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I. Vechtomov E. M., Chermnykh V. V. Main directions of the development of the semiring theory

DOI: 10.34130/1992-2752_2021_4_4

Vechtomov Evgeny Mikhailovich − Doctor of Physical and Mathematical Sciences, Professor, Head of the Department of Fundamental and Computer Mathematics, Vyatka State University, e-mail: vecht@mail.ru

Chermnykh Vasily Vladimirovich − Doctor of Physical and Mathematical Sciences, Pitirim Sorokin Syktyvkar State University, chief scientist, e-mail: vv146@mail.ru

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The article highlights and analyzes the main directions of formation and development of Semiring Theory. The first ring-module direction summarizes and extends the theory of rings and modules onto semirings and semimodules over them. The next one is a universal algebraic direction that is based on Universal Algebra and Group Theory. The third direction is connected with study of special classes of semirings and is aimed at using semirings within Mathematics, in Computer Sciences and in applications of Mathematics. The first two directions contain investigating of the general theory of semirings, building structural theories for certain important and interesting classes of abstract semirings. The third direction includes describing of finite semirings with certain conditions.

Keywords: semiring, semifield, semimodule, ring, distributive lattice, development of Theory of Semirings.

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For citation: Vechtomov E. M., Chermnykh V. V. Main directions of the development of the semiring theory. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2021. No. 4 (41), pp. 4−40. DOI: 10.34130/1992-2752_2021_4_4

II. Andryukova V. Yu. Variational approach to calculating critical loads in the case of spatial deformation of curved rods

DOI: 10.34130/1992-2752_2021_4_41

Andryukova Veronika Yuryevna − Associate Professor, Komi Science Center, Ural RAS Department, e-mail: veran@list.ru

Text

A detailed derivation of the formulas of elastic energy and work of external forces for rings loaded with central forces is given. xpressions for calculating the critical load are presented in the case of plane deformation of the ring, as well as in the case of the spatial form of buckling.

Keywords: curvilinear bar, critical load, stability, Euler equations, work of external forces, elastic energy

References

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For citation: Andryukova V. Yu. Variational approach to calculating critical loads in the case of spatial deformation of curved rods. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2021, No. 4 (41), pp. 41−49. DOI: 10.34130/1992-2752_2021_4_41

III. Yermolenko A. V., Melnikov V. A. Solving the problem of abstraction from platform-specific code for iOS and Android applications using the example of SadLion Engine

DOI: 10.34130/1992-2752_2021_4_50

Yermolenko Andrei Vasilievich − PhD in Physics and Mathematics, Associate Professor, Head of Department of Applied Mathematics and Computer Science, Pitirim Sorokin Syktyvkar State University, e-mail: ea74@list.ru

Melnikov Vadim Andreevich − Postgraduate student, Pitirim Sorokin Syktyvkar State University, e-mail: ea74@list.ru

Text

The paper examines existing solutions for cross-platform mobile development, compares their features, advantages and disadvantages. It describes the solution to various problems arising in the development of your own cross-platform engine for development for iOS and Android.
The construction of a system for displaying a visual interface on a user screen using a GPU is considered. The architectural solutions used to write high-performance logic of application behavior in the C ++ programming language are described. The life cycles of applications for the iOS and
Android platforms are considered and a way to abstract from the native life cycle is proposed to generalize the application code on both platforms.The implementation of interlanguage interaction between Java and C ++ using JNI on the Android platform and Objective-C and C ++ is described,
architectural solutions are given for building an abstraction layer that hides such low-level interactions in the engine core.

Keywords: cross-platform development, C ++, Android, iOS.

