I. Kalinin S. I., Sokolova D. A. Application of Jensen’s inequality to solving equations and optimization tasks
DOI: 10.34130/1992-2752_2021_1_04
Kalinin Sergey — Doctor of Education, Ph.D. in Physics and Mathematics, Professor, Department of Fundamental Mathematics, Vyatka State University, e-mail: kalinin_gu@mail.ru
Sokolova Darya — 4rd year student of the Faculty of Computer and Physical and Mathematical Sciences, Vyatka State University, e-mail: darya_sokoloval999@mail.ru
In this article, we consider equations and optimization tasks that can be effectively solved by using Jensen’s inequality for convex or concave functions. The main feature of the proposed problems is that when formulating and solving them, the convex (concave) functions, which are compositions or products of convex (concave) functions that are simple according to the analytical description are used. This circumstance makes it possible to determine the character of the convexity of the function used in a specific task without referring to its differentiability or its secondorder derivative. The work is addressed to everyone interested in the issues of convex functions and the themes of inequality. Its content can be useful in organizing the research activities of students and schoolchildren of specialized classes.
Keywords: Jensen’s inequality, product of functions, composition of functions, equation, optimization tasks.
References
- Kalinin S. I., Sokolova D.A. Konstruirovanive vypuklykh funktsiv bez obrashcheniva k proizvodnvm (Construction of convex functions without reference to derivatives), Mathematical bulletin of pedagogical universities and universities of the Volga- Vyatka region: period, interuniversity. Sat. scientific method, works, 2019, No. 21, pp. 146-153.
- Sokolova D. A. Ob odnom privome konstruirovaniya slozhnykh vypuklykh funktsiy bez obrashcheniva к proizvodnym (On one method of constructing complex convex functions without referring to derivatives), Mathematical education at school and university: experience,
problems, prospects (MATHEDU’2019) M-ly IX Intern, scientificpractical conf., Kazan: Kazan Federal University, 2019, pp. 166-171. - Kalinin S. I. Sredniye velichiny stepennogo tipa. Neravenstva Koshi i Ki Fana: Ucheb. posobiye po spetskursu (Average values of power type. Cauchy and Ki Fan inequalities: Textbook, special course manual), Kirov: VGGU Publishing House, 2002, 368 p.
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- Vychegzhanin S. V. Dokazatel’stvo neravenstva Yvensenametodom prvamogo i obratnogo induktsii (Proof of Jensen’s inequality by the method of direct and reverse induction), Mathematical bulletin of pedagogical universities and universities of the Volga- Vyatka region.
Issue 15: periodic interuniversity collection of scientific and methodological works, Kirov: Publishing house of ООО «Raduga-PRESS», 2013, pp. 166-172. - Kalinin S. I. Metod neravenstv resheniy uravneniy. Uchebnoye posobiye po elektivnomu kursu dlya klassov fiziko-matematicheskogo profilya (Method of inequalities for solutions of equations. Textbook for an elective course for classes of physical and mathematical profile),
Moscow: Publishing house «Moscow Lyceum», 2013, 112 p.
For citation: Kalinin S. I., Sokolova D. A. Application of Jensen’s inequality to solving equations and optimization tasks, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2021, 1 (38), pp. 4-12.
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II. Popov N. I. Using the area estimate for localizing the maximum of the conformal radius
DOI: 10.34130/1992-2752_2021_1_13
Popov Nikolay — Doctor of Education, Ph.D. in Physics and Mathematics, Professor, Head of the Department of physics, mathematics and information education, Pitirim Sorokin Syktyvkar State University, e-mail: popovnikolay@yandex.ru
A condition for the uniqueness of the critical point of the conformal radius is obtained using an isoperimetric inequality.
Keywords: area estimate, conformal radius, critical point of conformal radius, uniqueness of the solution to the exterior inverse boundary value problem.
References
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I. Aksent’ev L. A., Kazantsev A. V., Popov N. I. Ekstremal’nyve zadachi diva ploshchadev pri konformnom otobrazhenii i ikh primenenive (Extremal problems for areas under conformal mapping and their application), Izv. universities. Mathematics, 1995, no. 6, pp. 3-15. - Popov N.I. Ob odnom uslovii podchinennosti pri lokalizatsii maksimuma konformnogo radiusa (On one condition of subordination in the localization of the maximum of the conformal radius), Trudy Matematicheskogo tsentr im. N. I. Lobachevsky, Kazan: Kazan, unt, 2013, V. 46, Theory of functions, its applications and related issues, pp. 368-369.
