Bulletin 18 2013

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Issue 1 (18) 2013

I. Belyayev Yu.N., Popov S.À. Transfer matrix of elastic deformations in crystals

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Differential equations of elastic waves in crystals are solved using sixth-order symmetric polynomials and scaling method. Influence of layer thickness and frequency of the wave by the scaling factor is investigated. Analytic solution describing the transfer of elastic stresses in the crystalline layer of the cubic system is obtained.

Keywords: layered media, waves, matrix, symmetric polynomials, truncation error, scaling.

References

  1. Молотков Л. А. Матричный метод в теории распространения волн в слоистых упругих и жидких средах. Л.: Наука. 1984. 201 с.
  2. Бреховских Л. М., Годин О. А. Акустика слоистых сред. М.: Наука. 1989. 416 с.
  3. Красильников В. А., Крылов В. В. Введение в физическую акустику. М.: Наука. 1984. 400 с.
  4. Беляев Ю. Н. К вычислению функций матриц // Математические заметки, 2013. Т. 94, Вып. 2, С. 175-182.
  5. Сиротин Ю. И., Шаскольская М. П. Основы кристаллофизики. М.: Наука. 1979. 640 с.
  6. Беляев Ю. Н. Симметрические многочлены в расчётах матричной экспоненты // Вестник СыктГУ, Сер.1 Математика, механика, информатика, 2012. Вып. 16, С. 28-41.

II. Kalinin S.I. Flett’s theorem about the mean value and its generalizations

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References

  1. Flett T. M. A mean value theorem // Mathematical Gazette. 1958. Vol. 42, ќ 339. p. 38-39.
  2. Праздникова Е. В. Моделирование вещественного анализа в рамках аксиоматики для гипернатуральных чисел // Вестник Сыктывкарского университета. 2007. Сер. 1. Вып. 7. С. 41-66.
  3. Калинин С. И., Шихова А. В. Теорема Флетта в терминах односторонних производных // Математический вестник педвузов и университетов Волго-Вятского региона: Период. межвуз.сб. науч.-метод. работ. Выпуск 11. Киров: Изд-во ВятГГУ, 2009. С. 67-70.
  4. Калинин С. И. Теорема Флетта в терминах правосторонней производ-ной // Математика в образовании: Сб. статей. Вып. 8/Под ред. И. С. Емельяновой. Чебоксары: Изд-во Чуваш.ун-та, 2012. С. 275-278.
  5. Калинин С. И., Шихова А. В. Многомерный вариант теоремы Флетта //Математический вестник педвузов и университетов Волго-Вятского региона: Период. межвуз. сб. науч.-метод. работ. Выпуск 12. Киров: Изд-во ВятГГУ, 2010. С. 82-84.
  6. Калинин С. И. Теорема Флетта и ее обобщения // VI Уфимская международная конф., посв. 70-летию чл.-корр. РАН В. В. Напалкова: “Комплексный анализ и дифференциальные уравнения”: сборник тезисов. Уфа: ИМВЦ, 2011. С. 86-87.
  7. Finta B. A generalization of the Lagrange mean value theorem // Octogon. 1996. 4, № 2. p. 38-40.
  8. Калинин С. И. Теорема Ролля в контексте этапа обобщения работы с теоремой // Математика в школе. 2009. №3. С. 53-58.
  9. Брайчев Г. Г. Введение в теорию роста выпуклых и целых функций. М.:Прометей, 2005. 232 с.
  10.  Попов В. А. Новые основы дифференциального исчисления. Учеб. пособие для спецкурсов. Сыктывкар: “ПОЛИГРАФСЕРВИС”, 2002. 64 с.

III. Kostyakov Igor, KuratovVasiliy Schrodinger equations of RI systems

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The Schrodinger equation is derived by limiting transition of quantization procedure for relativistic particle.

References

  1. Ландау Л.Д., Лившиц Е.М. Квантовая механика (нерелятивистская теория).// М.: ФИЗМАТЛИТ, 2002. 808c.
  2. Henneaux M., Teitelboim C. Quantization of gauge systems. // Princeton Univ. Press, New Jersey, 1992. 540p.
  3. Deriglazov A, Rizzuti B.F. Reparametrization-invariant formulation of classical mechanics and the Schrodinger equation.// American Journal of Physics, V.79, N 8, 2011, Pp. 882-885. ArXiv:1105.0313 [math-ph].
  4. Дирак П.А.М. Лекции по квантовой механике. // Любое издание.
  5. Гитман Д.М., Тютин И.В. Каноническое квантование полей со связями.// М.: Наука, Гл.ред. физ.мат. лит., 1986. 216с.
  6. Уэст П. Введение в суперсимметрию и супергравитацию. // М.:Мир, 1989. 332с.

IV. Belyaeva N. A., Dovzhko E. S. Model of volume formation of the spherical product taking into account pressure

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The thermoviscoelastic model of volume formation of a polymeric product of a spherical form taking into account the nonzero critical depth of conversion of a hardening material is presented. Pressure is considered from a liquid layer on borders of the hardened part of a material. Results of the numerical analysis of dynamics of a tension, pressure are presented from a liquid layer on continuously growing firm part of a product.Keywords: thermoviscoelasticity, sphere, hardening, volume mode, critical depth of conversion, pressure, tension

References

  1. Беляева Н. А. Математические модели деформируемых структуриованных материалов. Монография. Изд-во СыктГУ, 2008. 116с.
  2. Беляева Н. А. Деформирование вязкоупругих материалов с изменяющейся структурой // Вестник Сыктывкарского университета.Сер1. Вып. 11. 2010. С. 52-75.
  3. Беляева Н. А. Деформирование вязкоупругих структурированных систем: монография. Lap Lambert Academic Publishing GmbH & Co. KG, Germany, 2011. 200 c.
  4. Беляева Н. А., Довжко Е. С. Отверждение сферического изделияс учетом давления перед фронтом // Вестн. Сыктывкарского ун-та.Сер.1: математ., мех., информ. Вып.12. 2010. С. 85-96.
  5. Довжко Е. С. , Беляева Н. А. Термовязкоупругое фронтальное отверждение сферического изделия с точки зрения непрерывно наращиваемого твердого тела с учетом давления перед фронтом отверждения. Федеральная служба по интеллектуальной собственности, патентам и товарным знакам РФ, Реестр программ для ЭВМ. Свидетельство о государственной регистрации программ для ЭВМ № 2010615793, 7 сентября 2010 г.
  6.  Беляева Н. А., Довжко Е. С. Напряженное состояние фронтально формируемого сферического изделия // Вестн. Удмуртского университета. Математика. Механика. Компьютерные науки. 2011. Вып. 2. С. 123-134.
  7. Отчет о научно-исследовательской работе в рамках федеральной целевой программы “Научные и научно-педагогические кадры инновационной России“ на 2009-2013 годы по теме: “Нелинейные модели и методы механики“, шифр 2010-1.1-112-024-024, № 02.740.11.0618(итоговый, этап № 6). Наименование этапа: “Отчетный“. М.: ВНТИЦ,2012. Инв. № 02301297038. 46 с.
  8. Довжко Е. С. , Беляева Н. А. Формирование осесимметричных полимерных изделий в режимах двустороннего фронта // Сб. статей Международной научно-практической конференции “Общество, Наука и Инновации“ 29-30 ноября 2013 г., в 4-х ч., Ч. 4., Уфа: РИЦ БашГУ, 2013. 272 с. С. 228-235.
  9. Беляева Н. А., Худоева Е. Е. Вычислительный комплекс “Термо вязкоупругие модели отверждения осесимметричных изделий“ // Вестн. Сыктывкарского ун-та. Сер.1: математ., мех., информ. Вып.14. 2011. C. 125-146.
  10. Беляева Н. А. Внутренние напряжения осесимметричных изделийв процессе их формирования с учетом ненулевой критической глубины конверсии // Вестн. Сыктывкарского университета. Сер.1. Вып. 16. 2012. С. 10-19.