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For citation: Yermolenko A. V., Melnikov V. A. Solving the problem of abstraction from platform-specific code for iOS and Android applications using the example of SadLion Engine. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2021, No. 4 (41), pp. 50−69.
DOI: 10.34130/1992-2752_2021_4_50

IV. Dorofeev S. N., Esetov E. N., Nazemnova N. V. Analogy as the basis for teaching students the vector method of geometric problem solving

DOI: 10.34130/1992-2752_2021_4_70

Dorofeev Sergey Nikolaevich – Doctor of Pedagogy, Professor of the Department of Higher Mathematics and Mathematical Education, Togliatti State University (Russia, 445020, Samara Region, Tolyatti, Belorusskaya St., 14)

Esetov Yelzhan Nurlykhanovich – postgraduate student of the department “Higher Mathematics and Mathematical Education” Togliatti State University (Russia, 445020, Samara region, Tolyatti, Belorusskaya st., 14)

Nazemnova Natalia Vladimirovna − Candidate of Pedagogical Sciences, Senior Lecturer, Department of Higher Mathematics, Penza State University (Russia, 440020, Penza region, Penza, Krasnaya st., 40

Text

This article examines the ways and the methods that contribute to improving the quality of teaching students the basics of vector algebra and methods of their application to solving geometric problems. For this purpose, the necessary knowledge of the basics of vector algebra, which students should learn in the process of studying the topic “Fundamentals of
vector algebra”, is highlighted and systematized. The paper substantiates the fact that such a method of cognition as analogy plays an important role in the effectiveness of the process of
teaching high school students to apply the basics of vector algebra to solving geometric problems. Some examples of interrelated tasks that contribute to improving the quality of teaching students the use of the vector method are given.

Keywords: Vector method, training in solving geometric problems, analogy.

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For citation: Dorofeev S. N., Esetov E. N., Nazemnova N. V. Analogy as the basis for teaching students the vector method of geometric problem solving. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2021, No. 4 (41), pp. 70−82. DOI: 10.34130/1992-2752_2021_4_70

V. Yermolenko A. V., Belyaev E. A., Turkova O. I. One contact problem for two plates

DOI: 10.34130/1992-2752_2021_4_83

Yermolenko Andrei Vasilievich − PhD in Physics and Mathematics, Associate Professor, Head of Department of Applied Mathematics and Computer Science, Pitirim Sorokin Syktyvkar State University, e-mail: ea74@list.ru

Belyaev Evgeniy Anatolievich − Postgraduate student, Pitirim Sorokin Syktyvkar State University, e-mail: ea74@list.ru

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Using the generalized reaction method, a numerical solution of the contact problem for two plates is given. One plate is hinged, the other one is rigidly fixed. It is shown that the distribution of contact reactions significantly depends on the relative position of the plates. In this case, the contact zone is either a segment or a point.

Keywords: plate, contact problem, generalized reaction method, numerical solution.

References

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For citation: Yermolenko A. V., Belyaev E. A., Turkova O. I. One contact problem for two plates . Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2021. No. 4 (41), pp. 83−89. DOI: 10.34130/1992-2752_2021_4_83

VI. Rogosin S. V. Remark to the paper

DOI: 10.34130/1992-2752_2021_4_90

Rogozin Sergey Vasilyevich − PhD in Physics and Mathematics, Associate Professor at the Department of Analytical Economics and Econometrics, Belarusian State University, Minsk, Belarus, e-mail: rogosin@bsu.by

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An assertion on p. 31 “Note that X(z) is a rational matrix which is analytic outside of the unit disc (but not necessary analytic at infinity) since. . . ” is imprecise. This assertion including the expression after it be omitted since on the first stage of factorization the corresponding
transformation is performed only on the unit circle and does not involve any analyticity properties of the matrix X(z).

For citation: Rogosin S. V. Remark to the paper. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2021. No. 4 (41), pp. 90−91. DOI: 10.34130/1992-2752_2021_4_90

I Andrykova V. Yu., Tarasov V. N. On the stability of rod with one-sided restrictions on the moving

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II Kostyakov I. V., Kuratov V. V. Contractions of Lagrangian in calssical mechanics

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III Mikhailovskii E. I., Korablev A. J. The longitudinal stability of a cylindrical cover supported by stringers in a multimoduls elastic surroundings

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IV Pevnyi A. B., Kotelina N. O. Complex spherical semidesigns

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V Vechtomov E. M., Petrov A. A. Multiplicative idempotent semirings with identity x+2xyx=x

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VI Ilchukov A. S. Singular integral with Cauchy kernel in spaces defined by modulus of continuity

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VII Mekler A. A. Multiplicativity of Marcinkiewicz Modulars. Tables of Bases

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VIII Mekler A. A. On semigroup of Marcinkiewicz Modulars.

