Presents the second part of the article (the first part was published in the previous issue this “Messenger”: 2010.- Vyp.11 – C.5-51) devoted to the stability and supercritical behavior of stractures and structures in unilateral restractions on the movement. The article, as stated in the preface, is a review. However, as set out in this part of the method of motion in the parameter stiffness of the elastic medium is published for the first time.
III. Gryshchenko A.E., Kononov A.I., Mikhailova N.A.Study the scale effect by the birefringence method
Studied by the birefrigency method are the properties of surface layers of some polymers of various molecular composition. It was shown that surface layers are characterized with orientational order of chain-like molecules in the films.the thicknesses of optically anisotropic surface layers are shown to be in the range of 10-400 micrometers. It was concluded that the odserved “scale” effect should be taken into account in the studies of thin films properties. Such the effect results from the fact that the surface layers properties differ significantly from those ones in bulk volume.
IV. Yermolenko A.V.On the solution of inverse problems using the Кarman-Timoshenko-Naghdi type theory
The aim of this paper is to prove the role of the Karman-Timoshenko-Naghdi type theory on the solution of inverse problems. Inverse problems are considered for cylindrical plates and round axis-symmetric paltes.
V. Nikitenkov V.L., Kholopov A.A.The optimal parameters of an additive-split method (ASM)
An equation x = b – Ax in a Banach space with continuous linear operator A is solving by so cold additive-split method when operator is split to some parts and an appropriate iteration procedure is used. The optimal parameters of splitting are those to extend mostly the spectral region of convergence for a self-conjugate operator.
VI. Kluchnikov E.A.Web-application performance tuning
The problems of performance of Web applications and solutions. Result of the research is to create a productive template library based on dynamic code generation.
VII. Belyaeva N.A., Dovzhko E.S.Spherical product hardening with pressure in front of
The stress state of a formed spherical product is considered from the view of the body continuously increases. The full stress tensor is given on the growing surface. The pressure from the liquid layer on the formed solid part is taken into account.
VIII. Belyaeva N.A., Pryanishnikova E.A.Granularity in a nonisothermal extrusion composite material
The structural mathematical model of non-isothermal extrusion of a composite material using a generalized model of Newton is presented. The novelty of the proposed model is the joint consideration of Reo-Dimamics, kinetics of structuring and temperature factor.
IX. Mikhailovskii E.I., Holmogorov V.V., Gintner V.V.The longitudinal stability of a cylindrical shell at external and internal Winkler’s restrictions
In this paper the problem of stability of a cylindrical shell, subjected to longitudinal compression, in the conditions of external and internal one–sided constraint restrictions Winkler’s type is considered. The local method of search of eigenvalues of positively homogeneous operator is applied. In the numerical study of the problem displacements are approximated by splines.
X. Nikitenkov V.L., Tyufyakov A.V.Tetris-eliminator and the algorithm of successive refinement of backlash in the vector requirements
To solve the integer problem of linear cutting proposed algorithms to obtain optimal solution either for the initial vector requirements, or if there is tighter tolerances. Discussed in the Ask the degeneracy of the obtained solutions and numerical results.
XI. Pevnyi A.B., Duriagin A.M.The maximal redundancy of real harmonic frames
The theorem of Delsarte for lower bound for cardinality of spherical design and its modification using only even polynomials are given. The corresponding grid problem of linear programming is considered and the results of calculations are given.
It is represented the examples of the continuous functions on the metric spaces for which the classical theorems of Weierstrass (about boundedness and about achievement of the face) and the theorem of Kantor (about uniformly continuity) are not true.
II. Sidorov V.V.Structure lattice isomorphisms of semirings generated by a one nonnegative function
In this paper we describe isomorphisms of lattices Af and Ag of all subalgebras with unit of semirings of functions [f] and [g] generated by nonnegative real-valued functions f and g, respectively. It is proved that any isomorphism of lattices Af and Ag is generated by an isomorphism of semirings [f] and [g]. A techniqe of unigenerated subalgebras is applied.
III.Grytczuk A.On the Diophantine equation x2 – dy2 = zn
In this Note we remark that there is some duality connected with the problem of solvability of the Diophantine equation
(*) x2 – dy2 = zn.
Namely, we prove that the equation (*) has no solution in positive integers x,y for every pime z = q* generated by an arithmetic progression and for every odd positive integer n if d is squarefree positive integer such that p|d, where p is an odd prime.
IV. Afonin R.E., Malozemov V.N., Pevnyi A.B.Delsarte bounds for the number of elements of the spherical design
The proof of the Delsarte’s theorem for lower bound for cardinality of spherical design is given. The exposition is closed, all auxiliary theorems are proved.
V. Belyaeva N.A., Dovzhko E.S.Model of the formation of spherical products with the nonzero critical depth conversion of the material
The mathematical model of the solidification of the spherical product in the mode of spread of the bilateral front. At the boundaries of the fronts are into account the conditions of coexistence of solid and liquid layers formed products. The results of numerical analysis.
VI. Belyaeva N.A., Kuznetsov K.P.The dissipative structure and domain of anomaly structural liquid Couette flow in a flat clearance
The bifurcation study of structural liquid Couette flow in a flat clearance in the superanomaly area was conducted. Bifurcation diagrams and the values of parameters corresponding to the superanomaly area were obtained. Bifurcation method allowed to obtain an analytical approximation of the stationary inhomogeneous solution in the neigborhood of the bifurcation point. A numerical simulation of the flow was conducted.
VII. Belyayev Yu.N.Wave scattering continuosly stratified elastic media
Method of calculating elements of the second order matrix, which characterizes the elastic continuously layered media is proposed. The representation of reflection and transmission coefficients of the layer through elements of characteristic matrix is given. General solution to the plane wave reflection and transmission in a periodic continuously stratified medium is found.
VIII. Kotelina N.O.Methods of estimating kissing numbers
Methods for estimating of kissing numbers based on linear programming, corresponding grid problems of linear programming and results of calculations in Matlab are given. The table of best known upper bounds for kissing numbers is also given.
IX. Belyaeva N.A., Istomina M.N.Computing System “Bifurcation method in nonlinear models Mechanics”
Computing system includes programs for the branching method in nonlinear mechanics models. The article discusses the general structure of the complex and a description of its constituent programs.
X. Mikhailovskii E.I., Mironov V.V., Podorov V.R.Contact free boundary problem for beams and discrete elastic foundation
The influence of the accounting of transverse shifts on the solution of contact problem for beams and supports of the unilateral action. A generalization to the case of beams, bent on the theory of Timoshenko, the method of enumeration of sets of active supports, based on the proof of the uniqueness of solutions of the nonlinear contact problem and the equations of the analytical version of the so-called theorem of three moments.
XI. Pevnyi A.B., Istomina M.N.A modification of Delsarte’s theorem for the estimation of kissing numbers
XII. Odyniec W.P.Two hundred years from the date of the birth of the creators of mechanical computers recommended for Demidov Prize H. Slonimsky and H. Kummer
Some materials of the creation of calculating gadgets by H. Slonimsky, H. Kummer and H. Ioffe is considered. In details the Theorem by H.Slonimsky which was the base of these gadgets is presented. This Theorem, devoted to a property of the Farey sequence, is now widely applied in informatics.
XIII. Professor Alexandr Grigiorievich Poroshkin: 60-th year in mathematics and education
In this paper we prove that the lattice of ideals (lattice of congruences) in lattice C(X,[0,1]) dtermines any compactum X. We study the lattice of all continuous [0,1]-value functions on topological spaces X. We proved that any compactum X determined by the lattice of ideals (the lattice of congruences) of a lattice C(X, I). We described the closed ideals of topological lattices Cp(X, I) with the topology of pointwise convergence. We have that a Tikhonov space X defined by the lattice Cp(X, I) as a consequence.
II. Vechtomov E.M., Petrov A.A.Semirings with idempotent multiplication
In this paper we study the structural properties of multiplicatively idempotent semitings. This class of semirings contains all Boolean rings and all kinds of distributive lattices with zero. Particular attention is paid to the finite multiplicatively idempotent semirings and twice idempotent semirings.
III. Mekler A.A.Remarks on the correspondence between the topological invariants of spaces, Marcinkiewicz and Orlicz, I
In this paper is presented a parallel approach to treating of some invariants of two kinds of classical Banach Function Spaces namely Marcinkiewcz and Orlicz spaces which are denoted Mψ and L*φ, respectively. The exposition has the goal to state that there is such a way of mutually associating into couples (Mψ, L*ψ-) (as well as (Mφ+, L*φ)) that isomorphic properties of one of counterpart transfer into they of another one. Moreover by the way the isomorphic properties at ∞ allow to be reduced to ones at 0.
IV. Mekler A.A.Remarks on the correspondence between the topological invariants of spaces, Marcinkiewicz and Orlicz, II
In terms of behavior of limit densities of positive integer sequences an unique interpretation of some topological invariants of Orlicz, respectively, Marcinkiewicz functional spaces (in particular their coincidence) is given.