V. Yermolenko A.V. Selecting a base surface in contact problems with a free boundary

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The contact problem for circular axisymmetric plates is considered. Values ofstress-strain state are compared using equations of Karman-Timoshenko-Naghdi reduced as to the lower face and to the middle surface.Keywords: theory of plates, contact problem, base surface.

References

  1. 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.
  2. Ермоленко А.В. Об одном варианте уточненной теории плоских пластин для решения контактных задач // Вестник Сыктывкарского университета. Серия 1. Мат. Мех. Инф. №14. 2011.С. 105 110.
  3. Ермоленко А.В. Аналитическое решение контактной задачи дляжестко закрепленной пластины и основания // В мире научных открытий. Красноярск: НИЦ, 2011. С.11-17.
  4. Михайловский Е.И., Ермоленко А.В., Миронов В.В., Тулубенская Е.В. Уточненные нелинейные уравнения в неклассических задачах механики оболочек. Сыктывкар: Изд-во Сыктывкарского ун-та, 2009. 141 с.
  5. Михайловский Е.И., Тарасов В.Н. О сходимости метода обобщенной реакции в контактных задачах со свободной границей //Российская АН. ПММ. 1993. Т. 57. Выпуск 1. С. 128-136.

VI. Nikitenkov V., Kholopov A. A stability of a flexible beam: (the critical forms in a non-uniform environment)

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Based on [1],[2],[4]we investigate the critical forms and the number (N) of sign-changing of a beam placed to a flexible environment both for the case of uniform environment and for the case of non-uniform environment when the rigidies on two sides differ. In the uniform case we investigate N in regard to the rigidity parameter. In the non-uniform case and for any N we offer the algorithm for finding the exact critical form.

References

  1. Никитенков В.Л., Жидкова О.А., Шехурдина Е.С. Границы нахождения критической силы для разномодульной среды// Вестн.Сыктывкарск. ун-та. Сер. 1. – 2012. – Вып. 15. – С. 127 – 136.
  2. Никитенков В.Л., Холопов А.А. Устойчивость гибкого стержня вупругой среде// Вестн. Сыктывкарск. ун-та. Сер. 1. – 2012. – Вып. 16. – С. 60 – 79.
  3. Михайловский, Е.И. Элементы конструктивно-нелинейной механики/ Е.И. Михайловский. – Сыктывкар: Изд-во СыктГУ, 2011. -212 с.
  4. Холопов А.А. Минимальные формы потери устойчивости стержняна границе жесткой упругой сред // Вестн. Сыктывкарск. ун-та.Сер. 1. – 1995. – Вып. 1. – С. 217 – 233.
  5. Вольмир, А.С. Устойчивость деформируемых систем/ А.С. Вольмир. – М.: Наука, 1967. – 984 с.

VII. Tarasov V.N., AndryukovaV.Yu.  On the stability of the rings with unilateral restrictions on the moving

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The problem of the stability of the ring with one-sided restrictions on the movement analytically solved. Two cases of external pressure: normal pressure and the external pressure of the central forces are considered. A comparative analysis of obtained results is made.Keywords: ring, critical load, sustainability, non-stretchable thread, variational problem, deflection.

References

  1. Тарасов В.Н. Об устойчивости упругих систем при односторонних ограничениях на перемещения. // Труды института математики имеханики. Российская академия наук. Уральское отделение. Том 11,№ 1, 2005. С. 177-188.
  2. Андрюкова В.Ю., Тарасов В.Н. Об устойчивости упругих систем с неудерживающими связями. // Известия Коми НЦ УрОРАН. 2013. №3(15). С. 12-18.
  3. Феодосьев В.И. Избранные задачи и вопросы по сопротивлению материалов./ – М.: Наука, 1967. 376 с.

VIII. Mironov V.V., Overin N.A. Tehnology of MPI of the solution of thestationary equation of heat conductivity

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In this work developed two parallel algorithms for finding solutions of the stationary heat conduction equation.

References

  1. Самарский А.А. Теория разностных схем. М. Наука. Гл. ред. физ.-мат. лит., 1989. 616 с.
  2. Антонов А.С. Параллельное программирование с использованием технологии MPI. М. Изд-во МГУ, 2004 . 71 с.
  3. Воеводин В.В., Воеводин В.В. Параллельные вычисления. СПб.: БХВ-Петербург, 2002. 602 с.

Bulletin 1 (19) 2014

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Issue 1 (19) 2014

I. Vechtomov Е. М ., Lubyagina Е. N. About semirings of partialfunctions

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The article is starting the study of semirings of partial functions and continuous partial functions with values in an arbitrary semiring S. It isshown that a semiring of partial S-valued functions is isomorphic to the corresponding semiring of total functions. It is proved that any T1-space Xis defined by the semiring of CP(X, S) of all continuous partial functionson X with values in a nonsingle-element topological semiring with a closedunit.

Keywords: semiring, topological space, semiring of partial functions.

References

  1. Вечтомов Е. М. Вопросы определяемости топологических пространств алгебраическими системами непрерывных функций / /Итоги науки и техники. ВИНИТИ. Алгебра. Геометрия. Топология. 1990. Т. 28. С. 3-46.
  2. Вечтомов Е.М. Определяемость топологических пространств полугруппами непрерывных частичных функций / / Киров, 1987. Деп.ВИНИТИ № 256-В88. 21 с.
  3. Вечтомов Е. М. О полугруппах непрерывных частичных функций на топологических пространствах / / УМН. 1990. Т. 46. Вып. 4-с. 143-144.
  4. Вечтомов Е. М., Лубягина Е. Н. Полукольца непрерывных[0, 1] -значных функций / / Фундаментальная и прикладная математика. 2012. Т. 17. Вып. 1. С. 53-82.
  5. Вечтомов Е. М ., Сидоров В. В., Чупраков Д . В. Полукольца непрерывных функций. Киров: Изд-во ВятГГУ, 2011. 312 с.
  6. Вечтомов Е. М ., Чупраков Д . В. Полукольца непрерывных функций со значениями в Т0-полукольцах / / Тенденции и перспективы развития математического образования: материалы XXXIII Междунар. науч. семинара преподавателей математики информатики ун-тов и пед. вузов, посвященного 100-летиюВятГГУ, 25-27 сент. 2014 г. Киров: Изд-во ВятГГУ, 2014 С. 145-147.
  7. Вечтомов Е. М ., Шалагинова Н. В. Простые идеалы в частичных полукольцах непрерывных [0,∞]-значных функций / / Вестник Пермского университета. Сер.: Математика. Механика. Информатика. 2014- Вып. 1 (24). С. 5-12.

II. PimenovR .R . On course «Aesthetic geometry» and importance of ymmetry with respect to a circle in mathematics education

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There is a method of teaching the key mathematical concepts throughthe construction of aesthetic images. This method is based on the symmetrybetween the circles (inversion). The concept of symmetry between the circlescan be cross-cutting element of mathematics education. This will simplifylearning the ideas of group theory, non-Euclidean geometry, the concept ofa limit and many otherconcepts of «Higher Mathematics».