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IX Moskin G. V., Nikitenkov V. L., Sitkarev G. A. Synthesis of perspective transformation matrix

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X Nikitenkov V.L., Koyushev P.I.Stability of a rod in a medium with linearly varying rigidity (solution using power series)

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XI Nikitenkov V.L., Pobrey A. A. Scanned text binarization and segmentation

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XII Odynec V. P. About Boris Zakharovich Vilikh – hereditary mathematician and typical St. Petersburg born and bred citizen (To centenary anniversary of his birth)

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I To the 25th anniversary of the MMIK department

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II Belyaeva N. A. Internal stresses symmetric products in their formation based nonzero critical depth conversion

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III Belyaeva N. A., Pryanishnikova E. A. Thr averaging method in the problem of mathematical modeling of composite extrusion

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IV Belyayev Yu. N. Symmetric polynomias in the calculation of the matrix exponential

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V Mikhailovskii E. I. The half century with the mechanics of shells (Part II – the nonlinear theory)

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VI Nikitenkov V. L., Kholopov A. A. Stability of a flexible core in elastic enviroment

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VII Grytczuk A. An effective algoritm to peivate-key in the RSA cryptosystem

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VIII Markov R. V., Chermnykh V. V. Pierce chains for semirings

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IX Mekler A. A. On Marcinkiewicz Modulars on [0, 1] and [0, ∞) – II

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X Orlova I. V. About finite cyclic semirings with nonidempotent non-commutative addition

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XI Martynov V. A., Mironov V. V. The problem of the optimization of the standart sorting through technology MPI

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I A word about Mikhailovsky Evgeny Ilyich

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II Prof. EI Mikhailovsky from prof. V. F. Demyanova

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III Mikhailovskii E. I. Mechanics of shells

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IV Belyaeva N. A., Pryanishnikova E. A. Mathematical modeling in the extrusion

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V Yermolenko A. V. On analitical solution of the contact problem

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VI Maloxemov V. N. On the fortieth anniversary of MDM-method

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VII Tarasov V. N., Andryukova V. Yu. On stability behavior of a toroidal shell with a one-sided reinforcement

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VIII Vechtomov E. M., Lubiagina E. N. Semirings of sc-functions

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IX Golovneva E. V. A class of matrices with diagonall domination

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X Grytczuk A. Ankeny, Artin and Chowla conjecture for even generators

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XI Mekler A. A. On Marcinkiewicz Modulars on [0, 1] and [0,∞)

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XII Mironov V. V., Mayburov A. S. The method of nonlinear integral equations in the problem of bending of a closed cylindrical shell with rigidly clamped edges

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XIII Nikitenkov V. L., Jidkova O. A., Shekhurdina E. S. The boundaries of finding the critical force in the environment multimoduls

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XIV Popova N. K., Ogirchyk T. A. 3D animation and simulation of an object with Autodesk 3ds Max 2009

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XV Odynec W. P. Returning to H. Kummer

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XVI Poroshkina A.A., Poroshkin A.G. Three counterexamples in analysis

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I Luca F., Odyniec W.P. The characterisation of Van Kampmen-Flores complexes by means of system of diopantine equations

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II Poroshkin A. G. On the problem of order continuity of Choquet functional

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III Andryukova V. Yu., Tarasov V. N. Some problems of stability of elastic system

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IV Antonova N. A. Dynamics of two demensional pulse-width modulated control system

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V Belyaeva N. A., Gorst D. L., Khudaev S. I. Cuat nonuniform flow of the structured liquid

