Full text

I. Tatyana M. Bannikova, Olga M. Nemtsova Geometrical and analytical characteristics of the constructing the polynomial of а circle division

https://doi.org/10.34130/1992-2752_2022_2_4

Tatyana M. Bannikova – Udmurt State University.

Olga M. Nemtsova – Udmurt State University.

Text

Abstract. The problem of finding circle division polynomials with the condition of specifying some of their coefficients is discussed. The problem of the existence of polynomials of this type is solved, but the problem of the ambiguity of finding circle division polynomials with a given simple or composite coefficient, as well as features of its number (such as decomposition into prime factors and a significant order with respect to a given coefficient) can be used in setting an open key in cryptographic systems. So it is known to use the roots of circle division polynomials as a cyclic group generator in the Berlekamp-Massey algorithm.

Keywords: circle division polynomials, cryptosystem, key’s generation, ciphertext.

References

1. Tripathi S. K., Gupta B., Soundra Pandian K. K. An alternative practical publickey cryptosystems based on the Dependent RSA Discrete Logarithm Problems. Expert Systems With Applications, 164 (2021), 114047.
2. Sreedharan S., Eswaran C. A lightweight encryption scheme using Chebyshev polynomial maps. Optik – International Journal for Light and Electron Optics, 240 (2021), 166786.
3. Biletsky A. A. Cryptografy applications of primitive matrices Galois and Fibonacci. Zashhita informacii [Information Security Research Journal], 15:32 (2013), pp. 128–132. (In Russ.)
4. Zelenevsky V. V., Zelenevsky V. Yu., Zelenevsky A. V. et al. Statisticheskiy i korrelyatsionnyy analiz adresnykh posledovatel’nostey v kanalakh peredachi s kodovym mul’tipleksirovaniyem dannykh. Izvestiya Instituta inzhenernoy fiziki [Proceedings of the Institute of Engineering Physics]. 4:58 (2020), pp. 31–34. (In Russ.)
5. Dai Z., Huang M. A criterion for primitivity of integral polynomial Mod 2d. Chinese Science Bulletin, 15 (1990), pp. 1128–1130.
6. Zhu Y., Wang X. A criterion for primitive polynomials over Galois rings. Discrete Mathematics, 303 (2005), pp. 244–256.
7. Fedorov G. V. On the Period Length of a Functional Continued Fraction over a Number Field. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniya [Papers of the Russian Academy of Sciences. Mathematics, computer science, control processes], 102 (2020), pp. 513–517. (In Russ.)
8. Susilo W., Tonien J. A Wiener-type attack on an RSA-like cryptosystem constructed from cubic Pell equation. Theoretical Computer Science, 885 (2021), pp. 125–130.
9. Pousin J. Least squares formulations for some elliptic second order problems, feedforward neural network solutions and convergence results. Journal of Computational Mathematics and Data Science, 2 (2022), 100023.
10. Prasolov V. V. Mnogochleny [Polynomials], Moscow Center For Continuous Mathematical Education, M., 2003 (In Russ.)
11. Van der Waerden B. L. Algebra. M.: Nauka, 1979. (In Russ.)
12. Vyalyi M. N., Gimadeev R. A. Separation of words by positions of subwords. Discretnyy analiz i issledovaniye operatsiy [Discrete Analysis and Operations Research], 21:1(115) (2014), pp. 3–14. (In Russ.)
13. Galieva L. I., Galyautdinov I. G. On a class of equations solvable in radicals. Izvestiya vysshix uchebnyx zavedenij. Matematika [Russian Math. (Iz. VUZ)], 55:2 (2011), pp. 18–25. (In Russ.)
14. Savel’ev I. V. Circular polynomials and singularities of complex hypersurfaces. Uspekhi Mat. Nauk [Advances in Mathematical Sciences], 48:2 (290) (1993), pp. 197–198. (In Russ.)
15. Liopo V. A., Sabut A. V. Point groups and syngonies of noncrystallographic symmetry. Vestnik Grodnenskogo gosudarstvennogo universiteta imeni Yanki Kupaly‘. Seriya 2. Matematika. Fizika. Informatika, vy‘chislitel‘naya texnika i upravlenie [Bulletin of Grodno State University named after Yanka Kupala. Series 2. Mathematics. Physics. Informatics, computer technology and management], 1:148 (2013), pp. 115–126. (In Russ.)
16. Fan S., Wang X. Primitive normal polynomials with the specified last two coefficientss. Discrete Mathematics, 309 (2009), pp. 4502–4513.
17. Fan S. Q., Han W. B., Feng K. Q. Primitive normal polynomials with multiple coefficients prescribed: An asymptotic result. Finite Fields and Their Applications, 13:4 (2007), pp. 1029–1044.
18. Fan S. Q., Han W. B., Feng K. Q., Zhang X. Y. Primitive normal polynomials with the first two coefficients prescribed: A revised p-adic method. Finite Fields and Their Applications, 13 (2007), pp. 577–604.
19. Brochero Martнnez F. E., Reis L., Silva–Jesus L. Factorization of composed polynomials and applications. Discrete Mathematics, 342 (2019), 111603.
20. Bakshi G. K., Raka M. A class of constacyclic codes over a finite field. Finite Fields Appl., 18:6 (2012), pp. 362–377.
21. Brochero Martнnez F. E., Giraldo Vergara C. R., de Oliveira L. Explicit factorization of xn – 1 ∈ Fq[x] . Des. Codes Cryptogr., 77 (2015), pp. 277–286.
22. Brochero Martнnez F. E., Reis L. Factoring polynomials of the form f(xn) ∈ Fq[x] . Finite Fields Appl., 49 (2018), pp. 166–179.
23. Li F., Yue Q. The primitive idempotents and weight distributions of irreducible constacyclic codes. Des. Codes Cryptogr., 86 (2018), pp. 771–784.
24. Liu L., Li L., Wang L., Zhu S. Repeated-root constacyclic codes of length nlps. Discrete Math., 340:9 (2017), pp. 2250–2261.
25. Wu Y., Yue Q., Fan S. Further factorization of xn – 1 over a finite fiel. Finite Fields Appl., 54 (2018), pp. 197–215.
26. WOLFRAM MATHEMATICA ONLINE [Электронный ресурс], WolframAlpha.com (2022), Available at:https://www.wolfram.com/mathematica/online/ (accessed05.06.2022).

For citation: Bannikova T. M., Nemtsova O. M. Geometrical and analytical characteristics of the constructing the polynomial of а circle division. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika=Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022, No. 2 (43), pp. 4−20. https://doi.org/10.34130/1992-2752_2022_2_4

II. Nadezhda A. Belyaeva, Ilya O. Mashin, Anastasia V. Nadutkina Phase transition of a viscous fluid in a nonisothermal flow

https://doi.org/10.34130/1992-2752_2022_2_21

Nadezhda A. Belyaeva – Pitirim Sorokin Syktyvkar State University.

Ilya O. Mashin – Institute of Physics and Mathematics of the Federal Research Center Komi
Scientific Center of the Ural Branch of the Russian Academy of Sciences.

Anastasia V. Nadutkina – Pitirim Sorokin Syktyvkar State University.

Text

Annotation. A mathematical model is constructed for a nonisothermal pressure flow of an incompressible viscous fluid between two parallel planes. The basic relations of the model are the Navier-Stokes equation of motion, the heat conduction equation, the corresponding initial and
boundary conditions. In the flow process the possible phase transition ¨liquid – solid¨is taken into account.The condition for matching the temperatures of the solid and liquid phases is specified at the interface.The corresponding dimensionless flow model is constructed. A numerical analysis of the flow is carried out with varying the dimensionless parameters of the problem.The graphical results of numerical experiments are presented and analyzed. Graphical results of numerical experiments are presented and analyzed.

Keywords: viscous fluid, non-uniform temperature field, phase transition, numerical analysis.

References

1. Belyaeva N. A., Nadutkina A. V. Non-isothermal flow of a viscous fluid. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mexanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics], 2019, V. 3 (32). Pp. 20–30. (In
   Russ.)
2. Belyaeva N. A. Heterogeneous flow of the structured liquid. Matematicheskoye modelirovaniye [Mathematical modeling], 2006, V. 18. Pp. 3–14. (In Russ.)
3. Belyaeva N. A., Yakovleva A. F. Frontal wave of pressure flow. [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics], 2017, V. 2 (23). Pp. 3–12. (In Russ.)
4. Belyaeva N. A., Stolin A. M., Stelmakh L. S. Dynamics of Solid-State Extrusion of Viscoelastic Cross-Linked polymeric Materials. Theoretical Foundations of Chemical Engineering, 2008, V. 42. Pp. 549– 556.
5. Pryanishnikova E. A., Belyaeva N. A., Stolin A. M. Compressible material flow in cylindrical channel with variable cross section. MATEC Web of Conferences 129, 06011 (2017), ICMTMTE 2017.
6. Khudyaev S. I. Porogovye yavleniya v nelinejnyh uravneniyah [Threshold phenomena in nonlinear equations]. Moscow: Fizmatlit,272 p. (In Russ.)
7. Belyaeva N. A. Matematicheskoye modelirovaniye: uchebnoye posobiye [Mathematical modeling: a training manual]. Syktyvkar: Publishing House of the Syktyvkar State University, 2014. 116 p. (In Russ.)
8. Belyaeva N. A. Osnovy gidrodinamiki v modelyakh: uchebnoye posobiye [Fundamentals of hydrodynamics in models: a training manual]. Syktyvkar: Publishing House of the Syktyvkar State University, 2011. 147 p. (In Russ.)

For citation: Belyaeva N. A., Mashin I. O., Nadutkina A. V. Phase transition of a viscous fluid in a nonisothermal flow. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika=Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022,
No. 2 (43), pp. 21−31. https://doi.org/10.34130/1992-2752_2022_2_21

III. Andrey S. Penin, Nikita O. Tursukov Development of components of a model for assessing the state of a cyberphysical system operator

https://doi.org/10.34130/1992-2752_2022_2_15

Andrey S. Penin – ITMO University.

Nikita O. Tursukov – ETU.

Text

Abstract. During the research work, the main biological markers of the human body were studied and those of them that met the requirements were selected for further research. A system for
evaluating employee performance based on a bidirectional LSTM network was developed, the accuracy of activity recognition was 88%, the value of the loss function was 0.504. In the future, the employee activity assessment system and biological markers will be combined into a model for assessing the state of the cyberphysical system operator.

Keywords: neural networks, LSTM-networks, biomarkers, models, systems, state.

References

1. Biomarkery – indikatory sostoyaniya zdorovya [Biomarkers – healthindicators] [Online]. Available at: https://medinteres.ru/interesnyiefaktyi/biomarkeryi.html (accessed: 28.03.2022).
2. Teplovaya inerciya temperaturnyx datchikov [Thermal inertia of temperature sensors] [Online]. Available at: https://isup.ru/articles/16/15436/ (accessed: 28.03.2022).
3. O saturacii kisloroda v krovi [About blood oxygen saturation] [Online]. Available at: https://aptstore.ru/articles/saturatsiya-kisloroda-vkrovi/ (accessed: 28.03.2022).
4. Pulsovoe davlenie v krovi [Pulse pressure in the blood] [Online]. Available at: https://cyberleninka.ru/article/n/pulsovoe-davleniekrovi-rol-v-gemodinamike-i-prikladnye-vozmozhnosti-v-funktsionalnoydiagnostike (accessed: 28.03.2022).
5. Povyshennoe davlenie: prichiny i osobennosti lecheniya [High blood pressure: causes and peculiarities of treatment] [Online]. Available at: https://aptstore.ru/articles/povyshennoe-davlenie-prichiny-iosobennosti-lecheniya/ (accessed: 28.03.2022).
6. Filtry vysokix i nizkix chastot [High-pass and low-pass filters] [Online]. Available at: https://elar.urfu.ru/bitstream/10995/36102/1/978-5- 7996-1577-2_2015.pdf (accessed: 28.03.2022).
7. Mediannaya filtraciya [Median filtering] [Online]. Available at: https://ru.bmstu.wiki/Медианная_фильтрация (accessed: 28.03.2022).
8. Filtr Kalmana [Kalman filter] [Online]. Available at: https://habr.com/ru/post/166693/ (accessed: 28.03.2022).
9. A Guide to RNN: Understanding Recurrent Neural Networks and LSTM Networks [Электронный ресурс]. URL: https://builtin.com/datascience/recurrent-neural-networks-and-lstm (дата обращения: 28.03.2022).
10. Niall Twomey, Tom Diethe, Xenofon Fafoutis, Atis Elsts, Ryan McConville, Peter Flach and Ian Craddock. A Comprehensive Study of Activity Recognition Using Accelerometers. URL:
    https://www.researchgate.net/publication/323847517_A_Comprehensive_Study_of_Activity_Recognition_Using_Accelerometers – March 2018
11. Ivan Ozhiganov. Using LSTM Neural Network to Process Accelerometer Data. URL: https://dzone.com/articles/using-lstmneural-network-to-process-accelerometer – 08.05.2017
12. Arumugam Thendramil Pavai. Sensor Based Human Activity Recognition Using Bidirectional LSTM for Closely Related Activities. California State University, San-Bernardino, Electronic Theses Projects and Dissertations – 776 – 12.2018
13. Matthew Chin Heng Chua, Youheng Ou Yang, Hui Xing Tan, Nway Nway Aung, Jing Tian. Time Series classification using a modified LSTM approach from accelerometer-based data: A comparative study for gait cycle detection. Gait & Posture 74 – 09.2019 – doi:10.1016/j.gaitpost.2019.09.007
14. Categorical crossentropy loss function [Online]. Available at: https://peltarion.com/knowledge-center/documentation/modelingview/build-an-ai-model/loss-functions/categorical-crossentropy
    (accessed: 28.03.2022).
15. Confusion Matrix [Online]. Available at: https://devopedia.org/confusion-matrix (accessed: 28.03.2022).
16. Pereobuchenie [Retraining] [Online]. Available at:http://www.machinelearning.ru/wiki/index.php?title=Переобучение (accessed: 28.03.2022).

For citation: Penin A. S., Tursukov N. O. Development of components of a model for assessing the state of a cyberphysical system operator. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika=Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022, No. 2 (43), pp. 32−54.
https://doi.org/10.34130/1992-2752_2022_2_32

IV. Nikolay I. Popov, Evgeniya A. Kaneva Forming schoolchildren’s cognitive interest in mathematics using computer educational games

https://doi.org/10.34130/1992-2752_2022_2_55

Nikolay I. Popov – Pitirim Sorokin Syktyvkar State University.

Evgeniya A. Kaneva – Pitirim Sorokin Syktyvkar State University.

Text

Annotation. At present, due to the effective development of information and communication technologies, global changes affect all spheres of human life, including the educational process at school. Teachers face the problem of combining traditional methods and teaching aids with innovative ones to improve the efficiency and quality of the educational process. Since it is difficult for students to keep their attention on one object of study in the conditions of a large flow of information, teachers need to use modern technologies in their work to increase the motivation and interest of students in the subject. One of such educational technologies is educational computer
games.

Keywords: computer learning games, teaching mathematics, game technologies.

References

1. Popov N. I. Fundamentalizaciya universitetskogo matematicheskogo obrazovaniya : monografiya [The fundamentalization of university mathematics education: monograph] / Yelets: EGU im. I.A. Bunina,174 p. (In Russ.)
2. Popov N. I., Kaneva E. A. The use of computer games in mathematics in the educational process of secondary school. Matematicheskoe modelirovanie i informacionnye technologii
   [Electronic resource]: V Vserossijskaya nauchnaya konferenciya s mezhdunarodnym ychastiem [Mathematical modeling and information technologies [Electronic resource]: V All-Russian scientific conference with international participation] (December 9–11, 2021, Syktyvkar):
   collection of materials: text scientific electronic edition on CD. Syktyvkar: Publishing House of SSU im. Pitirim Sorokina, 2021, pp. 57–58. (In Russ.)
3. Bocharov M. I., Mozharova T. N., Soboleva E. V., Suvorova T. N.Development of a personalized model of teaching mathematics by means of interactive short stories to improve the
   quality of educational results for schoolchildren. Perspektivy nauki i obrazovaniya [Prospects of Science and Education]. 2021. No. 5 (53). Pp. 306–322. (In Russ.)
4. Zinoveva L .V., Zinovev S.A. Role-playing video games in the space of psychocorrection and psychotherapy. Smalta. 2017. No. 4. Pp. 17–19.
5. Paiva J. C., Leal J. P., Queiros R. Fostering programming practice through games. Information (Switzerland). 2020. No. 11 (11). Pp. 1– 20.
6. Kaneva E. A.Computer game in mathematics for schoolchildren. Materialy VII nauchno-obrazovatelnoj studencheskoj konferencii, posvyashchennoj dnyu rozhdeniya Nikolaya Ivanovicha Lobachevskogo [Proceedings of the VII scientific and educational student conferencededicated to the birthday of Nikolai Ivanovich Lobachevsky]. Kazan.S. 126–131. (In Russ.)

For citation: Popov N. I., Kaneva E. A. Forming schoolchildren’s cognitive interest in mathematics using computer educational games. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika.
Mekhanika. Informatika=Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022, No. 2 (43), pp. 55−66. https://doi.org/10.34130/1992-2752_2022_2_55

V. Andrey V. Yermolenko, Viktoria R. Makarova Generalized reaction method for a plate with an inclined base

https://doi.org/10.34130/1992-2752_2022_2_67

Andrey V. Yermolenko – Pitirim Sorokin Syktyvkar State University.

Viktoria R. Makarova – Pitirim Sorokin Syktyvkar State University.

Text

Annotation. An effective way to solve problems on the interaction of plates and bases is the generalized reaction method. The presented article shows the application of the generalized reaction method to a cantilevered and rigidly fixed plate. The solution using the generalized reaction method is a system of iterated functions, the finding of which in a certain number of iterations will be reduced to solving the problem, which makes it possible to accurately and quickly determine the answer.

Keywords: plate, generalized reaction method, the Sophie Germain–Lagrange equation, contact reaction.