V. Nikitenkov V.L., Kholopov A.A.The exact formulae for the optimal parameters of ASM
An additive-split method (ASM) is used for solving an equation x=b-Ax in a Banach space with linear operator A. The exact formulae for the optimal parameters of ASM which extend mostly the real spectral interval of convergence are given.
VI. Belyaeva N.A., Stepanova A.S.Flow of viscous structure fluid among two cylinders
Presents the second part of the article (the first part was published in the [1]) devoted to the impact assessment transient viscosity on flow map of incompressible structure fluid among two cylinders with swirl. The state [1] analyzestationary axial flow of incompressible fluid with constant viscosity, it present numerical solution and checking findings with theretical research was presented in [2-4], where vortex deduced analytically by method solution determination in view of polynoms.
VII. Yermolenko A.V.A variant of the refined theory of flat plates for the solution of contact problems
Using the method of generalized reaction it was obtained the solution of contact problem for an axisymmetric circular plate and an absolutely rigid base. In addition the solution was obtained with using the Karman-Timoshenko-Naghdi type equations, which were given to the lower surface of the plate.
VIII. Belyaeva N.A., Kamburov D.M.Computing System “Solid-phase extrusion”
Computing system combines algorithms and software modules for calculating the parameters of viscoelastic flow of a compressible structured composite material in the solid-phase extrusion, developed at the Department of Mathematical Modelling and Cybernetics of Syktyvkar State University.
IX. Belyaeva N.A., Khudoyeva E.E.Computing complex “Thermoviscoelastic models of the formation of axisymmetric products”
The computing complex integrates series of programs developed within the mathematical models of the formation of axisymmetric products (cylinder, sphere) in the process of their obtaining in the parallel reactions of polymerization and crystallization. The article gives a description and operating principles of the complex.
X. Vasiliev A.A., Nikitenkov V.L., Kimask K.V., Malkov S.V.Internet-version course of mathematics for nonmathematical specialities (with chapters from elementary mathematics)
In this article considered generalization problem packing sliced rolls, that is consider in article [10]. Now we shall look at situation not only one diameter, but several diameters and problem of overspending would solved not by adding new formats packing paper (PP), it would solved by changing current formats by others, which would give us lesser overspending.
XII. Vasiliev A.N., Gintner A.N.Two approaches to the solution of one classical problem of computational geometry
In this work consider problem of finding the largest empty circle and the smallest covering circle. The implementation of algorithms for solving these problems by using methods of computational geometry, in particular of Delaunay triangulation and its dual Voronoi diagram is discribed. In the work also performed numerical experiments and graphically presents results of problems.
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.
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II. Kalinin S.I.Flett’s theorem about the mean value and its generalizations
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Праздникова Е. В. Моделирование вещественного анализа в рамках аксиоматики для гипернатуральных чисел // Вестник Сыктывкарского университета. 2007. Сер. 1. Вып. 7. С. 41-66.
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.
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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.
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.
Finta B. A generalization of the Lagrange mean value theorem // Octogon. 1996. 4, № 2. p. 38-40.
Калинин С. И. Теорема Ролля в контексте этапа обобщения работы с теоремой // Математика в школе. 2009. №3. С. 53-58.
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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
Henneaux M., Teitelboim C. Quantization of gauge systems. // Princeton Univ. Press, New Jersey, 1992. 540p.
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].
Дирак П.А.М. Лекции по квантовой механике. // Любое издание.
Гитман Д.М., Тютин И.В. Каноническое квантование полей со связями.// М.: Наука, Гл.ред. физ.мат. лит., 1986. 216с.
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
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
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Беляева Н. А. Деформирование вязкоупругих материалов с изменяющейся структурой // Вестник Сыктывкарского университета.Сер1. Вып. 11. 2010. С. 52-75.
Беляева Н. А. Деформирование вязкоупругих структурированных систем: монография. Lap Lambert Academic Publishing GmbH & Co. KG, Germany, 2011. 200 c.
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.
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.
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.
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.
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.
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.
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
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
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.
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.
Ермоленко А.В. Аналитическое решение контактной задачи дляжестко закрепленной пластины и основания // В мире научных открытий. Красноярск: НИЦ, 2011. С.11-17.
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)
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
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.
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
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Андрюкова В.Ю., Тарасов В.Н. Об устойчивости упругих систем с неудерживающими связями. // Известия Коми НЦ УрОРАН. 2013. №3(15). С. 12-18.
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VIII. Mironov V.V., Overin N.A.Tehnology of MPI of the solution of thestationary equation of heat conductivity
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
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Вечтомов Е. М., Лубягина Е. Н. Полукольца непрерывных[0, 1] -значных функций / / Фундаментальная и прикладная математика. 2012. Т. 17. Вып. 1. С. 53-82.
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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.
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
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.
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III. Yermolenko А. V. The refined theory of plates aimed at solving contact problems
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
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IV. Kotelina N. О. Constructing a circle using NURBS-curves
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.
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V. Kotelina N. О., Pevnyi А. В. Sidelnikov inequality and Gegenbauer polynomials
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.
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VI. Shilov S. V.Factors of defeat in case of depressurization of gas mains
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.
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VII. Mironov V. V., Martynov V. A.Parallel algorithms of sorting data using the MPI technology
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.
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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.
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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.
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Keywords: Ki Fang inequality , improper integral method.
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V. Popov V. A.Design, development and implementation of complex automated car fleet management system
In the article we justify the impossibility of the deduction of differentialanalogues of the mean value theorems of Rolle, Lagrange and Cauchy forcertain classes of analytic functions, even if the differential mean value(point C) is sought in a much wider set than a segment. A class of fullydifferentiable functions for which the point С of Lagrange’s equality belongsto some circle, containing originally given points, is determined. The simpleproof of Lagrange’s mean value inequality and the traditional criterion ofstationarity of functions of a complex variable is given.
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VII. Muzhikova A. V. Interactive teaching of mathematics in higher school
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VIII. Yermolenko A. V., Gintner A. N.Influence of transverse shears on decrease of strain state of plates
In the Karman–Timoshenko–Nagdi theory the moments consist of two components: the moments, related to the curvature of the middle surface, and the moments, related to the changes in transverse shears. It is shown, the maximum values of these components are in opposition in contact problems.Keywords:refined theory of plates, contact problem, antiphase.
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This article deals with the problem of interpolation with polynomial Bspline curves. It examines methods of global interpolation when systems of linear equations are set up and solved.
Keywords: NURBS, B-spline curves, interpolation.
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II. Makarov P. A.The recursive method for determining the reflective properties of multilayer film coatings
An algorithm for calculating the coefficients of reflection, transmission and absorption of electromagnetic energy plane-polarized monochromatic electromagnetic waves propagating in multilayer systems of film was developed. The limits of applicability of the method were determined.
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Diaz M. de Sihues, Durante-Rincon C.A., Fermin J.R. A ferromagnetic resonance study of NiFe alloy thin films // JMMM. Vol. 316. 2007. Pp. 462–465.
Antonets I.V., Kotov L.N., Makarov P.A., Golubev Y.A. Nanostructure, conductivity, and reflectivity of thin iron and (Fe)x(BaF2)yfilms // Technical physics. The Russian Journal of Applied Physics. 2010. Vol. 80. №9. Pp. 134–140.
Antonets I.V., Kotov L.N., Nekipelov S.V., Karpushov E.N. Conducting and reflecting properties of thin metal films // Technical physics. The Russian Journal of Applied Physics. 2004. Vol. 74. № 11. Pp. 102–106.
M. Born, E. Wolf Principles of optics. M.: Science, 1973. 720 p.
Buznikov N.A., Antonov A.S., D’yachkov A.L., Rakhmanov A.A. Frequency spectrum of the nonlinear magnetoimpedance of multilayer film structures // Technical physics. The Russian Journal of Applied Physics. 2004. Vol. 74. № 5. Pp. 56–61.
Buchel’nikov V.D., Babushkin A.V., Bychkov I.V. Electromagnetic-wave reflectivity of the surface of a cubic-ferrite plate // Physics of the Solid State. 2003. Vol. 45. № 4. Pp. 663–672.
Goncharov A.A., Ignatenko P.I., Petukhov V.V. et al. Composition, structure, and properties of tantalum boride nanostructured films // Technical physics. The Russian Journal of Applied Physics. 2006. Vol. 76. № 10. Pp. 87–90.
Kotov L.N., Antonets I.V., Korolev R.I., Makarov P.A. Resistance and oxidation films of iron and influence upper layer from dielectric and metal // Journal of the Chelyabinsk State University. Physics. Vol. 39 (254). № 12. 2011. Pp. 57–62.
Kurin V.V. Resonance scattering of light in nanostructured metallic and ferromagnetic films // PHYSICS-USPEKHI. 2009. Vol. 179. № 9. Pp. 1012–1018.