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VI Golovach P. A. L(2,1)-coloring of precolored cacti

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VII Mikhailovskii E. I., Ermolenko A. V., Mironov V. V. Elements of the applied tensor analysis in the deformed bodies

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VIII Mikhailovskii E. I., Nilitenkov V. L., Chernykh K. F. On some aspects of the account of transversal deformations in the theory of shells and plates

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IX Pevnyi A. B. Multiresolution analysis in the space of square summable discrete signals

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X Poleshikov S. M., Kholopov A. A. The problem of optimal positions for a triple of four-dimensional orts

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XI Kholmogorov D. V. Supercritical behavior of a substantianed plate

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XII Khudyaev S. I. Symmetrical flaming on phase transform conditions

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XIII Chernykh K. F. On anisotropic nonlinear elasticity

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XV Mikhailovskii E. I., Tulubenskaya E. V. The influence of transversal deformation on the frequency spectrum of round plate

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XVI Somorodnitski A. A., Kotelina N. O. Systems of generators in measure spaces

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XVII Somorodnitski A. A., Muravjev A. A. Kakutani-Oxtoby theorem in the non-separable

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XIX Kholopov A. A., Stenina N. A. A continuous model of equipment replacing problem

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XX Zvonilov V. I. Rigid isotopy classificatin of real algebraic curves of bidegree (4,3) on a hyperboloid

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I Bazhenov I. I. Atoms of set families and of vectors measures

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II Poroshkin A. A., Poroshkin A. G. On the topology generated by the collection of quasi-norms

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III Poroshkin A. A., Shergin Yu. V. On the Choquet functional and one its application in measure theory

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IV Timofeev A. Y., Cyvunina T. E. The problem of Ricaman-Hilbert for the generalized Cauchy-Riemann system with a singularity

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V Tikhomirov A. N. On the Central Limit Theorem

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VI Kholopova M. A. Generalized Caushy problem for the American Put option cost

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VII Yurchenko V. A. Limit theorems for wavelet-statistics

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VIII Antonova N. A. T-periodic models in linear integral pulse-width modulated control system

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IX Belyaeva N. A., Parshukova N. N. A thermoviscoelastic model of a spherical product hardering

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X Colovach P. A., Fomin F. V. Search and node search number of dual graphs

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XI Zheludev V. A., Pevnyi A. B. Lifting schemes for wavelet transform of discrete signals

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XII Karmanov O. G. Group analysis and invariant solutions of Carman equations

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XIII Mikhailovskii E. I., Ermolenko A. V. On the question of soft-flexible shells bending

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XIV Nikitenov V. L. Rarefied matrixes in problems of shell theory

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XV Khudyaev S. I., Koynova L. V. Approximate solution of the equation of V. A. Ambartsumyan

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XVI Afanasyev A.P., Gaverdovskiy V.S., Kuzivanova N.S.Automated geographic information system of etymologized geographical names of the Komi Republic

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XVII Gaverdovskiy V.S., Gerasimov E.P. Objective-oriented software package for developing applications in the environment of GIS technologies

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XVIII Ermakov A.A., Prokhorov V.N., Stepanenko V.I.Automated system of cadastres of natural resources of the Komi Republic

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XIX Polshvedkin R.V., Serov A.V., Stepanenko V.I., Prokhorov V.N., Gerasimov E.P., Popova O.I.Preparation for the reception and use of space information by means of GIS technologies in the forestry of the Republic Komi

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XX Serov A.V. Object identifier systems and work with them

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XXI Serov A.V. Review of the possibilities of using three-dimensional elevation models for solving various applied problems

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XXII Ezovskih V. E. Fast algorithm for transformation of lattices

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XXIII Sheyin A. A., Milnikov A. V. Optimal parametrs for samples processing

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XXIV Vityazeva V.A.Glare of informatization

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XXV Alexander Grigorievich Poroshkin (on the occasion of his seventieth birthday)

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XXVI Alexander Alekseevich Vasiliev (on the occasion of his fiftieth birthday)