References

1. Mikhailovskii E.I. Shkola mekhaniki akademika Novozhilova [The Novozhilov School of Mechanics]. Syktyvkar: Publishing House of the Syktyvkar University, 2005. 172 p.
2. Chernykh K.F., Mikhailovskii E.I., Nikitenkov V.L. Ob odnoy vetvi nauchnoy shkoly Novozhilova (Novozhilov – Chernykh – Mikhaylovskiy – Nikitenkov) [About one branch of the scientific school
   of Novozhilov (Novozhilov – Chernykh – Mikhailovsky – Nikitenkov)]. Syktyvkar: Publishing House of the Syktyvkar University, 2002.147 p.
3. Yermolenko A.V. Fundamentalizaciya universitetskogo matematicheskogo obrazovaniya : monografiya [Contact problems with free boundary: textbook]. Syktyvkar: Izd. Pitirim Sorokin, 2020. 1 opt. compact disc (CD-ROM). 105 p.
4. Mikhailovsky E.I., Tarasov V.N. O sxodimosti metoda obobshhennoj reakcii v kontaktnyx zadachax so svobodnoj granicej [Convergence of the generalized reaction method in contact problems with a free boundary]. RAS. PMM. 1993. V. 57. Issue. 1. Pp. 128–136.
5. Yermolenko A. V., Ladanova S. V. Kontaktnaya zadacha dlya dvux plastin s raznym zakrepleniem [Contact problem for two plates with different restraints]. Bulletin of the Syktyvkar University. Ser. 1: Mathematics. Mechanics. Informatics. 2020. Issue. 3 (36). Pp. 87-92.
6. Yermolenko A. V., Osipov K. S. On using Python libraries to calculate plates. Vestnik Syktyvkarskogo universiteta. Ser. 1: Matematika. Mexanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics]. 2019, 4 (33), pp. 86–95.
   (In Russ.)

For citation: Andrey V. Yermolenko., Makarova V. R. Generalized reaction method for a plate with an inclined base. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika=Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022,
No. 2 (43), pp. 67−74. https://doi.org/10.34130/1992-2752_2022_2_67

Full text

I. Chernov V. G. Non-cooperative antagonistic game with fuzzy estimates

https://doi.org/10.34130/1992-2752_2022_1_5

Vladimir G. Chernov – Vladimir State University, e-mail: vladimir.chernov44@mail.ru

Text

Abstract. In the study of operations a significant place is occupied by problems, the formal model of which are antagonistic games. The classical methods of solving such games are based on the principle of “common knowledge”according to which the participants in a game have full information about possible solutions and their consequences. Studies are known in which information reflexivity of the participants of the game is allowed, i.e. their uncertainty in
assessing the situation requiring a decision is allowed. To formalize this uncertainty, it is proposed that the values of the elements of the payment matrix should be presented in the form of fuzzy numbers. The choice of the best solution is based on the conversion of fuzzy estimates of the consequences of possible solutions in the form of equivalent fuzzy sets with triangular membership functions.

Keywords: antagonistic game, payment matrix, fuzzy set, membership function

References

1. Myerson R. B. Game theory: analysis of conflict. London Harvard: Harvard.Un.Press, 1991. 584 p.
2. Geanakoplos J. Common Knowledge. Handbook of Game Theory. V.ed. R. Aumann and S. Hart. Elsiever Science B.V. 1994. Pp. 1438– 1496.
3. Sigal A. V. Game theory model of investment decision making of investment decisions. Uchenye zapiski Tavricheskogo nacional’nogo universiteta imeni. V.I. Vernadskogo, seriya “Ekonomika i upravlenie” [Scientific Notes of the Taurida National University named after. V. I. Vernadsky. Series “Economics and Management”]. 2011. № 1, V. 24(63). Pp. 193–205. (in Ukrainian).
4. Butnariu D. Fuzzy games: a description of the concept. Fuzzy Sets and System. 1978. 1. Pp. 181–192.
5. Vovk S. P. The game of two persons with fuzzy strategies and preferences. Al’manah sovremennoj nauki i obrazovaniya [Almanac of Modern Science and Education]. 2014. № 7(85). Pp. 47–49. (In Russ.).
6. Ghosh D., Chakravorty S. On Solving Bimatrix Games with Triangular Fuzzy Payoffs. International Conference on Mathematics and Computing. 2018. Pp. 441–352.
7. Stalin T, Thirucheran M. Solving Fuzzy Matrix Games Defuzzificated by Trapezoidal Parabolic Fuzzy Number. SRDInternational Journal for Scientific Research and Development. 2015.
   V. 3. Issue 10. Pp. 341–345. 14 Чернов В. Г.
8. Verma Tina, Kumar Amit, Kacprzyk Janusz. A Novel Approach to the Solution of Matrix Games with Payoffs Expressed by Trapezoidal Intuitionistic Fuzzy Numbers. Journal of Automation, Mobile Robotics and Intelligent Systems. 2015. No 3. V. 9. Pp. 25–46.
9. Dubois D., Prade H. Theoriedes Possibilites. Applications a la representation des conisisancesen in for antique. Masson, 1980. 288 p.
10. Chernov V. G. Choosing a Solution Based on Fuzzy Game with Nature. Prikladnaya informatika [Journal of Applied Informatics]. V. 16. № 2(92). 2021. Pp. 131–142. (In Russ.)
11. Voroncov Ya. A., Matveev M. G. Methods of parametrized comparison of fuzzy and trapezoidal numbers. Vestnik VGU, Seriya Sistemnyj analiz I informacionnye tekhnologii [Vestnik VSU. Series System analysis and information technologies]. 2014. No 2. Pp. 90–96. (In Russ.)
12. Chernov V. G. Comparison of fuzzy number on the basis of construction linear order relation. Dinamika slozhnyh sistem – XXI vek [Dynamics of Complex Systems – XXI Century.]. 2018. No 2. Pp. 81–87. (In Russ.)

For citation: Chernov V. G. Non-cooperative antagonistic game with fuzzy estimates. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022, No. 1 (42), pp. 5−14. https://doi.org/10.34130/1992-2752_2022_1_5

II. Kotelina N. O., Pevnyi A. B. Quadratic problem of mathematical diagnostics

https://doi.org/10.34130/1992-2752_2022_1_15

Nadezhda O. Kotelina – Pitirim Sorokin Syktyvkar State University, nkotelina@gmail.com.

Aleksandr B. Pevnyi – Pitirim Sorokin Syktyvkar State University, pevnyi@syktsu.ru.

Text

Abstract. Let m points be given in n-dimensional space, and G is the convex hull of these points. In the simplest problem of mathematical diagnostics, it is checked whether a point p belongs to the set G. In other words, if the coordinates of the points are signs of some disease, it is necessary to determine whether a new patient has a disease by the similarity of its signs in him and in patients with a confirmed diagnosis. In this paper, we attach its epsilon neighborhood to G and check whether p belongs to an extended set. To do this, we solve a quadratic programming problem in which we need to find the point of the set G closest to the point p in the Euclidean norm. In the article, we write out the necessary minimum conditions, obtaining a problem that can be solved using a modified simplex method with an additional condition for the bases.

Keywords: mathematical diagnostics, machine learning, modified simplex-method, quadratic programming

References

1. Malozemov V. N., Cherneutsanu E. K. The simplest problem of mathematical diagnostics. Seminar «O & ML». Izbrannye doklady [Seminar «O & ML». Selected papers]. 2022-02-09. Available: http://www.apmath.spbu/oml/reps22.shtml#0209 (accessed: 04.04.2022).
2. Pevnyi A. B. Finding the point of polyhedron closest to the origin (in Russian). Optimizaciya [Optimization]. Issue 10 (4). Novosibirsk, 1972.
3. Wolfe P. The simplex method for quadratic programming. Econometrics. 1959. Vol. 27. Pp. 382–398.

For citation: Kotelina N. O., Pevnyi A. B. Quadratic problem of mathematical diagnostics. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022, No. 1 (42), pp. 15−22. https://doi.org/10.34130/1992-2752_2022_1_15

III. Maslyaev D. A. Current state of the higher school timetabling problem

https://doi.org/10.34130/1992-2752_2022_1_23

Denis A. Maslyaev – Komi republican academy of public service and administration, e-mail:
dmaslyaev@gmail.com

Text

Abstract. The article contains a review of Russian and foreign literature sources of solving the high school timetabling problem. The distinctive features of the schedule for the university are listed, as well as the peculiarities of scheduling in Russia. The comparison of various software tools for automatic scheduling is given. The existing software is not enough to solve this problem. A feature of the task is the presence of “block”classes that need to be compactly placed in the schedule, a large number of training streams, and a lot of external part-timers. Methods and algorithms for solving similar problems are considered. The existing heuristic methods have their advantages and disadvantages. A conceptual statement of the problem is formulated in a verbal form in relation to a specific educational institution. Hard and soft restrictions are formulated. Violation of soft restrictions will affect the penalty function – the only target function. The author came to the conclusion that it is necessary to develop a set-theoretic mathematical model for the problem under consideration and a hybrid heuristic solution method that would combine the advantages of various heuristic methods and offset their disadvantages. The data for the problem must be presented in an aggregated form.

Keywords: timetabling problem, high school, combinatorial optimization, automatization, methods, heuristic, literature review, algorithm, conceptual model

References

1. Klevanskij N. N. Formation of the schedule of classes of higher educational institutions. Obrazovatel’nye resursy i tekhnologii [Educational resources and technologies]. 2015. No 1(9). Pp. 34–44.
2. Chavez-Bosquez O., Hernandez-Torruco J., Hernandez-Ocana B., Canul-Reich J. Modeling and Solving a Latin American University Course Timetabling Problem Instance. Mathematics. 2020, Vol. 8(10), 1833 p.
3. Gafarov E. R. Software product for drawing up educational schedules of higher education institutions. XII Vserossijskoe soveshchanie po problemam upravleniya VSPU-2014 (16-19 iyulya, g. Moskva) [XII All-Russian Meeting on Management Problems VSPU-2014 (July 16-19, Moscow)]. M.: Institut problem upravleniya im. V. A. Trapeznikov RAN, 2014. Pp. 8804–8809.
4. Abuhaniya Amer Y. A. Modeli, algoritmy i programmnye sredstva obrabotki informacii i prinyatiya reshenij pri sostavlenii raspisaniya zanyatij na osnove evolyucionnyh metodov [Models, algorithms and software tools for information processing and decision-making when drawing up a class schedule based on evolutionary methods] Avtoreferat dissertacii na soiskanie uchenoj
   stepeni kandidata tekhnicheskih nauk. Novocherkassk, 2016. 20 p.
5. Sidorin A. B., Likucheva L. V., Dvoryakin A. M. Methods of automation of scheduling classes Part 1. Classical methods). Izvestiya Volgogradskogo gosudarstvennogo tekhnicheskogo universiteta [Proceedings of the Volgograd State Technical University]. 2009. No 12 (60). Pp. 116–120.
6. Maslov M. G. Razrabotka modelej i algoritmov sostavleniya raspisanij v sistemah administrativno-organizacionnogo upravleniya [Development of models and algorithms for scheduling in administrative and organizational management systems] Avtoreferat dissertacii na soiskanie uchenoj stepeni kandidata tekhnicheskih nauk. M., 2004. 25 p.
7. Sidorin A. B., Likucheva L. V., Dvoryakin A. M. Methods of automation of scheduling classes Part 2. Heuristic methods of optimization. Izvestiya Volgogradskogo gosudarstvennogo tekhnicheskogo universiteta [Proceedings of the Volgograd State Technical University] 2009. No 12 (60). Pp. 120–123.
8. Asvad Firas M. Modeli sostavleniya raspisaniya zanyatij na osnove geneticheskogo algoritma na primere vuza Iraka [Models of scheduling classes based on a genetic algorithm on the example of a university in Iraq]. Avtoreferat dissertacii na soiskanie uchenoj stepeni kandidata tekhnicheskih nauk. Voronezh, 2013. 16 p.
9. Kabal’nov Y. S., SHekhtman L. I., Nizamova G. F., Zemchenkova N.A. Compositional genetic algorithm for scheduling training sessions. Vestnik Ufimskogo Gosudarstvennogo Aviacionnogo Universiteta [Bulletin of the Ufa State Aviation University]. 2006. No 2. Vol. 7. Pp. 99–109.
10. Nizamova G. F. Matematicheskoe i programmnoe obespechenie sostavleniya raspisaniya uchebnyh zanyatij na osnove agregativnyh geneticheskih algoritmov [Mathematical and software for scheduling training sessions based on aggregate genetic algorithms]. Avtoreferat dissertacii na soiskanie uchenoj stepeni kandidata tekhnicheskih nauk. Ufa, 2006. 18 p.
11. Skiena S. Algoritmy. Rukovodstvo po razrabotke [Algorithms. Development guide] BHV-Peterburg, 2014. 720 p.
12. Matveev A. I. Algorithm for optimizing resource planning (on the example of the annealing method) Perspektivnye informacionnye tekhnologii (PIT 2018). Trudy mezhdunarodnoj nauchno-prakticheskoj konferencii. Pod redakciej S.A. Prohorova [Perspective Information Technologies (PIT 2018) : Proceedings of the International Scientific and Practical Conference / ed. by S. A. Prokhorov.] 2018. Pp. 1046–1059.
13. Lopatin A. S. Method of annealing. Stohasticheskaya optimizacii v informatike [Stochastic Optimization in Computer Science]. 2005. Vol. 1. Pp. 133–149.
14. Song T., Liu S., Tang X., Peng X., Chen M. An iterated search algorithm for the University Course Timetabling Problem. Applied Soft Computing, Vol. 68 (2018). Pp. 597–608.
15. Podinovskij V. V. Idei i metody teorii vazhnosti kriteriev v mnogokriterial’nyh zadachah prinyatiya reshenij [Ideas and methods of the theory of criteria importance in multicriterial decision-making problems]. M.: Nauka,103 p.
16. Silva J. D. L., Burke E. K., Petrovic S. An Introduction to Multiobjective Metaheuristics for Scheduling and Timetabling. Metaheuristics for multiobjective optimisation. Lecture notes in economics and mathematical systems, vol. 535, Pp. 91–129.
17. Aziz N. L. A., Aizam N. A. H. A Brief Review on the Features of University Course Timetabling Problem. AIP Conference Proceedings, 2016. 020001 (2018).

For citation: Maslyaev D. A. Current state of the higher school timetabling problem. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022, No. 1 (42), pp. 23−40.
https://doi.org/10.34130/1992-2752_2022_1_23

IV. Golchevskiy Y.V., Shchukin N. Yu. Design and Development of a Service Web Configurator for Computer Assembly

https://doi.org/10.34130/1992-2752_2022_1_41

Yuriy V. Golchevskiy – Pitirim Sorokin Syktyvkar State University, e-mail: yurygol@mail.ru

Nikolay Yu. Shchukin – Mobile Solution LLC, e-mail: sedfar.08.09@mail.ru

Text

Abstract. Thе paper presents a study of designing and implementing a service web configurator based on a configurator for computer assembly. The analysis of web configurators application and analog products is carried out. The specifics of the subject area are considered and the functional modules of the service with their goals and requirements are highlighted. The diagram of the web service main functional modules, the diagrams of the process of selecting components in the configurator, the database models, the interfaces of the developed product are provided.

Keywords: web configurator, computer assembly

References

1. Grosso C., Trentin A., Forza C. Towards an understanding of how the capabilities deployed by a Web-based sales configurator can increase the benefits of possessing a mass-customized product. 16th International Configuration Workshop, CEUR Workshop Proceedings, 2014, Vol. 1220. Pp. 81–88.
2. Sandrin E. Synergic effects of sales-configurator capabilities on consumerperceived benefits of mass-customized products. International Journal of Industrial Engineering and Management, 2017, Vol. 8, No. 3. Pp. 177–188.
3. Streichsbier C., Blazek P., Faltin F., Fr¨uhwirt W. Are de-facto standards a useful guide for designing human-computer interaction processes? The case of user interface design for web based B2C product configurators. 42nd Hawaii International Conference on System Sciences, 2009. Pp. 1–7. DOI: 10.1109/HICSS.2009.80.
4. Leclercq T., Davril J.-M., Cordy M., Heymans P. Beyond de-facto standards for designing human-computer interactions in configurators. CEUR Workshop Proceedings, 2016, vol. 1705. Pp. 40–43.
5. Abbasi E.K., Hubaux A., Acher M., Boucher Q., Heymans P. The anatomy of a sales configurator: An empirical study of 111 cases. Lecture Notes in Computer Science, 2013, LNCS, vol. 7908, Pp. 162–177. DOI: 10.1007/978- 3-642-38709-8_11.
6. Sandrin E., Trentin A., Grosso C., Forza C. Enhancing the consumerperceived benefits of a mass-customized product through its online sales configurator: An empirical examination. Industrial Management and Data System, 2017, vol. 117, no. 6. Pp. 1295–1315. DOI: 10.1108/IMDS-05-2016- 0185.
7. Leclercq T., Cordy M., Dumas B., Heymans P. Representing repairs in configuration interfaces: A look at industrial practices. ACM IUI2018 Workshop on Explainable Smart Systems (ExSS), 2018, Available at:https://explainablesystems.comp.nus.edu.sg/2018/wpcontent/uploads/2018/02/exss_12_leclercq.pdf (accessed 01.03.2022).
8. Leclercq T., Cordy M., Dumas B., Heymans P. On studying bad practices in configuration UIs. ACM IUI2018 Workshop on Web Intelligence and Interaction. Available at: http://ceur-ws.org/Vol-2068/wii1.pdf (accessed: 01.03.2022).
9. Grosso C., Forza C., Trentin A. Support for the social dimension of shopping through web based sales configurators. 17th International Configuration Workshop, CEUR Workshop Proceedings, 2015, vol. 1453. Pp. 115–122.
10. Grosso C., Forza C. Users’ Social-interaction Needs While Shopping via Online Sales Configurators. International Journal of Industrial Engineering and Management, 2019, vol. 10, no. 2. Pp. 139–154. DOI: 10.24867/IJIEM2019-2-235.
11. Mahlam¨aki T., Storbacka K., Pylkk¨onen S., Ojala M. Adoption of digital sales force automation tools in supply chain: Customers’ acceptance of sales configurators. Industrial Marketing Management, 2020, vol. 91. Pp. 162–173. DOI: 10.1016/j.indmarman.2020.08.024.
12. HardPrice – Sravnenie i dinamika cen na komplektuyushhie PK v internet magazinax [HardPrice – Comparison and dynamics of prices for PC components in online stores]. Available at: https://hardprice.ru/ (accessed: 01.03.2022). (In Russ.)
13. Konfigurator PK – sobrat‘ komp‘yuter na zakaz. Sobrat‘ sistemny‘j blok v onlajn konfiguratore [PC configurator – to assemble a computer to order. Assemble the system unit in the online configurator]. Available at: https://www.citilink.ru/configurator/ (accessed 01.03.2022). (in Russ.)
14. Sborka PK – DNS – internet-magazin cifrovoj i by‘tovoj texniki po dostupny‘m cenam [PC assembly – DNS – online store for digital and home appliances at affordable prices]. Available at: https://www.dns-shop.ru/configurator/ (accessed: 01.03.2022). (In Russ.)
15. Sobrat‘ komp‘yuter onlajn s proverkoj sovmestimosti Konfigurator/sborka igrovogo PK [Assemble a computer online with a compatibility check Configurator/build a gaming PC]. Available at: https://www.ironbook.ru/constructor/ (accessed: 01.03.2022). (In Russ.)
16. Shchukin N. Yu., Golchevskiy Yu. V. The logic of the software configurator at the stage of selecting compatible computer components // XXVIII godichnaya sessiya Uchenogo soveta SGU im. Pitirima Sorokina: Nacional‘naya konferenciya : sbornik statej [XXVIII annual session of the Academic Council of the Pitirim Sorokin Sykt. State Univ.: National conference: collection of articles: text. sci. electr. ed. Syktyvkar: Publishing House of Pitirim Sorokin Sykt. State Univ.] 2021, pp. 649–660. (In Russ.)