Keywords: geometry, aesthetic, symmetry, inversion, group theory, education reform.

References

  1. Пименов Р. Р. Эстетическая геометрия или теория симметрий.СПб.: Школьная лига, 2014. 288 с.
  2. Бахман Ф. Построение геометрии на основе понятия симметрии /пер. снем. Р.И. Пименова; под ред. И.М. Яглома. М.: Наука,1969. 380 с.
  3. Пименов Р. Р. В мире поломанных линеек / / Компьютерные инструменты в школе. № 5. 2011. С. 66-72.
  4. Коксетер Г. С. М., Грейтцер С. П. Новые встречи с геометрией. М.:    Наука, 1978. 225 с.

III. Yermolenko А. V. The refined theory of plates aimed at solving contact problems

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Using the classical theory to solve contact problems we obtain reactionswith concentrated efforts. But using the Karman – Timoshenko – Naghditype equations we obtain square-integrable reactions. To simplify the conditions of conjugation of interactive elements we propose to use the version of the refined theory of plates, which allows the equation to bereduced to an arbitrary surface.

Keywords: theory of plates, contact problem.

References

  1. Ермоленко А. В. Теория плоских пластин типа Кармана-Тимошенко Нагди относительно произвольной базовой плоскости // В мире научных открытий. Красноярск: НИЦ, 2011. №8.1(20). С. 336-347
  2. 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.
  3. Михайловский Е. И., Ермоленко А. В. Полудеформационный вариант граничных условий в нелинейной теории пологих оболочек // Нелинейные проблемы механики и физики деформируемого твердого тела: Тр. научн. школы акад. В.В. Новожилова. СПб.: СПбГУ, 2000. Вып. 3. С. 60-76.
  4. Михайловский Е. И., Ермоленко А. В. Уточнение нелинейнойквазикирхгофовской теории оболочек К.Ф. Черныха // Вестник Сыктывкарского университета. Серия 1. Мат. Мех. Инф. 1999.Вып. 3. С. 203-222.
  5. 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.
  6. Михайловский Е. И., Торопов А. В. Математические моделитеории упругости. Сыктывкар: Сыктывкарский университет, 1995.251 с.
  7. Черных К. Ф. Нелинейная теория упругости в машиностроительных расчетах. JL: Машиностроение, 1986. 336 с.

IV. Kotelina N. О. Constructing a circle using NURBS-curves

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The properties of NURBS-curves are considered. The weights and thenodes which make the corresponding NURBS-curve represent a circle aregiven and a detailed proof of this (well-known) fact is given.

Keywords: NURBS, B-spline, rational Bezier curve, Bernstein polynomial.

References

  1. Хилл Ф. OpenGL. Программирование компьютерной графики.Для профессионалов. СПб.: Питер, 2002. 1088 с.
  2. Piegl L., Tiller W. The NURBS book. 2nd Edition. NewYork: Springer-Verlag, 1995-1997. 327 c.
  3. Григорьев М. И., Малозёмов В. H., Сергеев А. Н. Можно ли построить окружность с помощью кривых Безье? / / Семинар «DHA & CAGD». Избранные доклады. 19 декабря 2006 г.(http://dha.spb.ru/reps06.shtml#1219).
  4. Голованов Н. Н. Геометрическое моделирование. М.: Изд-вофизико-математической литературы, 2002. 472 с.

V. Kotelina N. О., Pevnyi А. В. Sidelnikov inequality and Gegenbauer polynomials

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New proof of Sidelnikov inequality based on properties of Gegenbauer polynomials is given. The inequality turns to equality on the sphericalse midesigns and only on them.

Keywords: Sidelnikov inequality, Gegenbauer polynomials.

References

  1. Сидельников В. М. Новые оценки для плотнейшей упаковкишаров в n-мерном эвклидовом пространстве / / Матем. сб. 1974 Т. 95 № 1(9). С. 148-158.
  2. Котелина Н. О., Певный А. Б. Неравенство Сидельникова / / Алгебра и анализ. 2014. Т. 26. № 2. С. 45-52.
  3. Котелина Н. О., Певный А. Б. Экстремальные свойства сферическихполудизайнов / / Алгебра и анализ. 2010. Т. 22. № 5.С. 162-170
  4. Goethals J. М., Seidel J. J. Spherical designs / / Proc. Symp. Pure Math. A.M.S. 1979. V. 34. P. 255-272.
  5. Venkov В. B. Reseauxet designs spheriques / / ReseauxEuclidiens, Designs sphiriques et Formes Modulaires, L’Enseignement mathimatique Monograph, Geneve. 2001. №. 37. P. 10-86.
  6. Котелина H. О. Формула сложения для полиномов Гегенбауэра // Семинар «DHA & CAGD». Избранные доклады. 13 ноября2010 г. ( http://dha.spb.ru/repslO.shtml#1113).
  7. Андреев Н. Н. Минимальный дизайн 11-го порядка на трёхмерной сфере / / Математические заметки. 2000. Т. 67. № 4. С. 489-497.

VI. Shilov S. V. Factors of defeat in case of depressurization of gas mains

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In the work the comparative analysis of several procedures is led andthe model of calculation of factors of defeat at explosion of a cloud ofmetane is offered. The model of explosion allows to consider the character ofdevelopment area and to define possible zones of defeat about a gas main.

Keywords: gas main, blast effects, shock wave, impulse wave, the affectedarea.

References

  1. Вяхирев Д. А., Шушунова А. Ф. Руководство по газовой хроматографии. М.: Высшая школа, 1975. 302 с.
  2. Вяхирев Р. И., Макаров А. А. Стратегия развития газовой промышленности России. М.: Энергоатомиздат, 1997. 344 с.
  3. Обеспечение мероприятий и действий сил ликвидации ЧС: учебник / под ред. С. К. Шойгу Калуга: ГУП «Облиздат», 1998. Ч. 2.Кн. 2. 176 с.
  4. Пирогов С. Ю., Акулов JI. А., Ведерников М. В., Кириллов Н. Г. и др. Природный газ. СПб.: НПО «Профессионал»,2006. 848 с.
  5. РД 03-409-01. Методика оценки последствий аварийных взрывовтопливно-воздушных смесей.
  6. Ситтинг М. Процессы окисления углеводородного сырья. М.: Химия, 1970. 300 с.
  7. СНиП 42-01-2002. Газораспределительные системы.
  8. СП12.13130.2009. Определение категорий помещений, зданий и наружних установок по взрывопожарной и пожарной опасности.
  9. Храмов Г. Н. Горение и взрыв. СПб.: СПбГПУ, 2007. 278 с.

VII. Mironov V. V., Martynov V. A. Parallel algorithms of sorting data using the MPI technology

Text

The problem of optimization of the standard sorting through the MPItechnology is considered. The model of reception and transmission of messages, which is one of the most popular programming models in MPI, is used. Fornumerical experiments the C++ application is written. In the work results ofnumerical modeling of data sorting in parallel mode are given.Keywords: parallel algorithms, sorting, efficiency.