L.D. Landau, E.M. Lifshitz Course of Theoretical Physics. Volume 8. Second Edition: Electrodynamics of Continuous Media. M.: Fizmatlit, 2005. 656 p.
G.S. Landsberg Optics. M.: Fizmatlit, 2010. 848 p.
Perevalov T.V., Gritsenko V.A. Application and electronic structure of high-permittivity dielectrics // PHYSICS-USPEKHI. 2010. Vol. 180. № 6. Pp. 587–603.
Usanov D.A., Skripal A.V., Abramov A.V., Bogolyubov A.S. Determination of the metal nanometer layer thickness and semiconductor conductivity in metal-semiconductor structures from electromagnetic reflection and transmission spectra // Technical physics. The Russian Journal of Applied Physics. 2006. Vol. 76. № 5. Pp. 112–117.
Usanov D.A., Skripal A.V., Abramov A.V., Bogolyubov A.S. Changing the type of resonant reflection of electromagnetic radiation in the structures of nanometer metal film — dielectric // Letters in Technical Physics Journal. 2007. Vol. 33. № 2. Pp. 13–22.
For citation: Makarov P. A. The recursive method for determining the reflective properties of multilayer film coatings // Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics. 2016. №1 (21). Pp. 9–27.
III. Pimenov R. R.The generalization the Desargues’s theorem and geometry of perpendicularity
This article studies the generalization the Desargues’s theorem with using perpendicularity and the new concept of connector. We research application this generalization in planimetry and stereometry. We discovery connection between this generalization and the theorem about altitudes triangle and the theorem Hjelmslev-Morley.
Keywords: the Desargues’s theorem, foundation of geometry, perpendicularity, geometry of lines, stereometry
References
Kodokostas D. Proving and Generalizing Desargues’ Two-Triangle Theorem in 3-Dimensional Projective Space. Hindawi Publishing Corporation, Geometry. Volume 2014, Article ID 276108.
Bachmann F. Aufbau der Geometrie aus dem Spiegelungsbegriff, Die Grundlehren der mathematischen Wissenschaften Volume 96. 1973.
Odyniec W., S’le’zak W. Selected topics in graph theory. Translated. from pol. by W. Odyniec- M.-Izhevsk: Institute Computer’s Research, SRC: “RHD“, 2009. 504 с.
Skopenkov M. Visual geometry and topology // http://skopenkov.ru: Mikhail Skopenkov’s homepage. URL: http://skopenkov.ru/courses/ geometry-16.html (date of the application: 20.02.2016).
For citation:Pimenov R. R. The generalization the Desargues’s theorem and geometry of perpendicularity // Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics. 2016. №1 (21). Pp. 28–43.
IV. Pimenov R. R.The generalization of the Desargues’s theorem and hidden subspaces
This article studies the generalization of the Desargues’s theorem in 7-dimensional space. We consider lines as points and 3-dimensional spaces as lines. It provides us with the conception of the hidden spaces. The result is generalized for multidimensional spaces of arbitrary dimension. The article continues the research, started in the work. The generalization of the Desargues’s theorem and geometry of perpendicularity.
Keywords: The Desargues’s theorem, projective stereometry,many-dimensional space.
References
Cameron Peter J. Projective and Polar Spaces // www.maths.-qmul.ac.uk: School of Mathematical Sciences. 2000. URL: http: //www.maths.qmul.ac.uk/pjc/pps/ (date of the application: 01.04.2016).
Tabachnikov S. Skewers // https://arxiv.org/archive/math: Cornell University Library. Mathematics. [math.MG] 19 Sep 2015. URL: https://arxiv.org/pdf/1509.05903.pdf (date of the application: 01.04.2016).
Friedrich Bachmann. Aufbau der Geometrie aus dem Spiegelungsbegriff. Die Grundlehren der mathematischen Wissenschaften Volume 96, 1973.
Pimenov R. The generalization the Desargues’s theorem and geometry of perpendicularity // Bulletin of Syktyvkar State University. Series 1: Mathematics. Mechanics. Informatics. Edition 1 (21). 2016. Pp. 28–43.
For citation:Pimenov R. R. The generalization the Desargues’s theorem and hidden supspace // Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics. 2016. №1 (21). Pp. 44–57.
V. Odyniec W. P.Emergence of the name of discipline «Computer Sciences» — time command
The short history of emergence in the continental Europe (except of Denmark and Sweden) and also in the USSR, of name of new scientific discipline (and actually a number of sciences) «informatics», and in the rest of the world – «Computer Sciences» (in Denmark and Sweden – «datalogy»)— is presented. As by definition of the Great Russian Encyclopaedia (GRE) (2008) informatics formally is not bound to computer, it is more logical to call new discipline – «computer sciences».
Keywords: computer sciences, informatics, information value, G. Hopper, K. Steinbuch, L. Fein, G. Forsythe, Ph. Dreyfus, A.I. Mikhaylov, A.A. Harkevich, M.M. Bongard, A.P. Ershov, P. Naur.
References
Backgraund. Vol. 7, No. 2 (Aug., 1963). Pp.109–110. Oxford, New Jersey: Blackwell Publishing. The International Studies Association, 1963.
Hopper G. The education of a computer /Proceeding of 1952 ACM Meeting (Pittsburg). Pp. 243–249. New York: ACM, 1952.
McCorduck P. An Interview with Louis Fein. (9 May 1979). Palo Alto, California: Ch. Babbage Institute. The Center for the History of Information Processing University of Minnesota, 1979. 27 p.
Naur P. The Science of Datalogy. Letter to the editor Comm. ACM, Vol. 9, No. 7, 1966, p. 485.
Steinbuch K. Informatik: Automatische Informationsverarbeitung. Berlin: SEG–Nachrichten, 1957.
Sveinsdottir E., Frokjaer E. Datalogy — the Copenhagen Tradition of Computer Science. BIT(Nordisk Tidskrift for Informationsbehandling), Vol. 28(3), 1988. 22 p.
Wiener N. Cybernetics: Or Control and Communication in the Animal and the Machine. Paris: (Hermann&Сie) & Camb. Mass. (MIT Press), 1948. 2nd revised ed 1961. New York-London: Wiley, 1961. 212 p.
Ershov A.P., Monakhov V.M., Beshenkov S.A. and others. The basis of Computers Sciences and the Calculations. The Parts 1,2. Moscow: «Prosveshchenie», 1985. 96 p.
Ignatyev M.B. The cybernetic pictures of the universe. The complex cyberphysics systems. Saint-Petersburg: GUAP, 2014. 673 p.
Kraineva I.A. The pages of the biography academician A.P. Ershov // The papers of International Conferences to memory academician A.P. Ershov. Novosibirsk: Izd-vo Institute of System of Computer Sciences SO RAN, 2009.
Mihailov A.I. and others. The scientific information. Moscow: Izd-vo VINITI Akademii Nauk SSSR, 1961. 27 p.
Mihailov A.I., Cherniy A.I., Gilyarovsky R.S. The basis of scientific information. Moscow: «Nauka», 1965. 655 p.
Odyniec W.P. Sketches in the history of computer sciences. Syktyvkar: Izd-vo KGPI, 2013. 420 p.
Fradkov A.L. Cybernetic physic: principles and examples. Saint-Petersburg: «Nauka», 2003. 208 p.
Harkevich A.A. Selected topics in 3 Volumes. V.3. The Information Theory. The Identification of form. Moscow: «Nauka», 1973. 524 p.
Bol’shaya Rossiisrkaya Encyklopedia (The Grand Russian Encyclopedia). Vol. XI., p. 481 (Computer sciences). Moscow:«Rossiiskaya Encyclopedia», 2008.
Ivanov I.I. Harkevich A.A. // Bolshaya Sovetskaya encyclopedia (The Grand Soviet Encyclopedia) (The 3th ed.), V. 28, p. 590 (). Moskow: «Sovetskaya encyclopedia», 1978.
The mathematical encyclopedic Dictionary. (Computer sciences), p. 244. Moscow: «Sovetskaya encyclopedia», 1988. 847 p.
For citation:Odyniec W. P. Emergence of the name of discipline «Computer Sciences» — time command // Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics. 2016. №1 (21). Pp. 58–68.
VI. Odyniec W. P.Some comments to comparison of Unified State Examination in mathematics (expanded level, May, 2016) in Poland and in Russia
In work comparison of final works on mathematics (USE of expanded level) in form and in content in Poland and in Russia is carried out.
Keywords:final work on mathematics (USE), Mathematics Olympiads, experts.
References
Leontieva N.V. On the problem of the system of criteria for evaluating of the achievement the students of the school in the mathematic // Matematicheskii vestnik pedagog. institutes and university from Volga- Vyatsk. region; Vyp. 18. Pp. 271–276. Kirov: Nauch. Izd-vo Vyat GU, 2016. 400 p.
Odyniec V.P. Some problems of the training of the past-graduate students for the theory and principles of teaching mathematics // Vestnik MGU, Ser. 20, № 4 (2012) Pp.3–8.