For citation: Golchevskiy Yu. V., Shchukin N. Yu. Design and Development of a Service Web Configurator for Computer Assembly. Bulletin of Syktyvkar University, Series 1: Mathematics.
Mechanics. Informatics, 2022, No. 1 (42), pp. 41−60. https://doi.org/10.34130/1992-2752_2022_1_41

V. Melnikov V. A., Yermolenko A. V. Development of XML-based Markup Language

https://doi.org/10.34130/1992-2752_2022_1_61

Vadim A. Melnikov – Pitirim Sorokin Syktyvkar State University

Andrey V. Yermolenko – Pitirim Sorokin Syktyvkar State University, ea74@list.ru

Text

Abstract. Modern approaches in the field of software development assume not only the functionality of the product being developed, but also the convenience, clarity and familiarity of the interfaces. Today, the developed software can be used on various devices, with different configurations, and users may also need a different language to work with the software. To address the issue of universality in the field of 2D games, the approach used in the development of the user interface for the Sad Lion Engine is proposed. Within the framework of this approach, it is supposed to use the markup language Sad Lion Markup Language, the description and use of which is given in the article.

Keywords: user interfaces, C++, mobile development, markup languages

References

1. Rago A. S., Stevens W. R. Advanced programming in the UNIX environment. Addison-Wesley Professional, 2013. 1032 p.
2. Camden K. R. Apache Cordova In Action. Shelter Island: Manning, 2016. 230 p.
3. Thornsby J. Android UI design. Birmingham: Packt Publishing, 2016. 356 p.
4. Bennett G., Kaczmarek S., Lees B. Swidt 4 for Absolute Beginners. Phoenix: Apress, 2018. 317 p.
5. Petzold C. Cross-platform C# programming for iOS, Android and Windows. Redmond, Washington: Microsoft Press, 2013. 1161 p.
6. Petzold C. Applications = Code + Markup. A Guide To the Microsoft Windows Presentation Foundation. Redmond: Microsoft Press, 2006. 1002 p.
7. Windmill E. Flutter in Action. Shelter Island: Manning, 2020. 368 p.
8. Melnikov V. A. Development Process of game engine core for 2D games and interfaces Sad Lion Engine. Vestnik Syktyvkarskogo universiteta. Ser.1: Matematika. Mexanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics], 2019, 4 (33), pp. 21–37. (In Russ.)
9. Dogsa T., Meolic R. A C++ App for Demonstration of Sorting Algorithms on Mobile Platforms. International Journal of Interactive Mobile Technologies., 2014. Vol. 8, No 1. Available: https://www.onlinejournals.org/index.php/i-jim/article/view/3464/2940 (accessed: 17.07.2020).
10. Cao J., Cao Y. Application of human computer interaction interface in game design. Communications in Computer and Information Science, 2017, 714, pp. 103–108. DOI: 10.1007/978-3-319-58753-0_16.
11. Zaina L. A. M., Fortes R. P. M., Casadei V., Nozaki L. S., Paiva D. M. B. Preventing accessibility barriers: Guidelines for using user interface design patterns in mobile applications. Journal of Systems and Software, 2022, vol. 186. DOI: 10.1016/j.jss.2021.111213.
12. Quinones, J. R., Fernandez-Leiva, A. J. XML-Based Video Game Description Language. IEEE Access, 2020, vol. 8, pp. 4679–4692. DOI: 10.1109/ACCESS.2019.2962969.
13. Derakhshandi M., Kolahdouz-Rahimi S., Troya J., Lano K. A modeldriven framework for developing android-based classic multiplayer 2D board games. Automated Software Engineering, 2021, 28 (2). DOI: 10.1007/s10515- 021-00282-1.
14. Park, H. C., Baek, N. Design of SelfEngine: A Lightweight Game Engine. Lecture Notes in Electrical Engineering, 2020, vol. 621, pp. 223–227. DOI: 10.1007/978-981-15-1465-4_23.
15. West M. Evolve your hierarchy [Online] Cowboy Programming. Available: http://cowboyprogramming.com/2007/01/05/evolve-your-heirachy/ (accessed: 22.08.2020).
16. Hocking J. Unity in action: Multiplatform game development in C#. Manning, 2018. 400 p.
17. Lisovsky, K.Y. XML Applications Development in Scheme. Programming and Computer Software 28, 197–206 (2002). https://doi.org/10.1023/A:1016319000374

For citation: Melnikov V. A., Yermolenko A. V. Development of XML-based Markup Language. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022, No. 1 (42), pp. 61−73. https://doi.org/10.34130/1992-2752_2022_1_61

VI. Pavlova L. V. Methods of teaching elementary mathematics in preparation a mathematics teacher at a university

https://doi.org/10.34130/1992-2752_2022_1_74

Lydia V. Pavlova – Pskov State University, pavlovalida@mail.ru

Text

Abstract. Today, the education system is rapidly undergoing changes that future teachers should be ready for. Consequently, their training at the university cannot remain the same as 10 or even 5 years ago and requires revision and adaptation to modern requirements and demands of society. The professional training of a future mathematics teacher involves subject and methodological training. At the same time, the quality of subject training at the university depends on the level of proficiency in school mathematics. However, many first-year students are experiencing a number of difficulties, which the researchers note and which were identified by us during the control work on the school mathematics course and the survey of first-year students of the Institute of Mathematical Modeling and Igropractic Pskov State University. The identified problems and difficulties were taken into account when developing the program of the discipline «Introductory Course of Mathematics», which is aimed at repeating and studying the material necessary for the successful study of the university course of mathematics. The article presents the methodology of teaching elementary mathematics (using the example of the section «Trigonometry») to future teachers of mathematics, the feature of which is the inclusion of methodological aspects in the learning process. This allows not only to form subject knowledge on trigonometry, but also to show students how to teach schoolchildren in modern conditions, for example, with distance or mixed learning format. The proposed method has shown positive results.

Keywords: introductory mathematics course, elementary mathematics, school mathematics course, distance learning course, independent study, trigonometry

References

1. The working program of the discipline «Elementary Mathematics» for the direction of training Pedagogical education (with two training profiles «Computer Science and Mathematics»), full-time education. Developer: L. V. Pavlova. Pskov State University, 2020. Available: https://pskgu.ru/eduprogram (accessed: 01.02.2022). (In Russ.)
2. Sevostyanova S. A., Shumakova E. O., Martynova E. V. Rating system for assessing students’ knowledge in the study of the discipline «Introductory course of Mathematics». Vestnik Yuzhno-Uralskogo gosudarstvennogo gumanitarno-pedagogicheskogo universiteta [Bulletin of the
   South Ural State Humanitarian Pedagogical University]. 2018. No. 8. Pp. 116–129.
3. Drobysheva I. V., Drobyshev Yu. A. The design model of the introductory course of mathematics. Matematicheskoe modelirovanie v ekonomike, upravlenii i obrazovanii : sbornik nauchny‘x statej po materialam III Mezhdunarodnoj nauchno-prakticheskoj konferencii [Mathematical modeling in economics, management and education. Collection of scientific articles based on the materials of the III International Scientific and Practical Conference]. 2017. Pp. 150–155. (In Russ.)
4. Panfilova T. L. Some features of teaching elementary mathematics to students of pedagogical directions. Sovremennye problemy i perspektivy obucheniya matematike, fizike, informatike v shkole i vuze : mezhvuzovskij sbornik nauchno-metodicheskix rabot, otv. red. S. F. Miteneva [Modern problems and prospects of teaching mathematics, physics, computer science at school and university. Interuniversity collection of scientific and methodological works. Responsible editor S.F. Miteneva]. Vologda, 2018. Pp. 49–52. (In Russ.)
5. The work program of the discipline «Introductory course of mathematics» for the direction of training Pedagogical education (with two training profiles «Computer Science and Mathematics»), full-time education. Developer: L. V. Pavlova. Pskov State University, 2020. Available: https://pskgu.ru/eduprogram (accessed 01.02.2022). (In Russ.)
6. Bostanova M. M., Dzhaubaeva Z. K., Uzdenova M. B. Electronic textbook as a means of increasing the effectiveness of independent work of students in the conditions of distance learning in the study of the discipline «Elementary Mathematics». Sovremenny‘e problemy‘ matematicheskogo obrazovaniya : materialy‘ Mezhregional‘noj nauchno-prakticheskoj konferencii [Modern problems of mathematical education. Materials of the Interregional
   scientific and practical conference]. 2020. Pp. 44–48. (In Russ.)
7. Kochegurnaya M. Yu. The use of distance learning in teaching the discipline «Elementarnaya matematika». [Information systems and technologies in modeling and management. Proceedings of the V International Scientific and Practical Conference. Editor-in-chief K. A. Makoveychuk.] 2020. Pp. 411–413.
8. Popov N. I. On the effectiveness of using the model of learning technology in trigonometry in teaching mathematics students. Education and science. No. 9 (108). Pp. 138–153. (In Russ.)
9. Stefanova G. P., Baigusheva I. A., Tovarnichenko L. V., Stepkina M. A. Formation of cognitive independence of first-year students in the study of elementary mathematics at the university. Sovremennye problemy nauki i obrazovaniya [Modern problems of science and education]. 2018. No. 4. Pp.(In Russ.)