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XXVII Tarasov Vladimir Nikolaevich (on the occasion of his fiftieth birthday)

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I Bazhenov I. I. The property of nonatomicity under some constractions of nonatomic vector measures

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II Bobkov S. G. Remarks on Gromov-Miliman’s inequality

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III Ekisheva S. V. The Bahadir representation of sample quantile for sociatedstochastic sequence

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IV Zhubr A. V. The bordism groups of spin-maps and their application to the problem of classification of 6-manifolds

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V Zvonilov V. I.Rigid isotopy classification of real algebraic curves of bidigree (4,3) on a hyperboloid

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VI Karmanov O. G. Group analysis of Durbreil-Jacotin’s equations

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VII Lovyagin Y. N. About one class of the Boolean algebras

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VIII Lovyagin Y. N., Matveeva O. P. Classification of the Boolean algebras with sufficient number (o)-continuous kwasimeasures

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IX Samorodnitski A. A. Some questions of Lebesgue-Rohlin spaces theory

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X Antonova N. A. Dynamic of one dimentional pulse-width modulated control systems

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XI Golovach P. A. Invariants of graphs defined through optimal numbering of vertexes and the operation of join of graphs

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XII Zheludev V. A., Pevnyi A. B. On the cardinal interpolation by discrete splines

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XIII Kasev D. W., Khudyaev S. I. Analysis of spontaneous ignition conditions for cylinder with thermal insulated hole

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XIV Mikhailovskii E. I., Badolkin K. V., Ermolenko A. V. The plane plate bending theory of Karman’s type without Kirchhoff’s hypothesis

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XV Mikhailovskii E. I., Ermolenko A. V. Refiniment of nonlinear quasi Kirhhoffian K. Chernykh’s theory of shells

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XVI Poleshchikov S. M. The regularization of motion equations of fivedimentional Kepler problem

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XVII Tarasov V. N. Stability of hingle-fixed lamina with one-sided constrains on displacement

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XVIII Ezovskih V. E. Lowering the degree of Bezier curves

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XIX Student scientific conference in memory of F. A. Babushkin

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XX Poet and scientist: he worked both in poetry and in mathematics (for the 90th birthday of Professor N.A.Frolov)

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XXI Report at the plenary session of the scientific conference of graduate students and students dedicated to N.A.Frolov

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XXII Vladimir Dmitrievich Yakovlev (on his fiftieth birthday)

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I Bazhenov I. I, Extreme points of the range of Liapunov vector measure

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II Zhubr A. V. Calculation of spin bordism groups of some Elenberg-MacLane spaces, II

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III Zhubr A. V. KS-transformations and involutions of normed algebras

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IV Isakov V. N. On the problem of countable addivity of the abstract measures product

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V Poroshkin A. A. On the inclusion of generalised Boolean algebra to Boolean algebra

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VI Samorodnitski A. A. Basic conceptions of Lebesgue-Rohlin space theory. Measure theory on subspaces of generalized Cantor discontinuum

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VII Tichomirov A. N. The rate of convergence in the central limit theorem for weakly dependet random variables

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VIII Antonova N. A. Chaos and order in an integral pulse-width control systems

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IX Belyaeva N. A., Klichnikov L. V. Integral equation method in the volume hardering problem

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X Golovach P. A. Pathwidith and treewidth of joining of two graphs

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XI Kirushev V. A. The quadratic variational problem with nonnegativity condition

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XII Mikhailovskii E. I. The noncoordinate method of obtaining of the conjuctive couples of the tensors

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XIII Nikitenkov V. L. Elastic curve of an axis of multisupport cylindrical vessel of pressure at a thermo-mechanical bend and extreme problems connected with it

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XIV Pevnyi A. B. Discrete periodic splines and solutions of the problem concerning infinite cylindrical shell

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XV Poleshchikov S. M., Kholopov A. A. Generalized KS-transformations of 4-th order

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XVI Sokolov V. Ph. Robust performance of linear controller for linear discrete plant in l1-setting