Odyniec V.P. On the 10 th anniversary of the Bologna process in Russia // Vestnik MGU, Ser. 20. № 1 (2014). Pp. 3–10.
Testov V.A. The problem of the going over mathematical education to the new paradigm in information society // Trudy X mezhdunarodnyh Kolmogorovskih chtenii, pp. 94–97. Yaroslavl’: Izd-vo YaGPU, 2012. 248 p.
For citation:Odyniec W. P. Some comments to comparison of Unified State Examination in mathematics (expanded level, May, 2016) in Poland and in Russia // Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics. 2016. №1 (21). Pp. 69–76.
The article gives a brief historical overview of ferromagnetic resonance studies and describes a derivation of the Smith – Beljers formula. An example of the calculation of the resonance frequency of single-domain ellipsoidal particles is given.
Keywords: ferromagnetism, resonance frequency.
References
Coey, J. Magnetism and Magnetic Materials / J. Coey. Cambridge University Press, 2010. 633 p.
Osborn, J. A. Demagnetizing factors of the general ellipsoid / J. A. Osborn // Phys. Rev. B. 1945. vol. 67. Pp. 352–357.
Suhl H. Werromagnetic resonance in nickel ferrite / H. Suhl // Phys. Rev. 1954. Vol. 97. Pp. 555–557.
Smith J., Beljers H. J. Ferromagnetic resonance absorbtion in BaFe12O19, a highly anisotropic crystall // Philips Res. Rep. 1955. Vol 10. Pp. 113-130.
Ferromagnetic resonance / Ed. by S. V. Vonsovsky. Moscow: Gosudarstvennoe izdatelstvo fiziko-tekhnichskoi literatury, 1961. 344 p.
Gurevich A. G. Magnetic oscillations and waves / A.G. Gurevich, G.A. Melkov. Moscow: Fizmatlit, 1994. 464 p.
For citation:Ustyugov V. A. Smith-Beljers formula // Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics.2016. №1 (21). Pp. 77–85.
VIII. Nosov L. S.,Vecherskij V. V.,Zudin V. S.,Mozhajkin A. V.Encoding voice information in the IP-telephony
In this article, the voice data protection for its transmission over an IP-telephony systems is considered, since this channel is potentially exposed to interference in order to violate the confifidentiality of negotiations. The challenge of protecting speech information from interception is relevant for ordinary users (daily use) and for various organizations, fifirms or companies in order to prevent the interception of commercial secrets by competitors.
In this paper we propose a method of encoding audio channels, create our own minimalist software that allows to encode / decode the speech information in the frequency domain.
Keywords: IP telephony, Protection of IP telephony, speech intelligibility.
References
James W. Cooley, John W. Tukey An Algorithm for the Machine Calculation of Complex Fourier Series // Mathematics of Computation, 1965. Pp. 297–301.
Yukito Sato Illustrated Introduction to Mechatronics. Introduction to Signal Management (Revised 2nd Edition). Tokyo: Ohmsha, 1999. 176 p.
PulseAudio Documentation // http://freedesktop.org: Software development management system. URL: http://freedesktop.org/software/pulseaudio/doxygen/ (date of the application: 17.07.2016).
ALSA project – the C library reference // http://www.alsa-project.org: Advanced Linux Sound Architecture (ALSA) project homepage. URL: http://www.alsa-project.org/alsa-doc/alsa-lib/ (date of the application: 17.07.2016).
JACK Audio Connection Kit // URL: http://www.jackaudio.org/ (date of the application: 17.07.2016).
For citation:Nosov L. S., Vecherskij V. V., Zudin V. S., Mozhajkin A. V. Encoding voice information in the IP-telephony // Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics. 2016. №1 (21). Pp.86–99.
IX. Odyniec W. P.,Popov V. A.Valerian Nikolayevich Isakov (to the seventieth anniversary from the birthday)
Valerian Isakov rector of the Komi state pedagogical Institute // http://ktovobrnauke.ru/: Federal specialized magazine ”who’s Who in science and education“. № 1(1), 2009. URL: http://ktovobrnauke.ru/ 2009/1/innovacii-severnogo-vuza.html (date of the application: 10.05.2016).
Valerian Nikolayevich Isakov (to the 65-th anniversary from birthday) // Bulletin of Syktyvkar State University. Series 1: Mathematics. Mechanics. Informatics. Edition 13. 2011. Pp. 155–159.
Zhdanov L. A. Isakov Valerian Nikolaevich // Syktyvkar: Encyclopedia. Syktyvkar: Komi scientific center, UB RAS, 2010.
Natalia Kirillova. Innovation of the North high school // http:// ktovobrnauke.ru/: Federal specialized magazine ” who’s Who in science and education“. № 1(1), 2009. URL: http://ktovobrnauke.ru/2009/1/innovacii-severnogo-vuza.html (date of the application: 10.05.2016).
Odinets V.P. (Odyniec W.P.), Popov V. A. Isakov Valerian Nikolaevich // Rectors (Directors) of the Komi pedagogical Institute / L. A. Zhdanov, V. A. Popov, N. I., Surkov, etc. Syktyvkar: Komi pedagogical Institute, 2012. P. 100–107.
Popov V. A. Kafedra of mathematics Komi pedagogical Institute: history of formation and development / V. A. Popov. Komi pedagogical Institute. Syktyvkar, 2012. 216 p.
For citation:Odyniec W. P., Popov V. A. Valerian Nikolayevich Isakov (to the seventieth anniversary from the birthday) // Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics. 2016. №1 (21). Pp. 100–104.
This paper illustrates the text classification process using methods of pattern recognition. The problem of authorship of social and political essays attributed to A. S. Puskin is considered as an example. Means of increasing the reliability of the recognition system are suggested.
Keywords: text classification, methods of pattern recognition, authorship attribution, A. S. Puskin.
References
Bongard M. M. Problema uznavaniya (Recognition Problem), Moscow: Nauka, 1967, 320 p.
Marusenko M. A., Bessonov B. L., Bogdanova L. M., Anikin M. A., Miasojedova N. E. V poiskakh poteryannogo avtora: Etyudy atributsii (In search of the lost author. Studies in attribution), St. Petersburg: Faculty of Philology, Saint Petersburg University, 2001, 216 p.
Marusenko M. A. Atributsiya anonimnykh i psevdonimnykh literaturnykh proizvedenii metodami raspoznavaniya obrazov (Attribution of anonymous and pseudonymous literary works using methods of pattern recognition), Leningrad: Leningrad University, 1990, 168 p.
Rodionova E., Khozyainov S., Mitrofanova O. Text corpora in attribution of literary works, Proceedings of the International Conference «Corpus Linguistics — 2008», St. Petersburg: St. Petersburg State University, Faculty of Philology and Arts, 2008, pp. 338—349.
Khozyainov S. A. Atributsiya publitsistiki, pripisyvaemoi A. S. Pushkinu (Attribution of social and political essays attributed to A. S. Puskin), Prikladnaya i matematicheskaya lingvistika: Materialysektsii XXXVII Mezhdunarodnoi filologicheskoi konferentsii, 11—15 marta 2008 g., Sankt-Peterburg (Applied and mathematical Linguistics: Materials of the section XXXVII International philological conference, March, 11—15, St. Petersburg), St. Petersburg, 2008, pp. 20—30.
Khozyainov S. A. Atributsiya publitsistiki, pripisyvaemoi A. S. Pushkinu. Reshenie problemy avtorstva metodami raspoznavaniya obrazov (Attribution of social and political essays attributed to A. S. Puskin. Autorship attribution using methods of pattern recognition), LAP LAMBERT Academic Publishing, Saarbr¨ucken, 2012, 252 p.
Khozyainov S. Some problems and methods of quantitative and structural research of authors’ styles, Izvestiya RGPU im. A. I. Gertsena, № 28 (63), St. Petersburg, 2008, pp. 378—383.
Yakubaitis T. A., Sklyarevich A. N. Veroyatnostnaya atributsiyatipa teksta po neskol’kim morfologicheskim priznakam (Probability attribution of text type on the several morphological markings), Riga, 1982, 53 p.
For citation:Khozyainov S. A. Text classification using methods of pattern recognition, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №1 (22), pp. 3–20.
II. Vechtomov E. M.,Lubyagina E. N.Definability of T1-spaces by the lattice of subalgebras of semirings of continuous partial real-valuedfunctions on them
The article refers to the general theory of semirings of continuous functions. We consider subalgebras of semirings CP(X) of continuous partial functions on topological spaces X with values in the topological field R of real numbers. We study the minimal and maximal subalgebras of the R-algebra CP(X). We prove a definability theorem of an arbitrary T1-space X by the lattice A(X) of all subalgebras of the semiring CP(X).
Keywords: semiring, field of real numbers, partial real-valued function, subalgebra.
References
Vechtomov E. M. Lattice of subalgebras of the ring of continuous functions and Hewitt spaces, Mat. Zametki, vol. 62, issue. 5, 1997, pp. 687–693.
Vechtomov E. M., Lubyagina E. N. On semirings of partial functions, Vestnik of Syktyvkar University. Series 1: Mathematics. Mechanics. Computer science, 2014, issue. 19, pp. 3–11.
Vechtomov E. M., Lubyagina E. N., Sidorov V. V., Chuprakov D. V. Elements of functional algebra: a monograph: in 2 volumes, vol. 1 / ed. E. M. Vechtomov, Kirov: Publishing House «Raduga-Press», 2016, 384 p.
Vechtomov E. M., Lubyagina E. N., Sidorov V. V., Chuprakov D. V. Elements of functional algebra: a monograph: in 2 vol, vol. 2 / ed. E. M. Vechtomov, Kirov: Publishing House «Raduga-Press», 2016, 316 p.
Grettser G. The theory of lattices, Moscow: Mir, 1982, 456 p.
Engelking R. General topology, Moscow: Mir, 1986, 752 p.
Gillman L., Jerison M. Rings of continuous functions, N. Y.: Springer-Verlang, 1976, 300 p.
For citation:Vechtomov E. M., Lubyagina E. N. Defiinability of T1-spaces by the lattice of subalgebras of semirings of continuous partial real-valued functions on them, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №1 (22), pp. 21–28.
III. Vechtomov E. M.,Orlova I. V.Ideals and congruences of cyclic semirings
Bestuzev A. S., Vechtomov E. M. Cyclic Semirings with Commutative Addition, Bulletin of Syktyvkar State University. Series 1: Mathematics. Mechanics. Informatics, edition 1 (20), 2015, pp. 8–39.
Vechtomov E. M. Introduction to Semirings, Kirov: VGPU, 2000, 44 p.
Vechtomov E. M., Bestuzev A. S., Orlova I. V. The Structure of Cyclic Semirings, IX Vserossiiskaya nauchnaya conferenciya «Matematicheskoe modelirovanie razvivausheysya ekonomoki, ekologii i tehnologii», EKOMOD – 2016: Sbornik materialov conferencii, Kirov: Izdatelstvo VyatGU, 2016, pp. 21–30.
Vechtomov E. M., Lubyagina (Orlova) I. V. Cyclic Semirings with Idempotent Noncommutative Addition, Fundamentalnaya i Prikladnaya Matematika, 2011/2012, t. 17, vyp. 1, pp. 33–52.
Vechtomov E. M., Orlova I. V. Cyclic Semirings with Nonidempotent Noncommutative Addition, Fundamentalnaya i Prikladnaya Matematika, 2015, t. 20, vyp. 6, pp. 17–41.
Orlova I. V. Ideals and Congruences of Cyclic Semirings with Noncommutative Addition, Trudi Matematiteskogo Centra imeni N. I. Lobachevskogo, Kazan: Kazanskoe matematicheskoe obshestvo, 2015, t. 52, pp. 118–120.
Skornyakov L. A. Elements of Algebra, M.: Nauka, 1986, 240 p.
Brown T. Lazerson E. On Finitely Generated Idempotent Semi-groups, Semigroup Forum, 2009, vol. 78, iss. 1, pp. 183–186.
For citation:Vechtomov E. M., Orlova I. V. Ideals and congruences of cyclic semirings, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №1 (22), pp. 29–40.
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.
Viola P., Jones M. Rapid Object Detection using a Boosted Cascade of Simple Features, 2013 IEEE Conference on Computer Vision and Pattern Recognition, 2001, vol. 01, 511 p.
Freund Y., Schapire R. E. Decision-Theoretic Generalization of On-Line Learning and an Application to Boosting, Journal of computer and system sciences 55, 1997, №SS971504, pp. 119–139.
For citation:Belykh E. A. Teaching Haar cascade, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №1 (22), pp. 41–53.
V. Odyniec W. P.On the history of the mathematical Olympiads in Leningrad — St. Petersburg
Article is devoted to the history of a solution of the problem of competitiveness in school education, one of form which are the mathematical Olympiads, which appeared in Russia in 1934 year in St. Petersburg (thenLeningrad). The statement is finished to the last decade.
Keywords: mathematical Olympiads, specialized professional school.
References
Atiyah M. Mathematics and the Computer Revolution, Izvestiya of Russian Academy of Science, Ser. Math, t. 80, № 4, 2016, pp. 5–16.
Salgaller V. F. The convex polyhedrons with the regular face, Notes of sciences seminars LOMI, t. 2, Leningrad: «Nauka», 1967, 211 p.
Morosova E. A., Petrakov I. S. International mathematical Olympiads, Moskcow: Prosveshchenie, 1971, 254 p.
Odyniec W. P. From the memory about mathematical Olympiad of the beginning of 60th years, Matematika v shkole, 1998, № 2, pp. 94–96.
Rukhshin S. E. Mathematicals contests in Leningrad–St.-Petersburg, The first 50 years, Rostov-on-Don: Press centre «MarT», 2000, 320 p.
Fomin D.V. St.-Petersburg mathematical Olympiad, St. Petersburg: Polytechnic, 1994, 309 p.
Memoirs of I All-Russian congress of teachers and lecturers of mathematic, St.-Petersburg: Press «Sever», 1913, t. I, 609 p.; t. II, 363 p.; t. III, 113 p.
For citation:Odyniec W. P. On the history of the mathematical Olympiads in Leningrad — St. Petersburg, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №1 (22), pp. 54–60.
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.
Giordano N. J., Nakanishi H. Computational physics, Pearson/ Prentice Hall, 2006, 544 p.
Coey, J. Magnetism and Magnetic Materials, Cambridge University Press, 2010, 633 p.
Binder K., Heermann D. W. Monte Carlo methods in Statistical Physics, M.: FIZMATLIT, 1995, 144 p.
Gould H., Tobochnik J. Computer modelling in physics, M.: Mir, 1990, 400 p.
For citation:Ustyugov V. A. The Ising model, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №1 (22), pp. 61–71.
VII. Kalinin S. I.,Dozmorov A. V.Pompeiu theorem and its generalizations
Dragomir S. S. An inequality of Ostrowski type via Pompeiu’s mean value theorem // http://www.emis.de/journals/JIPAM/index-4.html: Journal of Inequalities in Pure and Applied Mathematics. 6(3) Art. 83, 2005. URL: http://www.emis.de/journals/JIPAM/article556.html?sid=556 (date of the application: 09.03.2017).
Pompeiu D. Sur une proposition analogue au th´eor`eme des accroissements finis. Mathematica. Cluj, Romania, 22, 1946, pp. 143–146.
Finta B. A generalization of the Lagrange mean value theorem. Octogon. 4. № 2, 1996, pp. 38–40.
For citation:Kalinin S. I., Dozmorov A. V. Pompeiu theorem and its generalizations, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №1 (22), pp. 72–78.
VIII. Pevnyi A. B., Yurkina M. N.Inequalities for the sum of three quadratic trinomials
Dannan F.M., Sitnik S.M. The Damascus inequality, Probl. Anal. Issues Anal, vol. 5 (23), №2, 2016, pp. 3–19.
For citation:Pevnyi A. B., Yurkina M. N. Inequalities for the sum of three quadratic trinomials, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №1 (22), pp. 79–84.
IX. OdyniecV. P.On the seventieth of professor alexander borisovich pevny
The interview in connection with the 70th anniversary of the professor, doctor of physical and mathematical sciences Alexander Borisovich Pevny, who was celebrated on March 1, 2017.
For citation: OdyniecV. P.On the seventieth of professor Alexander Borisovich Pevny, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №1 (22), pp. 85–86.
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.
1. Belyaeva N. A., Sazhina A. N. Analizusrednennogonapornogotecheniya (Analysis of the averaged pressure flow), Twenty-third annual session of the Academic Council of Syktyvkar State University named after Pitirim Sorokin (February readings): a collection of materials / Otv.red. N. S. Sergiev, Syktyvkar: Publishing House of SSU named after Pitirim Sorokin, 2016, pp. 60–69.
2. Kolmogorov A. N, Petrovsky I. G, Piskunov N. S. Issledovanieuravneniya diffuzii, soedinennoj s vozrastaniemkolichestvaveshchestva, i ego primenenie k odnojbiologicheskoj problem (An investigation of the diffusion equation, coupled with the increase in the amount of matter, and its application to a single biological problem), Bul. Moscow State University. Section A, 1937, 633 p.
3. Kholodnik M., Klich A., Kubichek M., Marek M. Metodyanalizanelinejnyhdinamicheskihmodelej (Methods of analysis of nonlinear dynamic models), Moscow: Peace, 1991, 368 p.
4. Khudyaev S. I. Porogovyeyavleniya v nelinejnyhuravneniyah (Threshold phenomena in nonlinear equations), M.: Fizmatlit, 2003, 272 p.
For citation:Belyaeva N. A., Yakovleva A. F. Frontal wave of pressure flow, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, 2 (23), pp. 3–12.
II. Mikhailov A. V. The fluctuations of the ring supported with threads
Problems of fluctuations of the elastic rings supported with elastic threads; problems of the stability of elastic rings under the action of a pulsating load are considered.
1. Abramowitz M., Stegun I. A. Spravochnikpospecial’nymfunkciyam (Handbook of mathimatical functions with formulas, graphs and mathematical tables, National bureau of standards, applied mathematics series„ 1964, 1046 p.
2. Vol’mir A. S. Ustojchivost’ deformiruemyhsistem (Stability of deformable systems), Moscow: Nauka, 1967, 984 p.
3. Gelfand I. M., Fomin S. V. Variacionnoeischislenie (Calculus of Variations), Moscow: Gos. izd-vofiz.-matem. literatury, 1961, 228 p.
4. Lerman L. M. Linejnye differencial’nye uravneniyaisistemy (The linear differential equations and systems), Nizhny Novgorod: Nizhegorodsliyuniversitet, 2012, 89 p.
5. Mathews J., Walker R. L. Matematicheskiemetody v fizike (Mathematical methods of physics), New York – Amsterdam: W. A. Benjamin INC., 1964, 475 p.
6. PanovkoYa. G. Osnovyprikladnojteoriiuprugihkolebanij (Basics of applied theory of elastic vibrations), Moscow: Mashinostroenie, 1967, 318 p.
7. Tarasov V. N. Metodyoptimizacii v issledovaniikonstruktivnonelinejnyhzadachmekhanikiuprugihsistem (Optimization methods in a research of constructively nonlinear problems of mechanics of elastic systems), Syktyvkar: KNC UrO RAN, 2013, 238 p.
8. Ulam S. M. Nereshennyematematicheskiezadachi (A Collection of mathematical problems), New York: 1960, 150 p.
9. Faddeev L. D., Yakubovskii O. A. Lekciipokvantovojmekhanikedlyastudentov-matematikov (Lectures on Quantum Mechanics for Mathematics Students), Leningrad: Izd-voLeningradskogouniversiteta, 1980, 200 p.
For citation:Mikhailov A. V. The fluctuations of the ring supported with threads, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, 2 (23), pp. 13–28.
III. Pimenov R. R. The interpretation and generalizations of the Pappus’s theorems: involutions and perpendicularity
If we draw the arrows on the picture of projection we can see involutive transformation. Geometric picture now is a diagram of involutions and their compositions. It gives useful interpretation for theorems of projective geometry.We generalize these arrows to multidimensional spaces that connect geometry of spheres with projective space and non-euclidian geometries. We study perpendicularity also. We change the word incidence for the word perpendicularity in the Pappus’s theorem and get true and meaningful propositions.
Keywords: theory of numbers, Fermat’s little theorem, Dirichlet’s theorem.
References:
1. Bachmann F. Postroeniegeometriinaosnoveponyatiyasimmetrii (Aufbau der GeometrieausdemSpiegelungsbegriff), М.: Nauka, 1969, 380 p.
2. Pimenov R. R. ObobshcheniyateoremyDezarga: geometriyaperpendikulyarnogo (The generalization of the Desargues’s theorem and geometry of perpendicularity), Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2016, №1 (21), pp. 28–43.
3. Pimenov R. R. ObobshcheniyateoremyDezarga: skrytyeprostranstva (The generalization of the Desargues’s theorem and hidden subspaces), Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2016, №1 (21), pp. 44–57.
4. Pimenov R. R. Otobrazheniyasferyineevklidovygeometrii (Mapping the sphere and non-euclidian geometries), Mathematical Education, 1999, ser. 3, № 3, pp. 158–166.
5. Pimenov R. R. Ehsteticheskayageometriyailiteoriyasimmetrij (Aesthetic geometry or theory of symmetries). SPb: School league, 2014, 288 p.
6. Hartshorne R. Osnovyproektivnojgeometrii (Foundations of Projective Geometry). Lecture notes at Harvard University. W. A. Benjamin 1nc, New York, 1967.
7. Tabachnikov S. Skewers, Arnold Mathematical Journal, 2, 2016, pp. 171–193.
For citation:Pimenov R. R. The interpretation and generalizations the Pappus’s theorems: involutions and perpendicularity, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, 2 (23), pp. 29–45.
IV. Makarov P. A. On the variational principles of the mechanics of conservative and non-conservative systems
On the basis of the Hamilton—Ostrogradsky principle, applied to the motion of conservative and non-conservative systems, homogeneous and inhomogeneous Euler—Lagrange equations are compiled. An example of a plane motion of a material point is considered. The influence of dissipative forces on the characteristics of motion is determined.
Keywords: Hamilton’s mechanical action, variational principles of motion, the Euler—Lagrange equation, straight and circuitous paths, energy dissipation.
References:
1. Veretennikov V. G., Sinitsin V. A. Metodperemennogodejstviya (Method of variable action), 2 ed, M.: FIZMATLIT, 2005, 272 p.
2. Veretennikov V. G., Sinitsin V. A. Teoreticheskayamekhanika (Theoretical mechanics (additions to the general sections)), M.: FIZMATLIT, 2006, 416 p.
3. Gantmacher F. R. Lekciipoanaliticheskojmekhanike (Lectures on analytical mechanics), 2 ed, M.: Science, 1966, 300 p.
4. Goldstein G. Klassicheskayamekhanika (Classical mechanics), M.: Science, 1975, 416 p.
5. Landau L. D., Lifshitz E. M. Teoreticheskayafizika (Theoretical physics: V.I, Mechanics), 5 ed, M.: FIZMATLIT, 2007, 224 p.
6. Sludsky F. A. Zametka o nachalenaimen’shegodejstviya (A note on the principle of least action), Varational principles of mechanics, M.: FIZMATGIZ, 1959, pp. 388–391.
For citation: Makarov P. A. On the variational principles of the mechanics of conservative and non-conservative systems, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, 2 (23), pp. 46–59.
V. Odyniec W. P. Zenon IvanovichBorewicz (1922–1995) (To the 95th anniversary)
The article is devoted to the biography of the famous algebraist professor ZenonIvanovichBorewicz (to pronounce Borevich), the dean of Mathematics and Mechanics faculty of the Leningrad state university in 1973–83 years, seen by Polish mathematicians, and also to Z.I. Borewicz contacts with Poland, with detailed comments of the author.
Keywords: Z.I. Borewicz, the Siege of Leningrad, homologous algebra, linear groups theory, society of «Polonia».
References:
1. Narkiewicz W., Wie¸s law W. ZenonBorewicz (1922–1995), Wiadomo´sciMatematyczne, 36, 2000, pp. 65–72.
2. Odyniec W. P. About mathematicians of Leningrad, Wiadomo´sciMatematyczne, 27, 1987, pp. 279–292.
3. Odyniec W. P. About mathematicians of Leningrad – (St. Petersburg) – and not only of them, Wiadomo´sciMatematyczne, 34, 1998, pp. 149–158.
4. Jakovlev A. V. ZenonIvanovichBorevich. Questions of the theory of representations of algebras and groups. 5, Zapiskinauchnyhseminarov POMI, t. 236, 1997, pp. 9–12.
For citation:Odyniec W. P. ZenonIvanovichBorevich (1922–1995) (To the 95th anniversary), Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, 2 (23), pp. 60–69.
VI. Lubyagina E. N., Timshina L. V. Experience in the organization of students’ educational and research activities in the study of second-order curves
In the article, we offer materials that can be used to organize students’ educational and research activities in studying second-order curves. We give examples of the use of the GeoGebra environment.
Keywords: research activity, second-order curves, GeoGebra.
References:
1. Akopyan A. V., Zaslavsky A. A. Geometricheskiesvojstvakrivyhvtorogoporyadka (Geometric properties of second-order curves), М ., 2007, 136 p.
2. Atanasyan L. S., Atanasyan V. A. Sbornikzadachpogeometrii (Collection of problems on geometry), Textbook for students of physical and mathematical sciences, I. M.: Enlightenment, 1973, 480 p.
3. Bezumova O. L., Ovchinnikova R. P., Troitskaya O. N., Troitsky A. G., Vorkunova L. V., Shabanova M. V., Shirokova T. S., Tomilova O. M. Obucheniegeometrii s ispol’zovaniemvozmozhnostejGeoGebra (Geometry training using GeoGebra capabilities), Arkhangelsk: Kira, 2011, 140 p.
4. Boltyanskii V. G. Ogibayushchaya (Envelope), Kvant, N. 3, 1987, pp. 2–7.
5. Vechtomov E. M. ,Lubyagina E. N. Geometricheskieosnovykomp’yuternojgrafiki (Geometric Foundations of Computer Graphics: A Training Manual), Kirov. Publishing house: «Rainbow-Press», 2015, 164 p.
6. Gurov A. E. Zamechatel’nyekrivyevokrugnas (Wonderful curves around us), M., 1989, 112 p.
7. Zabelina C. B. Formirovanieissledovatel’skojkompetentnostimagistrantovmatematicheskogoobrazovaniya (Formation of research competence of undergraduates of mathematical education (direction pedagogical education)). Dis. … cand. ped. sciences, M., 2015.
8. Kachalova L. P. Issledovatel’skayakompetenciyamagistrantov: strukturno-soderzhatel’nyjanaliz (Research competence of undergraduates: structurally-substantial analysis), Political journal of scientific publications «Discussion», 3 (55), 2015.
9. Ruinsky A. Inversnyepreobrazovaniyagiperboly (Inverted hyperbola transformations), Mathematical education, s. 3, 4 (2000), pp. 120–126.
10. Smirnov V. I. Kursvysshejmatematiki (Course of Higher Mathematics), t. 2, M.: «Science», 1974, 479 p.
11. Timshina L. V. Seminarskiezanyatiyapogeometrii v vuze (Seminars on Geometry in the University), Teaching Mathematics, Physics, Informatics in Universities and Schools: Content Problems, Technologies and Techniques: Proceedings of the V All-Russian Scientific Conference. Conf. Glazov: «Glazov printing house», 2015, p. 131–133.
12. Chebotareva E. V. Komp’yuternyjehksperiment s GeoGebra (Computer experiment with GeoGebra), Kazan: Kazan University, 2015, 61 p.
13. Shabanova M. V., Ovchinnikova R. P., Yastrebov A. V., Pavlova M. A., Tomilova A. E., Forkunova L. V., Udovenko L. N., Novoselova N. N., Fomina N. I., Artemieva M. V., Shirikova T. S., Bezumova O. L., Kotova S. N., Parsheva V. V., Patronova N. N., Belorukova M. V., Teplyakov V. V., Rogushina T. P., Tarkhov E. A., Troitskaya O. N., Chirkova L. N. Ehksperimental’nayamatematika v shkole. Issledovatel’skoeobuchenie (Experimental mathematics in the school. Research training. Monograph on research activities), M.: Publishing house Academy of Natural History, 2016, 300 p.
14. Shirikova T. S. Metodikaobucheniyauchashchihsyaosnovnojshkolydokazatel’stvuteorempriizucheniigeometrii s ispol’zovaniem Geo Gebra (Method of teaching students of the basic school the proof of theorems in the study of geometry using GeoGebra). Diss. … cand. ped. sciences. Arkhangelsk, 2014.
15. Jaglom I. M., Ashkinuz V. G. Ideiimetodyaffinnojiproektivnojgeometrii: CH. I (Ideas and methods of affine and projective geometry, I). M: 1962, 247 p.
For citation:Lubyagina E. N., Timshina L. V. Experience in the organization of students’ educational and research activities in the study of second-order curves, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, 2 (23), pp. 70–84.
VII. Yermolenko A. V., Osipov K. S. Parallel programming in contact problems with a free boundary
The method of generalized reaction requires a large number of iterations, on each of which a large number of calculations is carried out. To accelerate calculations, the article considers parallelizing a contact problem using the OpenMP technology in C ++.
Keywords: plate, method of generalized reaction, contact problem, parallel computing.
References:
1. Antonov A. S. Parallel’noeprogrammirovanie s ispol’zovaniemtexnologiiOpenMP (Parallel Programming Using OpenMP Technology), Moscow.: Publishing house of MSU, 2009, 77 p.
2. Yermolenko A. V., Gintner A. N. Vliyaniepoperechny’xsdvigovnaponizhenienapryazhennogosostoyaniyaplastiny (The effect of transverse shear on the lowering of the stressed state of the plate), Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2015, №1 (20), pp. 91–96.
3. Yermolenko A. V. TeoriyaploskixplastintipaKarmana–Timoshenko–Nagdiotnositel’noproizvol’nojbazovojploskosti (The Karman– Timoshenko–Naghdi theory of plane plates relative to arbitrary base surface), In the world of scientific discoveries, Krasnoyarsk: SIS, 2011, № 8.1 (20), pp. 336–347.
4. Mikhailovskii E. I., Yermolenko A. V., Mironov V. V., Tulubenskaya E. V. Utochnenny’enelinejny’euravneniya v neklassicheskixzadachaxmexanikiobolochek (Refined nonlinear equations in nonclassical problems of shell mechanics), Syktyvkar: Publishing house of the Syktyvkar university, 2009, 141 p.
5. Mikhailovskii E. I., Tarasov V. N. O sxodimostimetodaobobshhennojreakcii v kontaktny’xzadachax so svobodnojgranicej (On the convergence of the generalized reaction method in contact problems with a free boundary, Journal of Applied Mathematics and Mechanics, 1993, v. 57, №. 1, pp. 128–136.
For citation:Yermolenko A. V., Osipov K. S. Parallel programming in contact problems with a free boundary, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, 2 (23), pp. 85–91.
VIII. Chuprakov D. V., Vedernikova A. V. About structure of finite cyclic semirings with idempotent commutative addition
The paper deals with finite idempotent cyclic semirings with commutative addition. Authors present a criterion for existence of finite idempotent cyclic semirings with commutative addition, associated with ideal of nonnegative integers. They derive estimates of the cardinality of FIC-semiring. The article offers algorithms for calculation of cardinality of FIC-semiring by basis of associated ideal of nonnegative integers.
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.
The article is devoted to the description of scientific work with the wellknown mathematician and mechanic, the honored worker of the Russian Federation, the doctor of physical and mathematical sciences, professor EvgenyIlyichMikhailovskii (1937–2013).
Keywords: refined theory of plates, contact problem.
References:
1. Vavilina N. N., Yermolenko A. V., Mihajlovskii E. I. Ustojchivost’ podkreplennojshpangoutamicilindricheskojobolochki (Stability of a cylindrical shell reinforced by frames), In the world of scientific discoveries, Krasnoyarsk: SIS, 2013, № 2.1 (38), pp. 43–55.
2. Yermolenko A. V. O poludeformacionnomvariantegranichnyhvelichin v teoriigibkihplastinKarmana (On the semi-deformational variant of boundary values in the theory of the flexible Karman plates), Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 1996, №2, pp. 235–242.
3. Yermolenko A. V. TeoriyaploskixplastintipaKarmana–Timoshenko–Nagdiotnositel’noproizvol’nojbazovojploskosti (The Karman– Timoshenko–Naghdi theory of plane plates relative to arbitrary base surface), In the world of scientific discoveries, Krasnoyarsk: SIS, 2011, № 8.1 (20), pp. 336–347.
4. Yermolenko A. V., Mihajlovskii E. I. Granichnyeuslovijadljapodkreplennogokraja v teoriiizgibaploskihplastinKarmana (Boundary conditions for the reinforced edge in the Karman theory of bending of flat plates), IOO, 1998, № 3, pp .73–85.
5. Mihajlovskii E. I., Badokin K. V., Yermolenko A. V. TeorijaizgibaplastintipaKarmana bez gipotezKirhgofa (The theory of bending of Karman-type plates without the Kirchhoff’s hypotheses), Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 1999, №3, pp. 181–202.
For citation:Yermolenko A. V. Scientific work with Yevgeny Ilyich, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 4–10.
II. Melnikov V. A. Methods for representing figures of general kind for a two-dimensional cutting problem
This article introduces representation of figures as rastr matrixes. Also the algorithm of additional data processing for reducing future computations difficulty is given. The last part describes principles of positioning figures on the workpiece.
Keywords: figures of general kind, cutting, two-dimensional space, bottomleft principle.
References:
1. Dyckhoff H. A typology of cutting and packing problems, European Journal of Operational Research, № 44, pp. 150—152.
2. Zalgaller V. A., Kantorovich L. V. Ratsionalnyi raskroi promyshlennyh materialov (Rational cutting of industrial materials), Novosibirks: Nauka, 1971, 300 p.
3. Nikitenkov V. L., Holopov A. A. Zadachi lineynogo programmiriovaniya i metody ih resesheniya (Linear programming problems and methods for their solution), Syktyvkar: Izdatelstvo Syktyvkarskogo universiteta, 2008, 143 p.
4. Prasolov V. V. Zadachi po planimetrii (Planning problems), 4th ed., dopolnennoe, M.: MCNMO, 2001, 584 p.
5. Shabat B. V. Vvedenie v kompleksnyi analiz (Introduction to complex analysis), M.: Nauka, 1969, 91 p.
6. Benell A. J., Olivera F. J. The geometry of nesting problems: A tutorial, European Journal of Operational Research, 2008, № 184, pp. 399—402.
7. Coordinate Systems, Transformations and Units // https:// www.w3.org: W3C. 6 мая 2017. URL: https://www.w3.org/TR/ SVG/coords.html.W3C (date of the application: 05.10.2017)
For citation: Melnikov V. A. Methods for representing figures of general kind for a two-dimensional cutting problem, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 11–24.
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.