For citation: Pavlova L. V. Methods of teaching elementary mathematics in preparation a mathematics teacher at a university. Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022, No. 1 (42), pp. 74−89. https://doi.org/10.34130/1992-2752_2022_1_74

VII. Sotnikova O. A. ASLANOV RAMIZ MUTALLIM OGLY (ON THE 75TH ANNIVERSARY)

https://doi.org/10.34130/1992-2752_2022_1_90

Sotnikova Olga Alexandrovna – Pitirim Sorokin Syktyvkar State University

Text

Abstract. The article is dedicated to Aslanov Ramiz, PhD in Physics and Mathematics, Doctor of pedagogical sciences, professor, corresponding member of the International Academy of Sciences of Pedagogical Education.

Keywords: Aslanov Ramiz

For citation: Sotnikova O. A. Aslanov Ramiz (on his 75th birthday). Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 2022, No. 1 (42), pp. 90−94.
https://doi.org/10.34130/1992-2752_2022_1_90

Full text

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

Text

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.

References

1. Golan J. S. Semirings and their Applications. Dordrecht: Kluwer Academic Publishers, 1999. 38 p.
2. Vandiver H. S. Note on a simple type of algebra in which cancelation law of addition does not hold. Bull. Amer. Math. Soc., 1934, V. 40. Pp. 914–920.
3. Dedekind R. Uber die Theorie der ganzen algebraischen Zahlen ¨ Supplement XI to P.G. Lejeune Dirichlet: Vorlessungen Uber Zahlentheorie, 4 Anfl., Druck und Verlag, Braunschweig, 1894.
4. Hilbert D. Uber den Zahlbegriff. ¨ Jahresber. Deutsch. Math. Verein., 1899, V. 8. Pp. 180–184.
5. Hebisch U., Weinert H. J. Semirings: theory and applications in computer science. Series in Algebra. Vol. V. World Scientific, Singapore, 1998. 361 p.
6. Golan J. S. The theory of semirings with applications in mathemayics and theoretical computer science. Pitman monographs and syrveys in pure and applied mathematics, V. 54, 1992 (1991).
7. Glazek K. A Short Guide Through the Literature on Semirings. Preprint No. 39. University of Wroclaw, Math. Inst., Wroclaw, 1985.
8. Glazek K. A Short Guide to the Literature on Semirings and Their Applications in Mathematics and Computer Science. Technical University Press, 2002.
9. Maslyaev D. A., Chermnykh V. V. Skew Laurent polynomial semiring. Sibirskie elektronnye matematicheskie izvestiya [Siberian Electronic Mathematical News], 2020, V. 17. Pp. 521–533.
10. Vechtomov E. M. Vvedenie v polukoltsa: uchebnoe posobie [Introduction to semirings: A Tutorial], Kirov, Izd. Vyatskogo gospeduniversiteta, 2000. 44 p.
11. Lukin M. A. On universal congruence on semirings. Problemy sovremennogo matematicheskogo obrazovaniya v pedvuzah i shkolah Rossii: interaktivnye formy obucheniya matematike studentov i shkol’nikov. Materialy V Vserossiyskoy nauchno-metodicheskoy
    konferentsyi [Problems of Modern Mathematics Education in Pedagogical Universities and Schools of Russia: Interactive Forms of Teaching Mathematics to Students and Schoolchildren : Proceedings of the V All-Russian Scientific and Methodical Conference], Kirov, Izd. VyatGGU, 2012. Pp. 312–316.
12. Vechtomov E. M., Petrov A. A. Multiplicatively idempotent semirings. Fundamentalnaya i prikladnaya matematika [Fundamental and Applied Mathematics], 2013, V. 18. No. 4. Pp. 41–70.
13. Vechtomov E. M., Cheraneva A. V. On the theory of semidivision rings). Uspehi matematicheskih nauk [Advances in Mathematical Sciences], 2008, V. 63. No. 2. Pp. 161–162.
14. Vechtomov E. M., Cheraneva A. V. Semifields and their properties. Fundamentalnaya i prikladnaya matematika [Fundamental and Applied Mathematics], 2008, V. 14. No. 5. Pp. 3–54.
15. Polin S. V. Simple semisfields and semifields. Sibirskiy matematicheskiy zhurnal [Siberian Mathematical Journal], 1974, V. 15. No. 1. Pp. 90–101.
16. Chermnykh V. V. Funktsional’nye predstavleniya polukolets: monografiya [Functional representations of semirings: monography], Kirov, Izd. VyatGGU, 2010. 224 p.
17. Vechtomov E. M., Petrov A. A. Polukoltsa s idempotentnym umnozheniem: monografiya [Semirings with idempotent multiplication: monography], Kirov, OOO «Raduga-PRESS»,144 p.
18. Vechtomov E. M., Lukin M. A. Semirings which are the unions of a ring and a semifield. Uspehi matematicheskih nauk [Advances in Mathematical Sciences], 2008, V. 63. No. 6. Pp. 159–160.
19. Lukin M. A. Semiring joins of a ring and semifield. Izvestiya vuzov. Matematika [Proceedings of Higher Education Institutions. Mathematics], 2008. No. 12. Pp. 76–80.
20. Vechtomov E. M., Lubyagina E. N., Chermnykh V. V. Elementy teorii polukolets [Elements of semiring theory], Kirov, OOO «Raduga-PRESS», 2012. 228 p.
21. Vechtomov E. M., Starostina O. V. Structure of abelian regular positive semirings). Uspehi matematicheskih nauk [Advances in Mathematical Sciences], 2007. V. 62. No. 1. Pp. 199–200.
22. Vechtomov E. M., Starostina O. V. Generalized abelian regular positive semirings). Vestnik Syktyvkarskogo universiteta. Seriya Matematuka. Mehanika. Informatika [Bulletin of the Syktyvkar University. Series 1. Mathematics. Mechanics. Informatics], 2007, Vol.Pp. 3–16.
23. Chermnykh V. V., Mikhalev A. V., Vechtomov E. M. Abelianregular positive semirings. Journal of Mathematical Science [New York], 1999, V. 97. Pp. 4162–4176.
24. Vechtomov E. M. Annihilator characterizations of Boolean rings and Boolean lattices. Matematicheskie zametki [Mathematical Notes], 1993, V. 53. No. 2. Pp. 15–24.
25. Bogdalov I. F. Invertibility of the Hilbert basis theorem in the class of semirings. Problemy sovremennogo matematicheskogo obrazovaniya v pedvuzah i shkolah Rossii: Tezisy dokladov Mezhregional’noy nauchnoy konferentsyi [Problems of Modern Mathematics Education
    in Pedagogical Universities and Schools of Russia : Abstracts of the Interregional Scientific Conference], Kirov, Izd. Vyatskogo gospeduniversiteta, 1998. Pp. 171–172.
26. Il’in S. N. Regularity Criterion for Complete Matrix Semirings. Matematicheskie zametki [Mathematical Notes], 2001, V. 70. No. 3. Pp. 366–374.
27. Il’in S. N. On the applicability to semirings of two theorems from the theory of rings and modules. Matematicheskie zametki [Mathematical Notes], 2008, V. 83. No. 4. Pp. 563–574.
28. Il’in S. N. On the homological classification of semirings. Itogi nauki i tehniki. Sovremennaya matematika i ee prilozheniya. Tematicheskie obzory [Results of Science and Technology. Modern Mathematics and its Applications. Thematic reviews], 2018, V. 158. Pp. 3–22.
29. Dale L. Monic and monic free ideals in polynomial semirings. Proc. Amer. Math. Soc., 1976, V. 56. Pp. 45–50.
30. Babenko M. V., Chermnykh V. V. On skew polynomial semirings on Bezout semiring. Matematicheskie zametki [Mathematical Notes], 2022, V. 111.
31. Rao P. R. Lattice ordered semirings. Math. Sem. Notes, Kobe Univ., 1981, V. 9. Pp. 119–149.
32. Swamy K. L. N. Duallity residuated lattice ordered semigroups. Math. Ann., 1965, V. 159. Pp. 105–114.
33. Chermnykh O. V. On drl-semigroups and drl-semirings) Chebyshevskiy sbornik [Chebyshev collection], 2016, V. 17. No. 4. Pp. 167–179.