References

  1. Кнут Д. Э. Искусство программирования. Т. 3. Сортировка и поиск.М.: Вильямс, 2007. 800 с.
  2. Воеводин В. В., Воеводин В. В. Параллельные вычисления.СПб.: БХВ-Петербург, 2002. 602 с.
  3. Антонов А. С. Параллельное программирование с использованием технологии MPI. М.: Изд-во МГУ, 2004 . 71 с.
  4. Хьюз К., Хьюз Т. Параллельное и распределенное программирование сиспользованием C++. М.: Вильямс, 2004. 345 с

VIII. NikitenkovV . L., AnufrievA . E. Filtering data obtained by 3D reconstruction from multiple images

Text

In the given article the problem of filtering data obtained by 3D reconstruction from multiple images is considered and methods for solving this problem are represented. For the problem of data clustering from points cloud obtained by 3D reconstruction the noise removal in all steps of reconstruction algorithm is very important.Keywords:3D points filtering, filtering background.

References

  1. EnginTola, Vincent Lepetit, PascalFua. A Fast Local Descriptorfor Dense Matching / / Computer Vision and Pattern Recognition, 2008. CVPR 2008. IEEE Conference, 23-28 June 2008. Pp 1-8. DOI:10.1109/CVPR.2008.4587673.
  2. Charles Loop, Zhengyou Zhang. Computing Rectifying Homographies for Stereo Vision. / / Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, Vol.l, pages 125—131, June23-25, 1999. Fort Collins, Colorado, USA.
  3. Christopher M . Bishop. Pattern Recognition and Machine Learning. Springer, 2006. 738 p.
  4. John Canny, A Computational Approach to Edge Detection.IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINEINTELLIGENCE, VOL. PAMI-8, NO. 6, NOVEMBER 1986. Pp. 679-698.
  5. Martin A. Fischler, Robert C. Bolles. Random Sample Consensus:A Paradigm for Model Fitting with Applications to Image Analysisand Automated Cartography / / Comm. Of the ACM 24: 381—395.DOI: 10.1145/358669.358692
  6. Richard Hartley, Andrew Zisserman. Multiple View Geometry inComputer Vision. Cambridge: University Press, 2003. 655 p.
  7. Richard Szeliski. Computer Vision: Algorithms and Applications.Springer, 2011. 812 p.

Bulletin 1 (20) 2015

by

Issue 1 (20) 2015

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

Text

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 (∗) ax + by=czhas 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 by> ax if and onlyif there is some integer r1; 1 ≤ r1< ax such that (∗∗) by = ax + r1,cz = 2 · ax + r1. In the proof of this result we use some properties ofthe divisibility relation.

Keywords: Diophantine equations, Beal’s conjecture.

References

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

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

Text

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

  1. BestugevA. S., VechtomovE. M. Mulitiplicativelycyclicsemirings // XIII Международная научная конференцияим. академикаМ. Кравчука. Киев: Национальный технический университет Украины, 2010. Т. 2. С. 39.
  2. Golan J. S. Semirings and their applications. Dordrecht: Kluwer Academie Publishers. 1999. 381 p.
  3. Бестужев А. С. Конечные идемпотентные циклические полукольца //Математический вестник педвузов и университетов Волго–Вятского региона. 2011. Вып. 13. С. 71–78.
  4. Бестужев А. С. О строении конечных мультипликативно–циклических полуколец // Ярославский педагогический вестник.2013. Т. III. № 2. С. 14–18.
  5. 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.
  6. Вечтомов Е. М. Введение в полукольца: пособие для студентов иаспирантов. Киров: Изд-во Вятского гос. пед. ун-та, 2000. 44 с.
  7. 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

Text

Keywords: Ki Fang inequality , improper integral method.

References

  1. Калинин С. И. Средние величины степенного типа. Неравенства Коши и Ки Фана : учебное пособие по спецкурсу. Киров: Изд-во ВГГУ, 2002. 368 с
  2. 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

Text

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

References

  1. Бухштаб A. A. Теория чисел. М.: Просвещение, 1966. 384 с.
  2. 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

Text

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

  1. 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.
  2. Боярчук А. К. Справочное пособие по высшей математике. Т. 4:Функции комплексного переменного: теория и практика. М.: Едиториал УРСС, 2001. 352 с.
  3. Ловягин Ю. Н., Праздникова Е. В. Элементарные функциина множестве комплексных гиперрациональных чисел // Вестник Сыктывкарского университета. Сер. 1. Вып. 9. 2009. С. 30–42.
  4. 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.
  5. 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.
  6. Попов В. А. Новые основы дифференциального исчисления : учебное пособие для спецкурсов. Сыктывкар: Изд-во КГПИ, 2002. 64 с.
  7. 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.
  8. Попов В. А. Преднепрерывность. Производные. П-аналитичность.Сыктывкар: Коми пединститут, 2011. 228 с.
  9. Праздникова Е. В. Моделирование вещественного анализа в рамках аксиоматики для гипернатуральных чисел // Вестник Сыктывкарского университета. Сер. 1. Вып. 7. 2007. С. 41–66.
  10. 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

Text

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

  1. Dubowik J. Shape anisotropy of magnetic heterostructures // Phys. Rev. B. 1996. Vol. 54, no. 2. Pp. 1088–1091.
  2. Ishii Y., Okamoto T., Nishina H. Particle length and orientation distributions in magnetic recording media // JMMM. 1991. Vol. 98. Pp.210–214.
  3. 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

Text

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

References

  1. 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.
  2. Гузеев В. В. Методы и организационные формы обучения. М. :Народное образование. 2001. С. 54–55.
  3. Лебединцев В. Б. Модифицированные программы для разновозрастных коллективов на ступени основного общего образования. Биология. Химия. География : методическое пособие. Красноярск,2009. 84 с.
  4. Лебединцев В. Б., Горленко Н. М. Позиции педагогов при обучении по индивидуальным образовательным программам // Народное образование. 2011. №9. С. 224–231.
  5. 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.
  6. Литвинская И. Г. Коллективные учебные занятия: принципы, фазы, технология // Экспресс-опыт: приложение к журналу «Директор школы». 2000. №1. С. 21–26.
  7. Мкртчян М. А. Методики коллективных учебных занятий //Справочник заместителя директора школы. 2010. №12. С. 50–63.
  8. Мкртчян М. А. Концепция коллективных учебных занятий //Школьные технологии. 2011. №2. С. 65–72.
  9. Сорокопуд Ю. В. Педагогика высшей школы : учебное пособие.Ростов н/Д: Феникс, 2011. 541 с
  10. 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

Text

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

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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

Text

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

Keywords: NURBS, B-spline curves, interpolation.

References

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

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

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

Text

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

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

References

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

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

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

Text

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

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

References

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

For citation:Pimenov R. R. The generalization the Desargues’s theorem and geometry of perpendicularity // Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics. 2016. №1 (21). Pp. 28–43.

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

Text

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

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

References

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

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

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

Text

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

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

References

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

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

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

Text

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

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

References

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

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

VII. Ustyugov V. A. Smith – Beljers formula

Text

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

Keywords: ferromagnetism, resonance frequency.

References

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

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

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

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

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

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

References

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

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

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

Text

References

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

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

Bulletin 1 (22) 2017

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Issue 1 (22) 2017

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

Text

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

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

References

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

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

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

Text

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

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

References

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

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

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

Text

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

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

References

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

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

IV. Belykh E. A. Teaching Haar cascade

Text

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

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

References

  1. Viola P., Jones M. Rapid Object Detection using a Boosted Cascade of Simple Features, 2013 IEEE Conference on Computer Vision and Pattern Recognition, 2001, vol. 01, 511 p.
  2. Freund Y., Schapire R. E. Decision-Theoretic Generalization of On-Line Learning and an Application to Boosting, Journal of computer and system sciences 55, 1997, №SS971504, pp. 119–139.