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For citation: Popov N. I. Using the area estimate for localizing the maximum of the conformal radius, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2021, 1 (38), pp. 13-18.
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III. Sushkov V. V. About the discrete spectrum of the characteristic equation in case of the Bhatnagar – Gross – Crook model
DOI: 10.34130/1992-2752_2021_1_19
Sushkov Vladislav — Ph. D. in Physics and Mathematics, Associate professor, head of the educational department, Pitirim Sorokin Syktyvkar State University, e-mail: vvsu@mail.ru
The objective of the publication is to show that the technique used in the particular case of solving the problem for one-, two- and polyatomic gases can be effectively extended to a wider class of problems, in particular, arising when solving boundary problems for the Boltzmann equation with
the collision integral in the form of Bhatnagar-Gross-Crook. The case of a vector-matrix integrodifferential equation with a polynomial kernel is investigated, the structure of the continuous and discrete spectrum of the characteristic equation is determined. Eigenfunctions of the continuous spectrum are found.
Keywords: integrodifferential equations, Bhatnagar, Gross and Crook model, spectrum of characteristic equation, distributions.
References
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- Bedrikova E. A., Latyshev A. V. Reshenie zadachi о techenii Kuetta diva Fermi-gaza s pochti zerkal’nvmi granichnvmi uslovivami (Solution of the problem of the Couette flow for a fermi gas with almost specular boundary conditions), Russian Physics Journal, 2016, V. 59, No. 2, pp. 217-230.
- Khachatryan А. К., Khachatryan К. A. Kachestvennoe razlichie reshenij diva stacionarnyh model’nvh uravnenij Bol’cmana v linejnom i nelinejnom sluchavah (Qualitative difference between solutions of stationary model Boltzmann equations in the linear and nonlinear
cases), Theoretical and Mathematical Physics, 2014, V. 180, No. 2, pp. 272-288. - Zhvick V. V. Raskhod razrezhennogo gaza v techenii Puazejlva skvoz’ kruglyj kapillyar (Rarefied gas flow rate in Poiseuille flow through a circular capillary), Fluid Dynamics, 2015, V. 50, No. 5, pp. 711-720.
- Sushkov V. V., Latyshev A. V. Analiticheskoe reshenie granichnvh zadach diva semejstva BGK-uravnenij metodom kanonicheskoj matricv (Analytical solution of boundary problems for a family of BGK equations obtained by the application ofthe canonical matrix method), Izvestia: Herzen University Journal of Humanities & Sciences, 2002, No. 4, pp. 72-85.
- Cercignani C. Matematicheskie metody v kineticheskoj teorii gazov (Mathematical methods in the kinetic theory of gases), Moscow: Nauka, 1973, 245 p.
For citation: Sushkov V. V. About the discrete spectrum of the characteristic equation in case of the Bhatnagar – Gross – Crook model, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2021, 1 (38), pp. 19-26.
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IV. Babenko V. V., Kotelina N. O., Telnova О. P. Software and information support of the paleopalinological problem
DOI: 10.34130/1992-2752_2021_1_27
Babenko Victor — Ph.D., associate professor, Pitirim Sorokin Syktyvkar State University, e-mail: bvvskt@mail.ru
Kotelina Nadezhda — Ph.D. in Physics and Mathematics, Associate Professor of the Department of Applied Mathematics and Information Technologies in Education, Pitirim Sorokin Syktyvkar State University, e-mail: nkotelina@gmail.com
The article proposes promising options for optimizing studies of paleopalinologv (spore-pollen analysis of ancient rocks), which is one of the most important branches of paleontology.
Keywords: machine learning, deep learning, convolutional neural network, databases.
References
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For citation: Babenko V. V., Kotelina N. О., Telnova О. P. Software and information support of the paleopalinological problem, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2021, 1 (38), pp. 27-42.
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V. Gertner D. A., Leontiev D. О., Nosov L. S., Shuchalin D. S. Hardware and software complex for ensuring information security when using electronic signatures
DOI: 10.34130/1992-2752_2021_1_43
Gertner Dmitry — General Director of ООО «Kreif», e-mail: nosovvv@yandex.ru
Leontiev Denis — student, Pitirim Sorokin Syktyvkar State University, e-mail: nosovvv@yandex.ru
Nosov Leonid — Ph.D., Associate Professor, Head of the Department of Information Security, Pitirim Sorokin Syktyvkar State University, e-mail: nosovvv@yandex.ru
Shuchalin Denis — student, Pitirim Sorokin Syktyvkar State University, e-mail: nosovvv@yandex.ru
This paper presents prototype of a software and hardware complex for secure signing of electronic documents on the basis of a trusted device specialized for these operations.
Keywords: hardware and software system, electronic digital signature, Raspberry Pi, Python
References
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For citation: Gertner D. A., Leontiev D. 0., Nosov L. S., Shuchalin D. S. Hardware and software complex for ensuring information security when using electronic signatures, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2021, 1 (38), pp. 43-55.
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VI. Yermolenko A. V., Kotelina N. O., Startseva E. N., Yurkina M. N. On the demand for data parsing training for web developers
DOI: 10.34130/1992-2752_2021_1_56
Yermolenko Andrey — Ph.D., Associate Professor, Head of the Department of Applied Mathematics and Information Technologies in Education, Pitirim Sorokin Syktyvkar State University, e-mail: ea74@list.ru
Kotelina Nadezhda — Ph.D. in Physics and Mathematics, Associate Professor of the Department of Applied Mathematics and Information Technologies in Education, Pitirim Sorokin Syktyvkar State University, e-mail: nkotelina@gmail.com
Startseva Evgeniya — Senior Lecturer, Department of Applied Mathematics and Information Technologies in Education, Pitirim Sorokin Syktyvkar State University,
e-mail:startseva2011@gmail.com
Yurkina Marina — Senior Lecturer, Department of Applied Mathematics and Information Technologies in Education, Pitirim Sorokin Syktyvkar State University, e-mail: yurkinamn@gmail.com
In the article, from the point of view of training a modern web developer, the process of acquiring the skill of parsing data is considered. Approximate model problems that should be considered in laboratory classes are given. The practical tasks of data parsing solved in the framework of scientic
research are described. The solution to the problem of obtaining SEO characteristics of sites is described in detail.
Keywords: parser, web scraping, web development, training.
References
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the number of gene interactions in the cell of a particular organism), Mathematical modeling and information technologies: IV all-Russian scientific conference with international participation (12-14 November 2020, Syktyvkar): collection of materials, Executive editor A. V. Yermolenko, Syktyvkar: Publishing house of SSU Pitirima Sorokina, 2020, pp. 42. - Babenko V., Golchevskiy Yu., Yermolenko A. The strategy of development of educational programs connected with IT in the regional educational institutions, DEFIN ’20: Proceedings of the III International Scientific and Practical Conference, 2020, No. 38, pp. 1-4.
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- Kotelina N. O., Matviyuchuk B. R., Solovyev I. A. Rekonstruktsiva grafov vzaimodeystviya genov i ikh prioritizatsiya na osnovanii dostupnvkh baz dannvkh (Reconstruction of gene interaction graphs and their prioritization based on available databases), Mathematical modeling and information technologies: IV all-Russian scientific conference with international participation (12-14 November 2020, Syktyvkar): collection of materials, Executive editor A. V. Yermolenko, Syktyvkar: Publishing house of SSU Pitirima Sorokina, 2020, pp. 44.
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For citation: Yermolenko А. V., Kotelina N. О., Startseva Е. N., Yurkina M. N. On the demand for data parsing training for web developers, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2021, 1 (38), pp. 56-69.
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VII. Odyniec W. Р. About four mathematicians – victims of the siege of Leningrad period
DOI: 10.34130/1992-2752_2021_1_70
Odyniec Vladimir — Doctor of Physical and Mathematical Sciences, Professor, Pitirim Sorokin Syktyvkar State University, e-mail: W.P.Odyniec@mail.ru
The life and work of four Leningrad based mathematicians born on the late 19th and early 20-th century is sketched. All of them A. G. Kolpakov (1902-1942), A. A. Herzfeld (1885-1941), N. N. Khudekov (1900-1942), and S. A. Janczewski (Yanchevskv) (1900-1941) perished during the blockade of Leningrad period.
Keywords: A. G. Kolpakov, A. A. