematicheskoe modelirovanie: uchebnoe posobie (Mathematical modeling: tutorial). Syktyvkar: Publishing house of Syktyvkar state University, 2014. 116 p.
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.
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.
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.
Carslaw H. S., Jaeger J. S. Operatsionnyye metody v prikladnoy matematike (Operational methods in applied mathematics. M.: IL, 1948. 294 p.
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

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

Nielsen M. A., Chuang I. L. Kvantovyye vychisleniya i kvantovaya informatsiya (Quantum Computation and Quantum Information), Cambridge University Press, 2010, 676 p.
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.
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.
Gromov N. A. Kontraktsii klassicheskih i kvantovyh grupp (Contractions of classical and quantum groups), M.: Fizmatlit, 2012, 318 p.
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.
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

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

Cameron P. J. Projective and Polar Spaces, second edition, Sep 2000. http://www.maths.qmul.ac.uk/ pjc/pps/
Birkhoffff G. Teoriya reshetok (Lattice Theory), М.: Nauka, 1984, 565 p. Aigner M. Kombinatornaya teoriya (Combinatorial Theory), M .: Mir, 1982, 556 p.
Bachmann F. Postroenie geometrii na osnove ponyatiya simmetrii (Aufbau der Geometrie aus dem Spiegelungsbegriffff), М.: Nauka, 1969, 380 p.
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.
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)
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)
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.
Vasukov V. L. Kvantovaya logika (Quantum logic), M.: Per Se, 2005, 191 p.
Tabachnikov S. Skewers, Arnold Mathematical Journal, 2, 2016, pp. 171–193.
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.
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.
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»

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

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.
Kazakov A. In Commemoration of the Late Professor Lev N.Gutman, Ukrainskii gidrometeorologichnyi zhurnal, No. 4, 2009, pp. 11–12.
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.
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.
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.
Frankl F. Upon the theory of prime ends (Doctorate Thesis), Wien, University, 1927, 25 Bl, Verbund-ID-Nr.AC06513142.
Frankl F., Pontryagin L. A Knoth Theorem with the application to the dimension theory, Mathem. Annalen, v. 102, No.1, 1930, pp. 785–789.
Frankl F. Characterizing of (n-1)-dimension closed set of Rⁿ, Mathem. Annalen, vol. 103, No. 1, 1930, pp. 784–787.
Frankl F. Upon the theory of prime ends, Mat. Sbornik, 38, No. 3–4, 1931, pp. 66–69.
Frankl F. Upon the topology of the three-dimensional space, Monats-hefte f¨ur Mathem. und Physik, 38, 1931, p. 357–364.
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.
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.
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.
Frankl F. I., Khristianovich S. N., Alekseeva R. N. Osnovy gazovoy dinamiki (Foundation of Gas Dynamics), Issue 364, Moscow: CAGI, 1938, 111 p.
Frankl F. I., Karpovich E. A. Gazodinamika tonkikh tel (Gas dynamics of thin bodies), Moscow-Leningrad: GTTL, 1948, 175 p.
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.
Frankl F. I., Sukhomlinov G. A. Vvedeniye v mekhaniku deformiruyemykh tel (Introduction to the mechanics of deformed bodies), Frunze: 1954, 204 p.
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.
Frankl F. I. Izbrannyye trudy po gazovoy dinamike (Selected works of gas dynamics), Moscow: Nauka, 1973,711 p.
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.
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

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

Mikhailovskii E. I., Toropov A. V. Matematicheskie modeli teorii uprugosti (Mathematical models of the theory of elasticity). Syktyvkar: Syltyvkar University, 1995. 251 p.
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
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.
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.
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)

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

Zagashev I. O., Zair-Bek S. I. Kriticheskoye myshleniye: tekhnologii razvitiya (Critical thinking: development technologies), St. Petersburg, 2003. 284 p.
Pedagogika vysshey shkoly (Pedagogy of Higher School), Textbook. allowance, under the general ed. O. B. Uvarovskaya, Syktyvkar: Publishing House of Syktyvkar State University, 2013.
Polat E. S. Novyye pedagogicheskiye i informatsionnyye tekhnologii v sisteme obrazovaniya (New pedagogical and information technologies in the education system), Moscow: Academy, 2000.
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.
Kurosh A. G. Kurs vysshey algebry, devyatoye izdaniye (Course of Higher Algebra. Ninth edition), Moscow: Nauka, 1968.
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.
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.

Bulletin 4 (29) 2018

by

Issue 4 (29) 2018

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

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

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.
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

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

Gazovozy. Avtotsisterny SUG (Gas carrier. Tankers), Liquefied petroleum gas. URL: https://rodisgroup.ru (date of the application: 28.11.2018).
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.
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.
Rachevsky B. S. Szhizhennyye uglevodorodnyye gazy (Liquefied petroleum gases), Moscow, Oil and gas Publ, 2009, 164p.
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.
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.
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

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

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.
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.
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

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

Beale J. T., Rosencrans I. Acoustic boundary conditions, Bull. Amer. Math.Soc., 1974, 80, pp. 1276–1278.
Beale J. T. Spectral properties of an acoustic boundary condition, Indiana Univ. Math. J., 1976, 25, pp. 895–917.
Beale J. T. Acoustic scattering from locally reating surfaces, Indiana Univ. Math. J., 1977, 26, pp. 199–222.
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.
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.
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.
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

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

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.
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.
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

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

10 Principles of Citizen Science. URL: https://ecsa.citizen-science.net/engage-us/10-principles-citizenscience (date of the application 06.12.2018).
List of citizen science projects. URL: https://en.wikipedia.org/wiki/List_of_citizen_science_projects (date of the application 07.12.2018).
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).
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).
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).
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).
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).
Roboty (Robots), Documentation of Telegram. URL: https:// tjournal.ru/tech/56573-svyaznoy-bot-quest (date of the application 16.12.2018).
«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

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

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
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.
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.
Abramova G. S., Stepanovich V. A. Delovyye igry: teoriya i organizatsiya (Business games: theory and organization), Ekaterinburg: Business book Publ., 1999, 192 p.
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.
Dewey J. Obrazovaniye konservativnoye i progressivnoye / Demokratiya i obrazovaniye (Conservative and progressive education /Democracy and education), Moscow: Pedagogy Press Publ., 2000, 384 p.
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.
Clear J. Sistemologiya. Avtomatizatsiya resheniya sistemnykh zadach (Systematology. Automation of solving system problems), Moscow: Radio and communication Publ., 1990, 544 p.
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.
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.
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

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

Anfilatov V. S., Emelyanov A., Kukushkin A. A. Sistemnyy analiz v upravlenii (System analysis in management), Moscow, Finance and statistics Publ., 2002, 368 p.
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.
Clear J. Sistemologiya. Avtomatizatsiya resheniya sistemnykh zadach (Systemology. Automation of solving system problems), Moscow: Radio and communication Publ., 1990, 544 p.
Matematicheskiy entsiklopedicheskiy slovar’ (Mathematical encyclopedic dictionary / Prokhorov), Moscow, Big Russian encyclopedia Publ., 1995, 847 p.
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).
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.
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).
Pegat A. Nechetkoye modelirovaniye i upravleniye (Fuzzy modeling and control), translated from English, Moscow, BINOM. Laboratory of knowledge, 2009, 798 p.
Sovetov B. Y., Yakovlev S. A. Modelirovaniye sistem (Modeling of systems), Moscow, Higher school Publ., 1985, 271 p.
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)

References

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.
Arteev A. Most cherez propast’ Lagranzha (Bridge across the Lagrange chasm), Youth of the North, 2003, No. 38, September 18, p. 12.
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.
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.
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.
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.
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.