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

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

Text

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

Keywords: mathematical Olympiads, specialized professional school.

References

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

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

VI. Ustyugov V. A The Ising model

Text

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

Keywords: ferromagnetism, Ising model, thermodynamics.

References

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

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

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

Text

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

References

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

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

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

Text

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

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

Keywords: quadratic trinomial, optimization problem, minimum, inequality

References

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

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

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

Text

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

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

Bulletin 2 (23) 2017

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Issue 2 (23) 2017

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

Text

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

Text

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

Text

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

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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)

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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

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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

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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

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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

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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

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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

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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

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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

Text

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

Text

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

Text

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

Text

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)

Text

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

by

Issue 4 (25) 2017

I. Dubatovskaya M., Primachuk L., Rogosin S. On factorization of triangle matrix functions

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

by

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

Text

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

  1. Shavrov V. G., Shcheglov V. I. Magnitostaticheskiye i elektromagnitnyye volny v slozhnykh strukturakh (Magnetostatic and electromagnetic waves incomplex structures), M.: FIZMATLIT, 2017, 360 p.
  2. 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.
  3. Vinogradov A. P. Elektrodinamika kompozitnykh materialov (Electrodynamics of composite materials), M.: URSS, 2001, 207 p.
  4. 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).
  5. 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.
  6. Barta O., et al. Magneto-optics in bi-gyrotropic garnet waveguide // Opto-electronics review. Vol. 9. № 3. 2001. Pp. 320–325.
  7. 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.
  8. 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.
  9. 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.
  10. Rychly J. et al. Magnonic crystals — Prospective structures for shaping spin waves in nanoscale // Low Temperature Physics. Vol. 41. № 10. 2015. Pp. 745–759
  11. Gurevich A. G., Melkov G. A. Magnitnyye kolebaniyai volny (Magneticoscillations and waves), M.: Nauka, 1994, 464 p.
  12. 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.
  13. 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.
  14. Elsgolz L. E. Differentsialnyy euravneniya i variatsionnoye ischisleniye(Differential equations and the calculus of variations), M.: URSS,2002, 320p.
  15. 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

Text

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

  1. 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.
  2. 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.
  3. Malenkov G. G. Struktura i dinamika zhidkoyvody (Structure and dynamics of liquid water), Journal of Structural Chemistry, 2006, v. 47, pp. 5–35.
  4. 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.
  5. Landau L. D., Lifshitz E. M. Statisticheskaya fizika (Statistical physics), Part 1, Moscow: Fizmatlit, 2010, 616 p.
  6. Wang Kuo-Ting, Brewster M.Q. An Intermolecular Vibration Model for Lattice Ice //International Journal of Thermodynamics. 2010. V. 13. № 2. Pp. 51–57.
  7. Eisenberg D., Kautsman V. Struktura i svoystvavody (Structure and properties of water), Moscow: Direct-Media, 2012, 284 p.
  8. Enochovich A. S. Spravochnik po fizike i tekhnike (Reference book on physics and techniques), Moscow: Prosveshenie, 1989, 224 p.
  9. Zatsepina G. N. Fizicheskiye svoystva i strukturavody (Physical properties and structure of water), Moscow: Moscow State University, 1998, 184 p.
  10. 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.
  11. 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

Text

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

  1. 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.
  2. Nikolai E. L. Trudi po mexanike (Works on mechanics), M.: Isdatelstvotexniko-teoretiteskoiliteraturi, 1955, 376 p.
  3. 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.
  4. 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

Text

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

  1. Pierrard V., Lazar M. Kappa distributions: theory and applications in space plasmas // Solar Physics. 2010. V. 267. Pp. 153–174.
  2. 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).
  3. 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

Text

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

Keywords: two-dimensional ternary search, competitive programming.

References

  1. Distantcionnaya podgotovka po informatike (Distance training in computer science). URL: http://informatics.mccme.ru (date of usage: 29.10.2017).
  2. MAXimal. Sayt M. Ivanova (MAXimal. Site of M. Ivanov) URL: http://e-maxx.ru (date of usage: 12.09.2017).
  3. Knuth D. E. Iskusstvo programmirovaniya (The Art of Computer Programming. Vol. 3. Sorting and Searching) M. :Williams (2007). 832 p.
  4. Konspektystudentovkafedrykomp’yuternykhtekhnologiyUniversiteta ITMO (Conspects of students of ITMO) URL: http://neerc.ifmo.ru/wiki (date of usage: 12.09.2017).
  5. Mathews J. H., Fink K. D. Chislennyyemetody. Ispol’zovaniye MATLAB (Numerical Methods: Using MATLAB) 3rd Edition. Spb.: Williams, 2001, 716 p.
  6. 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

Text

Keywords: genetic algorithms, optimization, genom, individuals.

References

  1. MacLeod C. An Introduction to Practical Neural Networks and Genetic Algorithms For Engineers and Scientists, p. 85.
  2. 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.
  3. Panchenko T. V. Geneticheskie algotritmy (Genetic algorithms), pod red. U. U. Tarasevicha, Astrahan: Izdatelskiydom «Astrahanskiyuniversitet», 2007, p. 16.
  4. Kudryavcev L. D. Matematicheskiyanaliz (Mathematical analysis), 2-e izd, M.: Vyshayashkola, 1973, v. 1, 687 p.
  5. 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).
  6. 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

Text

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

  1. 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).
  2. 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).
  3. 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).
  4. Sorevnovaniya po programmirovaniyu 2.0 (Programming competitions 2.0) URL: http://codeforces.com (date of usage: 19.02.2018).
  5. 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).
  6. 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.

Text

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

  1. 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).
  2. Arkhiv Sankt-Peterburgskogo gosudarstvennogo universiteta (St. Petersburg State University Archive), File 7240.14 № 191 (Order № 352а from 20/X–1932).
  3. Bergmann S. Uberdie Kernfunktioneines Bereichs und ihrVerhalten am Rande. Teil 1 // J. furreine und angewandte Math. Bd. 169. Heft 1. 1932. S. 1–42.
  4. Bergmann S. Uberdie Kernfunktioneines Bereichs und ihrVerhalten am Rande. Teil 2 // J. furreine und angewandte Math. Bd. 172. Heft 2. 1934. S. 89–128.
  5. Bergmann S. Zur Theorie von pseudokon formen Abbildungen, Matem. Sbornik, t. 1 (43), No. 1, 1936, pp. 79–96.
  6. 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.
  7. Bergmann S. Zur Theorie der linearen Integral — und Funktional gleichun genimcomplexen Gebiet, Izvestiya NIIMM TGU, Tomsk, vol. 1, issue 3, 1937, pp. 242–257.
  8. Bergmann S. The Kernel Function and Conformal Mapping.- Cambridge (Massachusetts): Amer. Math. Society, 1950. 161 p.
  9. Bergman S., Schiffer M. M. Kernel functions and elliptic differential equations in mathematical physics. New York: Academic Press, 1953. 432 p.
  10. Bergmann S. Integral operators in the theory of linear partial differential equations. Berlin-New York: Springer, 1961, 2thed., 1969.
  11. Brewer J. W., Smith M. K. (eds.) Emmy Noether: a tribute to her life and work. New York: Marcel Dekker, Inc., 1981. 237 p.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. Muntz Ch. Zum Randwertproblem der partiellen Differential gleichung der Minimal flachen // J. fur Reineund Angew. Math. 139. 1911. S. 52–79.
  17. Muntz Ch. Uber den Approximationssatz von Weierstrass / H. A. Schwarz–Festschrift. Berlin: 1914. S. 303–312.
  18. Muntz Ch. Die Losung des Plateauschen Problems uberkonvexen Bereichen // Math. Ann., 94. No. 1–2. 1925. S. 53–96.
  19. Gottfried Noether, 76: Educator in Statistics // New York Times. August 27, 1991. P. 22. (Obituary).
  20. 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.
  21. Noether Fr. Asymptotische Darstellungen und Geometrische Optik, Izvestiya NIIMM TGU, Tomsk: 1937, t. 1, issue 3, p. 175–189.
  22. NoetherFr. Zur Kinematik des starren Korpers in der Relativtheorie // Annalen der Physik. 336 (5). 1910. S. 914–944.
  23. Noether Fr. Bemerkunguber die Losungszahlzueinan deradjungierten Randwertaufgaben beilinearen Differentialgleichungen // Sitzungsberichte der Heidelberger Akad. der Wissenschaft. Math. Nat. Klasse. 1920, I. Abhandlung. S. 37–52.
  24. Noether Fr. Ubereine Klassesingularer Integralgleichungen // Math. Ann. Bd. 82. 1921. S. 42–63.
  25. 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.
  26. Ortiz E. L., Pinkus A. Herman Muntz: A Mathematician’s Odyssey //Mathem. Intellig. Berlin. 27. 2005. S. 22–30.
  27. Segal, Sanford L. Mathematicians under the Nazis. Princeton: Princeton University Press, 2003. 536 p.
  28. Siegmund-Schulze R. Mathematiker auf der Fluchtvor Hitler.- Wiesbaden: Vieweg Verlag, 1998. 324 s.
  29. 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.

Text

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

  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. andApplics. Vol. 2010. Article ID 507560, 11 pages, doi:10.1155/2010/507560.
  3. 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

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The article is devoted to the jubilee, XV Open Syktyvkar State University Programming Championship. It tells about the experience of the event, as well as about the people who have made a significant contribution to the olympiad movement.

Keywords: sports programming, ACM, ICPC.

References

  1. Kotelina N. O., Popova N. K. Podgotovka internet-turch empionatapo programmirovaniyuna Yandex. Contest (The preparation of the online round of the championship on programming on Yandex.Contest platform), Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2018, 1 (26), pp. 73–79.
  2. Komiinform. https://komiinform.ru. Pervyygorodskoy otkrytyy chempionat poprogrammirovaniyu proshel v Syktyvkare v vykhodnyye (The first city open programming championship was held in Syktyvkar at the weekend). https://komiinform.ru/news/4351 (the date of circulation: 12.12.2018).
  3. Kiryukhin V. M. Metodika provedeniya i podgotovki k uchastiyu v olimpiada po informatike. Vserossiyskaya olimpiada shkol’nikov (Methods of carrying out and preparing for participation in computer science competitions. All-Russian School Olympiad). M.: BINOM. Laboratory of Knowledge, 2011, 271 p.

For citation: Kotelina N. O., Popova N. K., Yurkina M. N. About open championship of SSU on programming, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 3 (28), pp. 3–18.

II. Makarov P. A. On the application of the vector graphics language Asymptote for illustrating educational, methodical and scientific works of physics and mathematics

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The possibility of using the Asymptote vector graphics language to illustrate the physics and mathematics educational and scientific works is explored. A few of images illustrating the solution of problems from various fields of physics and mathematics have been developed. It is shown that the Asymptote language has convenient high-level syntax and a fairly developed object-oriented architecture.

Keywords: vector graphics, Asymptote, high-level programming language.

References

  1. Lamport L. LATEX: a document preparation system. 2 ed., AddisonWesley, 1994. 291 p.
  2. Lvovski S. M. Nabor i verstka v sisteme LATEX (Typesetting in the LATEXsystem), 3rd ed, M.: MCNMO, 2003, 448 p.
  3. Kotelnikov I. A., Chebotarev P. Z. LATEX 2εpo-russki (LATEX 2ε in Russian), 3rd ed, Novosibirsk: Siberian chronograph, 2004, 496 p.
  4. Znamenskaya O. V., Znamenski S. V., Leinartas D. E., Trutnev V. M. Matematicheskaya tipografiya: Kurslektsiy (Mathematical typography: The course of lectures), Krasnoyarsk: SFU, 2008, 421 p.
  5. Knut D. E. Vse pro TEX (All about TEX), M.: Williams, 2003, 560 p.
  6. Hammerlindl A., Bowman J., Prince T. Asymptote: the Vector Graphics Language, 2016. 189 p.
  7. KryachkovYu. G. Yevklidova geometriya na yazyke vektornoygra fiki ASYMPTOTE (Euclidean geometry with a symptote), Volgograd: VGSPU, 2015, 88 p.
  8. Goossens M., Rahtz S., Mittelbach F. The LATEX graphics companion: illustrating documents with TEX and PostScript. Addison Wesley, 1997. 299 p.
  9. Goossens M., Rahtz S., Mittelbach F. Putevoditel’ popaketu LATEX i yegogra ficheskimrasshireniyam. Illyustrirovaniye dokumentov pripomoshchi TEX’a i PostScript’a (The LATEX graphics companion. Ilustrating documents with TEX and PostScript), M.: Binom, 2002, 621 p
  10. KiryutenkoYu. A. TikZ&PGF. Sozdaniyegrafiki v LATEX 2εdokumentakh (TikZ& PGF. Creating graphics in LATEX 2ε-documents), Rostov-on-Don, 2014, 277 p.
  11. Tantau T. The TikZand PGF Packages. Manual for version 2.10. Institutf¨ ur Theoretische Informatik Universit¨ atzuL¨ubeck, 2010. 880 p.
  12. Taft E., Chernicoff S., Rose C. PostScript language reference manual. 3 ed. Adobe Systems Incorporated, 1999. 912 p.
  13. Reid G. C. Thinking in PostScript. Addison-Wesley Publishing Company, 1990. 239 p.
  14. PostScript language. Tutorial and cookbook. Addison-Wesley Publishing Company, 1985. 247 p.
  15. Casselman B. Mathematical illustrations: a manual of geometry and PostScript. Cambridge University Press, 2004. 264 p.
  16. Kryachkov Yu. G. Asimptotadlyan achinayushchikh. Sozdaniye risunkov na yazyke vektornoy grafiki Asymptote (Asymptote for beginners. Creating pictures in the vector graphics language Asymptote), Volgograd: VGSPU, 2015, 131 p.
  17. Hobby J. D. METAPOST. Rukovodstvopol’zovatelya (METAPOST. User guide), 2008, 106 p. URL: http://mirrors.ibiblio.org/CTAN/info/ metapost/doc/russian/mpman-ru/mpman-ru.pdf (date of the application: 20.12.2018).
  18. Baldin E. M. Sozdaniye illyustratsiy v METAPOST (Creating illustrations in METAPOST), Linux Format, № 6–10, 2006.
  19. Knut D. E. Vse pro METAFONT (All about METAFONT), M.: Williams, 2003, 376 p.
  20. Volchenko Yu. M. Nauchnaya grafikanayazyke Asymptote (Scientific graphics in the Asymptote language), 2018, 220 p. URL: http://www.math.volchenko.com/AsyMan.pdf (date of the application: 20.12.2018).
  21. Guibe O., Ivaldi P. geometry.asy. Euclidean geometry with asymptote. 2011. 95 p.
  22. Belyaev Yu. N. Vektornyy i tenzornyyanaliz (Vector and tensor analysis), Syktyvkar: Syktyvkar State University, 2010, 298 p.
  23. Kabardin O. F. Tranzistornaya elektronika. Spetspraktikum (Transistor electronics. Special Practice), M.: «Education», 1972, 207 p.
  24. Zherebtsov I. P. Osnovyelektroniki (Fundamentals of Electronics), 5th ed, L.: Energoatomizdat, 1989, 352 p.

For citation: Makarov P. A. On the application of the vector graphics language Asymptote for illustrating educational, methodical and scientific works of physics and mathematics, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 3 (28), pp. 19–37.

III. Ustyugov V. A. The queue on the microcontrollers

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The article substantiates the need to study the algorithms and data structures for developers of the software for embedded systems. The advantages obtained by the rational organization of the program code are considered. An embodiment of a simple data structure — a queue is described.

Keywords: microcontroller, embedded system, data structure, queue.

References

  1. Polikarpova N. Avtomatnoye programmirovaniye (Automata programming), SPb: Piter, 2011, 176 p.
  2. Morton J. Mikrokontrollery AVR. Vvodnykurs (AVR microcontrollers. Introductory course), M.: Dodeka, 2010, 271 p.
  3. Shpak Yu. Programmirovaniye na yazyke C dlya AVR i PIC mikrokontrollerov (C programming for AVR and PIC microcontrollers), SPb:Korona-Vek, 2011, 546 p.

For citation: Ustyugov V. A. The queue on the microcontrollers, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 3 (28), pp. 38–46.

IV. Gromov N. A., Kostyakov I. V., Kuratov V. V.  Complex moment, Minkowski geometry and light propagation in metamaterials

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It is shown that the classical equations of motion of a two-dimensional particle on a Euclidean plane with an imaginary moment are equivalent to the equations of motion of a particle on a pseudo-Euclidean plane with a real moment. A similar equivalence is preserved in the quantum case for the Schr¨odinger equations on the Euclidean plane and the Minkowski plane. An ansatz for solving Maxwell’s equations is proposed, in which the propagation of electromagnetic waves in metamaterials with anisotropic dielectric constant of a different sign is described by the Schr¨odinger equation for a free particle on the Minkowski plane.

Keywords: Minkowski geometry, Schr¨odinger equation, metamaterials

References

  1. Remnev M. A., Klimov V. V. Metapoverhnosti: novyj vzglyad na uravneniya Maksvella i novye metody upravleniya svetom (Metasurfaces: a new look at Maxwell’s equations and new methods of controlling light), UFN, 2018, t. 188, N 2, pp. 169–205
  2. Smolyaninov I. I. Hyperbolic metamaterials, ArXiv:1510.07137 [physics. optics].
  3. Katanaev M. O. Geometricheskie metody v matematicheskoj fizike (Geometric methods in mathematical physics), ArXiv:1311.0733[mathph].
  4. Shabad A. E. Singulyarnyj centrkaknegravitacionnaya chernaya dyra (Singular center as a non-gravitational black hole), TMF, 2014, t. 181, N 3, pp. 603–613.
  5. Perelomov A. M., Popov V. S. «Padenienacentr» v kvantovoj mekhanike («Fall on the center» in quantum mechanics), TMF, 1970, t. 4, N 1, pp. 48–65.
  6. Gitman D. M., Tyutin I. V., Voronov B. L. Samosopryazhenny y erasshireniya v kvantovoymekhanike: obshchayateoriya i prilozheniya k uravneniyamShredingera i Diraka s singulyarny mipotentsialami (Self-Adjoint Extensions in Quantum Mechanics: General Theory and Applications to Schrodinger and Dirac Equations with Singular Potentials), Progress in Mathematical Physics, 2012, v. 62, Birkh¨auser, New York, 2012, 511 p. In: Progress in Mathematical Physics, vol. 62, Birkh¨auser: New York, 2012, 511 p.
  7. Case K. M. Singular potentials, Phys. Rev., 1950, vol.80, pp. 797–806.
  8. Neznamov V. P., Safronov I. I. Padeniechasticna centr. Gipoteza Landau-Lifshica i chislennyeraschety (Particles fall on the center. Landau-Lifshitz hypothesis and numerical calculations), Voprosy atomnoj nauki i tekhniki: teoreticheskaya i prikladnaya fizika, N 4, 2016, pp. 3–8.
  9. Gromov N. A., Kuratov V. V. Kvantovaya chastica naploskosti Minkovskogo (The quantum part on the Minkowski plane), IzvestiyaKomi NC UrO RAN, vyp. 3(35), Syktyvkar, 2018, s. 5–7.

For citation: Gromov N. A., Kostyakov I. V., Kuratov V. V. Complex moment, Minkowski geometry and light propagation in metamaterials, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 3 (28), pp. 47–55.

V. Efimov D. B. The hafnian of Toeplitz matrices of special type, perfect matchings and Bessel polynomials

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In this paper, we present a simple and convenient analytic formula for exact computing of the hafnian of Toeplitz matrices of a special type. An interpretation of the obtained results in the language of perfect matchings and Bessel polynomials is given.

Keywords: hafnian, perfect matching, Bessel polynomial.

References

  1. Caianiello E. R. On quantum field theory – I: Explicit solution of Dyson’s equation in electrodynamics without use of Feynman graphs // IL Nuovo Cimento. 1953. V. 10 (12). Pp. 1634–1652.
  2. Bjorklunя A., Gupt B., Quesada N. A faster hafnian formula for complex matricesandits benchmarking on the Titansupercomputer // arXiv:1805.12498v2 [cs.DS] 25 Sep 2018.
  3. Vyaly M. N. Pfaffiany, iliiskusstvorasstavlyat’ znaki (Pfaffians, or the art to set signs), Matematich eskoeprosv eshchenie, 2005, vyp. 9, pp. 129–142.
  4. Schwarz M. Efficiently computing the permanent and Hafnian of some banded Toeplitz matrices // Linear Algebra and its Applications. 2009. V. 430. Pp. 1364–1374.
  5. Efimov D.B. The hafnian and a commutative analogue of the Grassmann algebra // Electronic Journal of Linear Algebra. 2018. V. 34. Pp. 54–60.
  6. Sloane N. J. A., editor The On-Line Encyclopedia of Integer Sequences, published electronically at https://oeis.org.
  7. Krall H. L., Frink O. A new class of orthogonal polynomials: The Bessel polynomials // Transactions of the American Mathematical Society. 1949. V. 65. Pp. 100–115.
  8. Chatterjea S. K. On the Bessel polynomials // Rendicontidel Seminario Matematicodella Universit`a di Padova. 1962. V. 32. Pp. 295–303

For citation: Efimov D. B. The hafnian of Toeplitz matrices of special type, perfect matchings and Bessel polynomials, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 3 (28), pp. 56–64.

VI. Kalnitsky V. S., Matveeva I. A. About the book, signed by Karl Weierstrass, from the library of St. Petersburg State University

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The article outlines several possible versions, as a geometry textbook of the German mathematician Paul von Zech, signed by Karl Weierstrass, could get into the library of St. Petersburg State University. This book, apparently from the personal library of Weierstrass. In this intriguing story several well-known scientists are directly involved, among them V.I. Schiff, SofyaKovalevskaya, and Magnus Mittag-Leffler.

Keywords: Karl Weierstrass, V.I. Schiff, SofyaKovalevskaya, Magnus Mittag-Leffler.

References

  1. Gallica. http://gallica.bnf.fr (date of the application: 05.10.2018)
  2. Poiskovo-istoricheskiy forum ( Poiskovo-istoricheskiy forum) http:// smolbattle.ru Smolenskiye dvoryane ShiffizBel’skogouyezda (Smolensk nobles Schiff from Belsky). http://smolbattle.ru/threads/Смоленскиедворяне-Шифф-из-Бельского-уезда.44170/ (date of the application: 05.10.2018).
  3. Vachromeyeva O. B. Dukhovnoy eprostranstvo universiteta: Vysshiyezhenskiye (Bestuzhevskiye) kursy. 1878–1918 gg (Spiritual space of the university: Higher Women (Bestuzhev) Courses. 1878–1918), Invest. and Materials, Diada-SPb, St.P., 2003.
  4. Depman I. Ya. S.-Peterburgskoye matematicheskoy eobshchestvo (S.-Petersburg Mathematical Society), Historical-mathemftical investigation, 13, 1960, pp. 11–106.
  5. Protokoly S.-Peterburgskogom atematicheskogo obshchestva (S.-Petersburg Mathematical Society protocols), St.P., 1899.
  6. Brockhaus F. A., Efron I. A. Enciclopedia, Ripol Classic, Moscow, 2013.
  7. Biblioteka Bestuzhevskikh kursov: Istoricheskayakhronika v svidetel’stvakh i dokumentakh (Library of Bestuzhev Courses: Historical Chronicle in Testimonies and Documents), Ed. Vostrikov A. V., St.P.,StPSU Publ. Hause, 2009.
  8. Government of Saint-Petersburg, Law N 88/1-rp 11.07.2005.
  9. Galanova Z. S., Repnikova N. M. Vera Schiff — professor of mathematics on the Bestuzhev Courses Proc. XIII Internetional Kolmogorov readings, 782, Yaroslavl, 2015, pp. 258–263.
  10. Kochina P. Ya. S. V. Kovalevskaya, Moscow, Nauka, 1981.
  11. Ushakova V. G. Zhenshchiny v Sankt-Peterburgskom gosudarstvennom univercitete: istoriko-sotsiologicheskiya spekt (Women in SaintPetersburh state university: hystorical-sociological aspect), A woman in Russian society, 1, 1996, pp. 57–59.

For citation: Kalnitsky V. S., Matveeva I. A. About the book, signed by Karl Weierstrass, from the library of St. Petersburg State University, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 3 (28), pp. 65–75.

VII. Odyniec W. P. The Immigration to the USSR: Profiles of Mathematicians. Part II

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The life and work of three mathematician who emigrated from Germany to the USSR in the 1920s/1920’s by ideological motives. They are the only woman mathematician Stefanie Bauer (neo Szilard) (1898–1938), born Scilard in old town of Gyor; Celestin Burstin (1888–1938), native of Tarnopol (both the towns of the Austria–Hungarian Empire); and Jacob Grommer (1881–1933), born in Brest–Litovsk of the Russian Empire.Keywords: Schwarz differential invariant, double relation, Stefanie Bauer (Szil´ard), Riemann spaces (the problems of embedding and immersion), Pfaff equations, hypersurface bending, Celestin Burstin, transcendental functions, general relativity theory, classes of complex numbers, Jacob Grommer, Albert Einstein.

References

  1. Bauer M. E. Reminiscences of an ordinary man. SPb: ASSPIN Peterhof, 2003, 87 p.
  2. Bauer S. Upon the Schwarz differential invariant, Mat. sbornik, V. 41, No. 1, 1934, p. 104–106.
  3. Bibliografiyaizdanii Akademiinauk Belorusskoi SSR. Knigi i stat’iza 1929-1939 gg. (Bibliography of publications of the Academy of Science of Belorussian SSR. Books and articles for 1929–1939. Minsk: Izd-vo Acad. Nauk BSSR, 1961. 134 p.).
  4. Burstin C. Beitragezum Problem von Pfaff und zurTheorie der Pfaffschen Aggregate. I. Beitrag // Матем. сборник. Т. 37, № 1–2. 1930. C. 13–22.
  5. Burstyn C. Mathematical Works, Minsk: Institute for Physics and Mathematics of the Belorussian Academy of Sciences, 1932, 76 p.
  6. Burstyn C. A. Course of differential geometry, Mensk: State publishes of Belorussia. Scientific and Educations Sector, 1933, 338 p.
  7. Burstyn C. Physical methods of mathematics, Minsk:Institute for Physics and Technics of the Belorussian Academy of Sciences, 1933, 34 p.
  8. Grommer J. Ganzetranszendente Funktionenmitlauterreelen Nulstelen // J. fur reineundangew. Math., Bd. 144. 1914. S. 114–165.
  9. Grommer J. Betragzum Energiesatz in der allgemeinen Relativit¨atstheorie // Sitzungberichte der Prussschen Akademie der Wissenschaft, Kl. 1919. S. 860–862.
  10. Grommer J., Einstein A. A General Relativity Theory and the Principle of Motion, Sitzungberichte der Prus. Akademie der Wissenschaft, KI., 1927, p. 2–13. (Einstein A. Collection of Scientific Works., V. 2, Works on Relativity Theory ,pp. 198–210. Moscow: Nauka, 1966. 689 p.).
  11. Grommer J. Elementary consideration of the formation of complex numbers and their interpretation, Notes of the Belorussian Academy of Sciences, No. 5, 1936, p. 59–63.
  12. Elbert A., Garay G. M.  Differential equations, Hungary, the extended first haf of the 20th century. pp. 245-294 // in: A panorama of Hungarian Mathematics in Twentieth Century. I. (ed. J. Horvath) — Berlin–NewYork: Springer Science & Business Media, Janos Bolyai Math. Soc. 14. 2010. 639 p.
  13. Joffe A. F. Vstrechi s fizikami. Moivospominaniya o zarubezhnykhfizikakh (Encounters with physicists. My recollection of foreign physicists). Leningrad: Nauka, 1983, 262 p.
  14. Matematika v SSSR za 40 let 1917–1957 (Mathematics in the USSR duringthe Forty Years 1917–1957), V. 2, Bibliography, Moskow: Fizmatgiz, 1959, 819 p.
  15. Luca F., Odyniec W. P. The characterization of Van KampenFlores complexes by means of system of Diophantine equations, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, V. 5, 2003, pp. 5–10.
  16. Pervaya Mezhdunarodnaya Konferenciya po tensornoidifferecialnoi geometrii i eeprilozheniya. (The First International Conference on tensor differential geometry and its applications. (Moscow, 17/V – 23/V, 1934), Moscow: Moscow Pokrovsky State University, 1934. 7 p.
  17. Trudy PervogoVsesoyuznogos’yezdamatematikov (Kharkov, 1930). (Proceedings of the 1st All-Union Congress of Mathematicians (Kharkov, 1930), Moscow-Leningrad: ONTI NKTPof the USSR, 1936. 376 p.)
  18. Trudy Vtorogo Vsesoyuznogo Matematicheskogos’ yezda (Leningrad 24/VI–30/VI, 1934). ( Proceedings of the 2nd All-Union Mathematician Congress (Leningrad, 24–30 June 1934), V. 1, Moscow-Leningrad: Academy of ScienceoftheUSSR Press, 1935, 371 p.
  19. Zusmanovich P. Mathematicians Going East. arXiv: 18.05. 00242

For citation: Odyniec W. P. The Immigration to the USSR: Profiles of Mathematicians. Part II, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, 3 (28), pp. 76–90.