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XVII Kholopov V. M. , Khudyaev S. I. To asymptotic theory of combustion wave in gases

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XVIII Ermolenko A. V. On the semideformational variant of the boundary values in Karman’s theory of the flexible plates

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XIX Martynov Y. I. The determining equations in the contact problem for bending of plate on the theory of Timoshenko

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XX Teryohin D. E. The stability of cylindrical panel with the inside strengthenings

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XXI Zinchenko I. L. About one classical problem of variational calculs

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XXII Zinchenko I. L., Sangadjieva S. T. Periodicity of a sum of continuous periodic functions

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XXIII Poleshchikov S. M. Proper and improper KS-matrices

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XXIV 25 years of the Faculty of Mathematics

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XXV Evgeny Ilyich Mikhailovsky (on the occasion of his sixtieth birthday)

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I Bazhenov I. I. On some properties of Liapunov vector measure

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II Bobkov S. G. On inequalities of Gross and Talagrand on the discrete cube

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III Yekisheva S. V. A uniform Central Limit Theorem for a set-indexed processes

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IV Lovyagin J. N. On some questions of nonstandart theory of Kantorovich spaces

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VI Poroshkin A. A. On one generalization of the theorem on completeness

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VII Poroshkin A. G. On the metrizability of sequental order topology in ordered groups and vector spaces

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VIII Ryabinin A. A. On rise of Kantor-Fouries measure on imaginary axis

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IX Salnikova T. A. On complete and minimal systems of exponents

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X Samorodnitsky A. A. A Boolean principle of exhaustion and a construction of measure spaces

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XI Saveliyev L. J. Generational functions in the theory of series

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XII Antonova N. A. Chaos and order in pulse-width control systems

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XIII Belyaeva N. A., Belyaev Yu. N. The regulation of strained state of forming cylindrical product

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XIV Gerasin M. L. Stability of cilyndrical shell with ine-sided support

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XV Golovach P. A. On one invariant of graphs defined through optimal numbering of vertices

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XVI Kazakov A. Y. The maximazation of the first eigenvalue for the little displacement equation of a composite

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XVII Kondratieva T. V., Kholopov V. M. The asymptotic of stationary combustion wave for autocatalitic reaction of the first order

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XVIII Mikhailovskii E. I. Nonlinear theory of ridge shells under small trnsversal shears

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XIX Nikitenkov V. L. Nonlinear equations for cylindrical shell with eliptic ovality of the cross section

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XX Tarasov V. N. The problems on eigenvalues for positively homogeneous operators

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XXI Holmogorov D. V. The stability of bar on two elastic surrounding boundary

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XXII Kholopov A. A. Minimal stability losing forms of bar placed between elastic and rigid spaces

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XXIII Khudyaev S. I. To mathematical theory of flame propagation

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I Babenko M. V. On the polynomial semiring over a Bezout semiring

DOI: 10.34130/1992-2752_2020_4_05

Babenko Marina − Senior Lecturer of the Department of applied mathematics and computer science, Vyatka State University, e-mail: usr11391@vyatsu.ru

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The article examines a polynomial semiring over a Bezout Rickart semiring. Namely, let all left annihilator ideals of the semiring S be ideals. Then the semiring of polynomials R = S[x] is a semiring without nilpotent elements and every finitely generated left monic ideal from R is principal iff S is a left Rickart left Bezout semiring and any non-zero divisor of the semiring S is convertible to S. This result is analogous to the statement for rings, if the condition each finitely generated left monic ideal of R is principal replaced by R is left Bezout ring. The left monic ideal of a polynomial semiring is a left ideal that contains each monomial of its polynomial. The principal left monic ideals over a left Rickart left Bezout semiring are described.

Keywords: polynomial semiring, Rickart semiring, Bezout semiring, monic ideal.

References

1. Tuganbaev A. A. Kol’ca Bezu, mnogochleny i distributivnost’ (Bezout rings, polynomials and distributivity) Mathematical notes, 2001, 70:2, pp. 270288.
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6. Maslyaev D. A., Chermnykh V. V. Polukol’ca kosyh mnogochlenov Lorana (Semirings of skew Laurent polynomials), Siberian electronic mat. reports., 2020, Vol. 17, pp. 512-533.

For citation: Babenko M. V. On the polynomial semiring over a Bezout semiring, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2020, 4 (37), pp. 5-15.

II Efimov D. B. A method for computing the hafnian

DOI: 10.34130/1992-2752_2020_4_16

Efimov Dmitry − Ph. D., research associate, Institute of Physics and mathematics of the Komi national research center of the Ural branch of the Russian Academy of Sciences, e-mail: dmefim@mail.ru

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The hafnian was initially introduced by E.R. Caianiello, by analogy with the Pfaffian, as a convenient mathematical apparatus for working with certain quantum-mechanical quantities. From a combinatorial point of view, the hafnian of a symmetric matrix is equal to the sum of weights of perfect matchings of a graph with the given incidence matrix. In contrast to the Pfaffian, the hafnian has a smaller set of good properties, and determining its value is an example of a complex computational problem. We consider a new method for calculating hafnian of a matrix in terms of permanents of its submatrices. We also give a comparison with other methods in terms of computational complexity. The property underlying the method could also be used outside the context of the computation speed, for example, to estimate the hafnian of a nonnegative matrix based on known estimates of the permanent.

Keywords: hafnian, permanent, computational complexity

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.
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For citation: Efimov D. B. A method for computing the hafnian, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2020, 4 (37), pp. 16-25.

III Gabova M. N., Muzhikova A. V. Ñontext approach in the teaching of mathematics future engineers

DOI: 10.34130/1992-2752_2020_4_26

Gabova Maria − Senior Lecturer of the Department of the Department of higher mathematics, Ukhta state technical University, e-mail: amuzhikova@mail.ru

Muzhikova Alexandra − Ph. D., associate Professor of the Department of the Department of higher mathematics, Ukhta state technical University, e-mail: amuzhikova@mail.ru

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There is a problem of reducing the mathematical education of school graduates, and as a result, the lack of motivation and cognitive activity of first-year students when studying mathematics in higher school. Mathematics, devoid of professional direction, is not of interest to most students of a technical higher school. The efectiveness of the teaching process can be achieved by using a context approach. Context teaching is teaching in which the subject and social content of students’ professional activity is modeled in the language of science and with the help of the entire system of forms, methods and means of teaching. Considering context teaching as an integral system that meets the corresponding principles, the article presents the developed methodological and organizational support for educational activities.
The main idea in developing the content is a gradual transition from abstract mathematical concepts to their applied meaning in related sciences, and then to their application in professional fields. The principles of context teaching are best implemented when using active and interactive forms of teaching and their corresponding methods. The most efective methods in terms of achieving the goals of teaching, development and education were shown by such methods as problem-based lecture format, swapping of topics in pairs and partners rotation, paragraph-by-paragraph study of theoretical material in small groups, task swapping in practical classes, etc.
The use of a context approach allows students to develop social interaction, motivation and cognitive activity, mathematical literacy, the ability to apply mathematics in their educational and professional activities and contribute to the formation of a modern engineer capable of creative activity and self-realization.

Keywords: mathematics for engineer, context approach, active and interactive methods of teaching.

References

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17. Prudnikova O. M., Gabova M. N., Kaneva E. A. K voprosu formirovaniya u studentov kriticheski-refeksivnogo stilya myshleniya (To the Question of Formation of Students Critical-Refiexive Style of Thinking), Nauchno-tehnicheskaja konferencija, Ukhta: UGTU, 2011, Vol. 3, pp. 226-229.
18. Muzhikova A. V. Interaktivnoe obuchenie matematike v VUZe (Interactive Teaching of Mathematics in Higher School), Vestnik Syktyvkarskogo universiteta. Serija 1: Matematika. Mehanika. Informatika, 2015, Vol. 1 (20), pp. 74-90.
19. Muzhikova A. V. Issledovanie efektivnosti kollektivnyh uchebnyh zanyatij po vysshej matematike (Study the Interactive Teaching Efiectiveness in Higher Mathematics), Vestnik Tomskogo gosudarstvennogo pedagogicheskogo universiteta, 2018, No 7 (197), pp. 174-181.
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For citation: Gabova M. N., Muzhikova A. V. Ñontext approach in the teaching of mathematics future engineers, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2020, 4 (37), pp. 26-50.