1. Guan Kaizhong. GA-convexity and its applications, Anal. Math. 2013, 39, № 3, pp. 189–208.
2. Xiao-Ming Zhang, Yu-Ming Chu, and Xiao-Hui Zhang. The Hermite-Hadamard type inequality of GA-convex functions and its application, J. of Inequal. and Applics., Vol. 2010, Article ID 507560, 11 pages, doi:10.1155/2010/507560.
3. Kalinin S. I. (α,β)-vypuklye funkcii, ix svojstva i nekotorye primeneniya ((α,β)-convex functions, their properties and some applications), Ufa international mathematical conference. Abstracts / Executive editor R. N. Garifullin. Ufa: RITS Bashgu, 2016, pp. 75–76.
4. Abramovich S., Klariˇci´c Bakula M., Mati´c M. and Peˇcari´c J. A variant of Jensen–Steffensen’s inequality and quasi-arithmetic means, J. Math. Anal. Applics., 307 (2005), pp. 370–385.
5. Mercer A. McD. A variant of Jensen’s inequality, J. Inequal. In Pure and Appl. Math., Vol. 4, Issue 4, Article 73, 2003, pp. 1–2.
For citation: Kalinin S. I. GA-convex functions, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 25–42.
IV. Lovyagin Yu. N. Some remarks on the problem of the normability of Boolean algebras
We study the connection between the property of normability of a Boolean algebra and the existence on it of a semi-additive (o) -continuous essentially positive function. Criteria are given, under which the seminormalized Boolean algebra has no measure.
Keywords: Boolean algebra, measure, problem D. Magaram.
References:
1. Poroshkin A. G. Teoriyameryiintegrala (Theory of measure and integral), Moscow: KomKniga, 2006, 184 p.
2. Poroshkin A. G. Uporyadochennyemnozhestva. Bulevyalgebry (Ordered sets. Boolean algebras), Syktyvkar: Syktu State University, 1987, 85 p.
3. Halmos P. Measure theory, Berlin-Haidelberg-New York: Springer, 1950, 304 p.
4. Kelley J. General topology, Toronto-London-New York: D van Nostard company, 1957, 432 p.
5. Vladimirov D. A. Bulevyalgebry (Boolean algebras), Moscow: Nauka, 1969, 318 p.
6. Vladimirov D. A. Teoriyabulevyhalgebr (The theory of Boolean algebras), St. Petersburg: Publishing house of the St. Petersburg University, 2000, 616 p.
7. Halmos P. Lectures on Boolean algebras, Prinston, New-Jersey. D. vanNostardcompany, 1963, 96 p.
8. Mayaram D. An algebraic characterization of measure algebras, Ann. Math., 1947, v. 48, № 1, pp. 154–167.
9. Popov V. A. Additivnyeipoluadditivnyefunkciinabulevyhalgebrah (Additive and semiadditive functions on Boolean algebras), Sibirsk. mat., 1976, vol. 17, No 2, pp. 331–339.
10. Alexyuk V. N. Teorema o minorante. Schetnost’ problemyMagaram (The Minorant Theorem. The countability of the problem of Magaramz), Mathematics, 1977, t. 21, No. 5, pp. 597–604.
11. Lovyagin Yu. N. Bulevyalgebry s dostatochnymchislomnepreryvnyhkvazimer (Boolean algebras with a sufficient number of continuous quasimers), Syktyvkar: Dep. in VINITI, № 3111-В97, 1997, 24 p.
12. Lovyagin Yu. N. O nekotoryhsvojstvahbulevyhalgebr (On some properties of Boolean algebras), Some actual problems of modern mathematics and mathematical education: Proceedings of the scientific conference «Herzen readings — 2009», SPb: RSPU them. A. I. Herzen, 2009, pp. 131–135.
13. Lovyagin Yu. N. Regulyarnyeipolunormirovannyebulevyalgebry (Regular and semi-normalized Boolean algebras), Some actual problems of modern mathematics and mathematical education: Proceedings of the scientific conference «Herzen readings — 2011», SPb: RSPU them. A. I. Herzen, 2011, pp. 146–148.
14. Lovyagin Yu. N. Primer regulyarnoj, no nenormirovannojbulevyalgebry (An example of a regular but not normalized Boolean algebra), Some actual problems of modern mathematics and mathematical education: Proceedings of the scientific conference «Herzen Readings — 2012», SPb: RSPU them. A. I. Herzen, 2012,pp. 129–130.
15. Lovyagin Yu. N. O problemenormiruemostibulevyhalgebr (On the problem of normability of Boolean algebras), Proceedings of the Russian Pedagogical University. A. I. Herzen, 2013, № 154, pp. 23–33.
16. Gaifman H. Cjncerning measure on Boolean algebras, Pacif. J. Math., 1964, v. 14, № 1, pp. 61–73.
For citation:Lovyagin Yu. N. Some remarks on the problem of the normability of Boolean algebras, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 43–55.
V. Pimenov R. R. The geometry of perpendicularity: obtuse and acutes angles in known theorems
In the article we introduce and research the conception of «the impossible configuration of obtuse and acute angles» and its relation to theorems about perpendicularity in the plane and Rn. We study two theorems, about intersection altitudes in triangle and about projections, the last we named as «the domino theorem». We generalise both theorems for arbitrary numbers of lines and discover related with them impossible configuration of angles. We show as using continuity and method of «small moving» we can derive theorems about perpendicular lines from impossible configurations of angles. We view at the right angle as the boundary between acute and obtuse angles for this. We consider the using of these methods in non-Euclidean geometry, in Rn and express them in terms of vector algebra.
Keywords: perpendicularity, continuity, projection, orientation, altitude of triangle.
References:
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2, 2016, pp. 171–193.
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For citation:Pimenov R. R. The geometry of perpendicularity: obtuse and acutes angles in known theorems, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 56–73.
VI. Gulyaeva S. T., Kabanova S. L., Mironov V. V. To a problem of increase in effectiveness of educational process when using the modern systems of the organization of videoconferences
In work topical issue of increase in effectiveness of educational process when using the modern systems of the organization of videoconferences is considered. The chart of business process of use of videoconferences is provided and technologies and most the videoconferences popular systems are considered.
Keywords: education, videoconference, effectiveness, business process, videoconferencing.
References:
1. Videokonferencsvjaz’. Avtor: KompanijaTrueConf // https:// trueconf.ru/: TrueConf 7.2 для Windows. URL: https:// trueconf.ru/ videokonferentssvyaz/070 (date of the application: 10.07.2017).
2. Chtotakoe VoIP? // http://aver.ru/: Vsyo o novinkaxtexniki. URL: http://aver.ru/all/chto-takoe-voip/ (date of the application: 10.07.2017).
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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).
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7. O kompanii Life size // http:// av-pro.com.ua/: Kompaniyaavpro. URL: http://av-pro.com.ua/taxonomy/term/15/0 (date of the application: 10.07.2017).
8. Videokonferencsvjaz’. Chast’ 1: Vvedenie v predmet // http://networklab.ru/: Setevayaakademiya CISCO. URL: http:// network-lab.ru/ videokonferentssvyaz-chast-1-vvedenie/ (date of the application: 10.07.2017).
9. Prodazhaoborudovanija Polycom // http:// www.polycom-spb.ru: Polycom. URL: http://www.polycom-spb.ru/Polycom_HDX_70001080 (date of the application: 10.07.2017).
For citation:Gulyaeva S. T., Kabanova S. L., Mironov V. V. To a problem of increase in effectiveness of educational process when using the modern systems of the organization of videoconferences, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 74–87.
VII. Odyniec W. P. On a history of some mathematical models in ecology
The prehistory of the appearance of some mathematical models and methods in ecology is briefly reviewed. History the five mathematical models reviewed in detail: the model, which based on multifractal analysis, the model of absorption by rain of pollution of atmosphere, the Lotka–Volterramodelsand their development, the model of the population stability by the genetic level.
Keywords:Margalef index, Hedervari estimation, multifractal analysis, the Lotka–Volterra models, repressilator.
References:
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For citation:Odyniec W. P. On a history of some mathematical models in ecology, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 88–103.
VIII. Ustyugov V. A., Chufyrev A. E. The percolation problem
The article gives an overview of algorithms for solving the problem of finding a spanning cluster on a square lattice. A technique for determining the percolation threshold is described. The singular behavior of the last dependence in the vicinity of the critical concentration is explained. The solution of the problem in the form of a program in Python programming lagnuage is given.
For citation:Ustyugov V. A., Chufyrev A. E. The percolation problem, Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 104–113.
IX. Vechtomov E. M. Yevgeny IlyichMikhailovsky (to the fiftieth anniversary from the birthday)
The article is devoted to the prominent scientist, the deserved figure of science of the Russian Federation, the head of the school of mechanics of the Komi Republic, the doctor of physics and mathematics, professor EvgenyMikhailovsky.
For citation:Vechtomov E. M. Yevgeny IlyichMikhailovsky (to the fiftieth anniversary from the birthday), Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2017, №3 (24), pp. 114– 117.