34. Burgess W. D., Stephenson W. Pierce sheaves of noncommutative rings. Comm. Algebra, 1976, V. 39. Pp. 512–526.
35. Grothendieck A., Dieudonne J. El´ements de G´eom´etrie ´ Alg´ebrique 1. I.H.E.S., Publ. Math. 4. — Paris, 1960.
36. Pierce R. S. Modules over commutative regular rings. Mem. Amer. Math. Soc., 1967, V. 70. Pp. 1–112.
37. Simmons H. Compact representations — the lattice theory of compact ringed spaces. J. Algebra, 1989, V. 126. Pp. 493–531.
38. Chermnykh V. V. Sheaf representations of semirings. Uspehi matematicheskih nauk [Advances in mathematical sciences], 1993, V. No. 5. Pp. 185–186.
39. Chermnykh V. V. Functional representations of semirings. Fundamentalnaya i prikladnaya matematika [Fundamental and Applied Mathematics], 2012, V. 17. No. 3. Pp. 111–227.
40. Markov R. V., Chermnykh V. V. On Pierce stalks of semirings. Fundamentalnaya i prikladnaya matematika [Fundamental and Applied Mathematics], 2014, V. 19. No. 2. Pp. 171–186.
41. Markov R. V., Chermnykh V. V. Semirings close to regular and their Pierce stalks) Trydy IMM UrO RAN [Proceedings of IMM UB RAS], 2015, V. 21. No. 3. Pp. 213–221.
42. Babenko M. V., Chermnykh V. V. Pierce stalks of semirings of skew polynomials. Trydy IMM UrO RAN [Proceedings of IMM UB RAS], 2021, V. 27. No. 4. Pp. 48–60.
43. Chermnykh V. V., Chermnykh O. V. Functional representations of lattice-ordered semirings. Sibirskie elektronnye matematicheskie izvestiya [Siberian Electronic Mathematical News], 2017, V. 145. Pp. 946–971.
44. Chermnykh O. V. Functional representations of lattice-ordered semirings. III. Sibirskie elektronnye matematicheskie izvestiya [Siberian Electronic Mathematical News], 2018, V. 15. Pp. 677–684.
45. Chermnykh V. V., Chermnykh O. V. Functional representations of lattice-ordered semirings. III. Trydy IMM UrO RAN [Proceedings of IMM UB RAS], 2020, V. 26. No. 3. Pp. 235–248.
46. Polin S. V. Minimal varieties of semirings. Matematicheskie zametki [Mathematical Notes], 1980, V. 27. No. 4. Pp. 527–537.
47. Pastijn F. Varieties Generated by Ordered Bands. II. Order., 2005, V. 22. Pp. 129−143.
48. Guterman A. E. Frobeniusovy endomorfizmy prostranstva matrits: dissertatsiya na soiskanie uchenoy stepeni doktora fiziko-matematicheskih nauk [Frobenius endomorphisms of the matrix space: dissertation for the degree of Doctor of Physics and Mathematics], M.: MSU, 2009. 321 p.
49. Shitov Ya. N. Lineynaya algebra nad polukoltsami: dissertatsiya na soiskanie uchenoy stepeni doktora fiziko-matematicheskih nauk [Linear algebra over semirings: dissertation for the degree of Doctor of Physics and Mathematics], M.: MSU, 2015. 302 p.
50. Krivulin N. K. On the solution of generalized linear vector equations in idempotent algebra. Vestnik Sankt-Peterburgskogo universiteta. Seriya 1 [Bulletin of Saint Petersburg University. Series 1], 2006. No.Pp. 23–36.
51. Krivulin N. K., Romanova E. Yu. Approximate factorization of positive matrices using tropical optimization methods. Vestnik SanktPeterburgskogo universiteta. Seriya 10 [Bulletin of Saint Petersburg University. Series 10], 2020, V. 16. No. 4. Pp. 357–374.
52. Vorob’ev N. N. Extreme algebra of positive matrices. Elektronische Informatiosverarbeitung und Kybernetik [Electronic information processing and cybernetics], 1967, V. 3. Pp. 39–71.
53. Joswig M. Essentials of Tropical Combinatorics. Graduate Studies in Mathematics. V. 219, 2021. 398 p.
54. Maslov V. P., Kolokol’tsov V. N. Idempotentnyi analiz i ego primenenie v optimal’nom upravlenii [Idempotent analysis and its application in optimal control], M.: Nauka, 1994.
55. Gondran M., Minoux M. Graphs, Dioids and Semirings. New Models and Algorithms. New York: Springer, 2008. 400 p.
56. Kolokoltsov V. N., Maslov V. P. Idempotent Analysis and its Applications. Mathematics and its Applications, V. 401, Dordrecht: Kluwer Academic Publishers, 1997.
57. Litvinov G. L., Maslov V. P., Shpiz G. B. Idempotent functional analysis: an algebraic approach. Matematicheskie zametki [Mathematical Notes], 2001, V. 69. No. 5. Pp. 758–797.
58. Gillman L., Jerison M. Rings of continuous functions. New York,300 p.
59. Varankina V. I., Vechtomov E. M., Semenova I. A. Semirings of continuous non-negative functions: divisibility, ideals, congruences. Fundamentalnaya i prikladnaya matematika [Fundamental and Applied Mathematics], 1998, V. 4. No. 2. Pp. 493–510.
60. Vechtomov E. M., Lubyagina E. N., Sidorov V. V., Chuprakov D. V. Elementy funktsionalnoy algebry: monografiya. V 2 tomah [Elements of functional algebra: monography. In 2 volumes] [edited by Vechtomov], Kirov, OOO «Raduga-PRESS», 2016, V. 1, 384 p.; V. 2. 316 p.
61. Vechtomov E. M., Mikhalev A. V., Sidorov V. V. Semirings of continuous functions Fundamentalnaya i prikladnaya matematika [Fundamental and Applied Mathematics], 2016, V. 21. No. 2. Pp. 53– 131.
62. Vechtomov E. M., Chuprakov D. V. The principal kernels of semifields of continuous positive functions. Fundamentalnaya i prikladnaya matematika [Fundamental and Applied Mathematics],
    2008, V. 14. No. 4. Pp. 87–107.
63. Vechtomov E. M., Chuprakov D. V. Extension of congruences on semirings of continuous functions. Matematicheskie zametki [Mathematical Notes], 2009, V. 85. No. 6. Pp. 803–816.
64. Bestuzhev A. S., Vechtomov E. M. Cyclic semirings with commutative addition.Vestnik Syktyvkarskogo universiteta. Seriya Matematika. Mehanika. Informatika [Bulletin of the Syktyvkar University. Series 1. Mathematics. Mechanics. Informatics], 2015, V.Pp. 8–39.
65. Vechtomov E. M., Chuprakov D. V. Finite cyclic semirings with semilattice addition given by the two-generated ideal of natural numbers. Chebyshevskiy sbornik [Chebyshev collection], 2020, V. 21. No. 1. Pp. 82–100.
66. Vechtomov E. M., Orlova (Lubyagina) I. V. Cyclic semirings with idempotent noncommutative addition. Fundamentalnaya i prikladnaya matematika [Fundamental and Applied Mathematics],
    2012, V. 17. No. 1. Pp. 33–52.
67. Vechtomov E. M., Orlova I. V. Cyclic semirings with idempotent commutative addition. Fundamentalnaya i prikladnaya matematika [Fundamental and Applied Mathematics], 2015, V. 20. No. 6. Pp. 17– 41.
68. Bestuzhev A. S., Vechtomov E. M., Orlova I.V. Structure of cyclic semirings. Sbornik materialov IX nauchnoy konferentsii EKOMOD-2016 “Matematicheskoe modelirovanie razvivayuscheysya
    ekonomiki, ekologii i tehnologii” [Proceedings of the IX Scientific Conference ECOMOD-2016 “Mathematical modeling of developing economy, ecology and technology”], Kirov: Izd. VyatGU, 2016. Pp. 21–30.
69. Vechtomov E. M., Petrov A. A. Multiplicatively idempotent semirings with three elements. Matematicheskiy vestnik Vyatskogo gosudarstvennogo universiteta [Mathematical Bulletin of Vyatka State University], 2021. No. 2. Pp. 13−23.
70. Zhao X., Ren M., Crvenkovic S., Shao Y., Dapic P. The varietygenerated by an ai-semiring of order three. Ural Mathematical Journal,2020, V. 6. No. 2. Pp. 117–132.

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

1. Perel’muter A. V., Slivker V. I. Ustoychivost’ ravnovesiya konstruktsiy i rodstvennyye problemy [Stability of the structures equilibrium and related problems]. Vol. 2. Moscow, Izdatel’stvo SKAD SOFT, 672 p.
2. Nikolai Ye. L. Trudy po mekhanike [Writings on mechanics]. Moscow, Gostekhizdat, 1955. 584 p.
3. Andryukova V., Tarasov V. Nonsmooth problem of stability for elastic rings. Abstracts of the International Conference “Constructive Nonsmooth Analysis and Related Topics” Dedicated to the Memory of Professor V.F. Demyanov. CNSA-2017. 22-27 may 2017, Part I. SaintPetersburg. Publisher: BBM. Pp. 213–218.
4. Birger I. A. Prochnost’. Ustoychivost’. Kolebaniya [Strength. Stability. Oscillations]. M.: Mashinostroenie, 1988. 831 p.

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.

References

1. Bosnic S., Papp I. The development of hybrid mobile applications with Apache Cordova. 24th Telecommunications Forum. 2016. Pp. 1−4.
2. Tomozei C. Assessment of the evolution in quality for XamarinAndroid Multimedia Applications. 19th International Conference on Informatics in Economy. Education, Research and Business
   Technologies. 2020. Pp. 47−52.
3. Melnikov V. A. Development Process of game engine core for 2D games and interfaces Sad Lion Engine. Vestnik Syktyvkarskogo universiteta. Ser. 1: Matematika. Mexanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics], 2019, 4
   (33). Pp. 21–37.
4. Fisz K., Kopniak P., Galan D. A multi-criteria comparison of mobile applications built with the use of Android and Flutter Software Development Kits. Journal of Computer Sciences Institute. Vol. 19.Pp. 107−113.
5. Dabit N. React Native in action. Shelter Island: Manning Publishing. 320 p.
6. Java Native Interface Specification [Online]. Oracle. Available: https://docs.oracle.com/javase/7/docs/technotes/guides/jni/spec/ jniTOC.html (Accessed: 22.10.2020).
7. Rago S., Stevens W. Advanced programming in the UNIX environment, 3rd ed. Upper Saddle River, NJ, Boston, Indianopolis, San Francisco, New York, Toronto, Montreal, London, Munich, Paris, madrid, Capetown, Sydney, Tokyo, Singapore, Mexico City: AddisonWesley, 2013. 1032 p.
8. Corbet J., Kroah-Hartman G., McKellar J., Rubini A. Linux device drivers, 4th ed. Beijing, Cambridge, Farnham, Koln, Sebastopol, Taipei, Tokyo. 2017. 600 p.
9. Thornsby J. Android UI design. Birmingham: Packt Publishing. 2016. 356 p.
10. Anugerah M. A., Sekar G. S. Designing Android User Interface for University Mobile Library. International Conference on Computing, Engineering, and Design (ICCED). 2021. Pp. 224−229.
11. Neuburg M. Programming iOS 13: Dive Deep into Views, View Controllers, and Frameworks. Sebastopol: O’Reilly. 2020. 1208 p. New York: Oracle.
12. Nystrom R. Game programming patterns. San Bernardino: Genever Benning, 2018. 345 p.
13. Ginsburg D., Purnomo B. OpenGL ES 3.0 Programming Guide 2nd Edition. Upper Saddle River, NJ, Boston, Indianopolis, San Francisco, New York, Toronto, Montreal, London, Munich, Paris,
    madrid, Capetown, Sydney, Tokyo, Singapore, Mexico City: AddisonWesley, 2014. 560 p.
14. Sellers G. Vulkan Programming Guide. The Official Guide to Learning Vulkan. Boston, Columbus, Indianapolis, New York, San Francisco, Amsterdam, Cape Town Dubai, London, Madrid, Milan, Munich, Paris, Montreal, Toronto, Delhi, Mexico City San Paulo, Sydney, Hong
    Kong, Seoul, Singapore, Taipei, Tokyo: Addison-Wesley, 2017. 480 p.
15. Clayton J. Metal programming guide. Addison-Wesley. 2018. 352 p.
16. Stroustrup B. The C++ programming languege 4th edition. Uppder Saddle River, Boston, Indianopolis, San Francisco, New York, Toronto, Montral, London, Munich, Paris, Madrid, Capetown, Sydney, Tokyo, Singapore, Mexico city: Addison-Wesley. 2013. 1345 p.
17. Stroustrup B. Programming: Principles and Practice using C++. 2nd Edition. New Jearsey: Pearson Education. 2015. 1312 p.
18. Shieldt H. Java: The Complete Reference, Eleventh Edition 11th Edition. 2019. 1248 p.
    

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.

References

1. Boltyanskij V. G. Analogy — commonality of axiomatics. Sovetskaya pedagogika [Soviet pedagogy], 1975. No. 1. Pp. 83−93.
2. Dorofeev S. N. Teoriya i praktika formirovaniya tvorcheskoj aktivnosti budushhix uchitelej matematiki v pedagogicheskom vuze, dissertaciya na soiskanie uchenoj stepeni doktora pedagogicheskix nauk [The theory and practice of forming the creative activity of future
   teachers of mathematics in a pedagogical university], Penza, 2000. 410 p.
3. Atanasyan L. S., Butuzov V. F., Kadomcev S. B. et al. Geometriya. 7−9 klassy [Geometry. 7-9th grade]. M.: Prosveshhenie, 384 p.
4. Aleksandrov A. D., Verner A. L., Ry‘zhik V. I. Geometriya. 9 klass [Geometry. 9th grade]. M.: Prosveshhenie, 2015. 175 p.
5. Atanasyan L. S., Butuzov V. F., Kadomcev S. B. et al. Geometriya. 7−9 klassy [Geometry. 7-9th grade]. M.: Prosveshhenie, 255 p.
6. Dorofeev S. N., Zhuravleva O. N., Ry‘bina T. M., Sarvanova Zh. A. Formation of research competencies of students in the mathematics classroom. Sovremenny‘e naukoemkie texnologii
   [Modern knowledge-intensive technologies]. 2018. No. 10. Pp. 181−185.
7. Uteeva R. A. Teoreticheskie osnovy‘ organizacii uchebnoj deyatel‘nosti uchashhixsya pri differencirovannom obuchenii matematike v srednej shkole. Dissertaciya doktora ped. nauk [Theoretical foundations of the organization of students’ learning activities in differentiated learning of mathematics in high school]. Moscow, 1998. 363 p.
8. Kudryavcev L. D. Mysli o sovremennoj matematike i ee izuchenii [Thoughts on Modern Mathematics and its Study]. M.: Nauka, 1977. 123 p.
9. Dorofeev S. N. UDE as a method of preparing future bachelors of teacher education for professional activities. Gumanitarny‘e nauki i obrazovanie. MordGPI im. M. E. Evsev‘eva [Humanities and Education / M. E. Evsevyev Mordovian State Pedagogical University].
   No. 1, 2013. Pp. 14−17.
10. Sarancev G. I. Kak sdelat‘ obuchenie matematike interesny‘m [How to make learning math interesting]. M.: Prosveshhenie. 2011. 160 p.
11. Dorofeev S., Pavlov I., Shichiyakh R., Prikhodko A. Differentiated Training as a Form of Organization of Education and Cognitive Activity of Future Masters of Pedagogical Education.
    Applied Lingvistics Research Jounal, 2021, 5(3), Pp. 216−222.

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

Text

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

1. Yermolenko А. V., Ladanova S. V. Contact problem for two plates with different fixing. Vestnik Syktyvkarskogo universiteta. Ser. 1: Matematika. Mexanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics], 2020, 3 (36). Pp. 87- 92.
2. Ермоленко А. В. Kontaktnye zadachi so svobodnoj granicej [Free Boundary Contact Problems]. Syktyvkar: Izd-vo SGU im. Pitirima Sorokina, 2020. (CD-ROM). 105 p.
3. Yermolenko A. V., Osipov K. S. On using Python libraries to calculate plates. Vestnik Syktyvkarskogo universiteta. Ser. 1: Matematika. Mexanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics], 2019, 4 (33). Pp. 86–95.
4. Mihajlovskii E. I., Toropov A. V. Matematicheskiye modeli teorii uprugosti [Mathematical models of the theory of elasticity]. Syktyvkar: Sykt Publishing House. University, 1995. 251 p.
5. Mikhailovskii E. I., Tarasov V. N. On the convergence of the generalized reaction method in contact problems with a free boundary. Jurnal prikladnoy matematiki i mekhaniki [Journal of Applied Mathematics and Mechanics], 1993, v. 57, No. 1. Pp. 128–136.

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

I To the 25th anniversary of the MMIK department

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

I A word about Mikhailovsky Evgeny Ilyich

Text

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

Text

III Mikhailovskii E. I. Mechanics of shells

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

XV Odynec W. P. Returning to H. Kummer

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

XIII Chernykh K. F. On anisotropic nonlinear elasticity

Text

XIV Mikhailovskii E. I., Osipova O. P. About one a form of dynamic equilibrium of compressed part for drill column

Text

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

Text

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

Text

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

Text

XVIII Tarasov V. N., Loginov I. N. The influence of boundary conditions to lamina’s stability with rigid constraints on displacement

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

V Tikhomirov A. N. On the Central Limit Theorem

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

XXIV Vityazeva V.A.Glare of informatization

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

XXII Vladimir Dmitrievich Yakovlev (on his fiftieth birthday)

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

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

Text

XXIV 25 years of the Faculty of Mathematics

Text

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

Text