IV Odyniec W. P. The Fate of two mathematicians: Perelman and Perelman Jr.

DOI: 10.34130/1992-2752_2020_4_51

Odyniec Vladimir − Doctor of Physical and Mathematical Sciences, Professor, Syktyvkar state University named after Pitirim Sorokin, e-mail: W.P.Odyniec@mail.ru

Text

In the article the work of Jacob I. Perelman (1882-1942) in the area of mathematics and its application to the theory of elasticity is described for the first time at the ever of the Grand Patriotic War. Also described the life and work of his son Michael J. Perelman (1919-1942).

Keywords: J. I. Perelman, M. J. Perelman, Galerkin method, continuity modulus, the least power and pseudo-power of a topological space.

References

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8. Odyniec W. P. O leningradskih matematikah, pogibshih v 1941-1944 godah (On some Leningrad based Mathematicians perished in 1941 -1944), Syktyvkar: Izd- vo SGU im. Pitirima Sorokina, 2020, 122 p.
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For citation: Odyniec W. P. The Fate of two mathematicians: Perelman and Perelman Jr., Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2020, 4 (37), pp. 51-65.

V Pevnyi A. B., Yurkina M. N. Sieve of Eratosphenes complexity and distribution of primes

DOI: 10.34130/1992-2752_2020_4_66

Pevny Alexander − Doctor of Physics and Mathematics, Professor, Department of Applied Mathematics and Information Technologies in Education, Pitirim Sorokin Syktyvkar State University, e-mail: pevnyi@syktsu.ru

Yurkina Marina − Senior Lecturer, Department of Applied Mathematics and Information Technologies in Education, Syktyvkar State University named after Pitirim Sorokin, e-mail: yurkinamn@gmail.com

Text

Primes are widely used not only in pure mathematics, but also in related disciplines. And although they have been known for a long time, many problems concerning prime numbers are still open and the questions of their study do not lose their relevance. One of the well-known algorithms for finding all primes not exceeding a given N is the sieve of Eratosthenes. To estimate the number of operations required to execute this algorithm, the authors used one result of P. L. Chebyshev. In 1849 P. L. Chebyshev proved a two-sided estimate for the number of primes not exceeding a given N. Based on these estimates, the article establishes that the number of operations in the Eratosthenes algorithm is estimated as O (N ln ln N).

Keywords: sieve of Eratosthenes, primes, Chebyshev.

References

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For citation: Pevnyi A. B., Yurkina M. N. Sieve of Eratosphenes complexity and distribution of primes, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2020, 4 (37), pp. 66-72.

VI Popov N. I., Yakovleva E. V. Use of the schematization method in teaching students and pupils in math

DOI: 10.34130/1992-2752_2020_4_74

Text

The publication objective is to highlight and generalize the features of using the schematization method in teaching mathematics as a means of developing thinking and mathematical abilities of learners. The research is based on analyzing scientific and methodical works of Russian and foreign scientists on both activity theory, pedagogy, and author’s researches on applying the schematization method in teaching mathematics. The article proposes a schematic model to teach pupils and students solve mathematical problems. The methodological approaches developed in the research can be used in teaching mathematics at diferent levels of education. We believe that the method described in this paper can be successfully applied in studying natural sciences.

Keywords: a method of schematization; teaching mathematics; stages of mathematical problems solving; schematic model.

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For citation: Popov N.I., Yakovleva E.V. Use of the schematization method in teaching students and pupils in math, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2020, 4 (37), pp. 74-87.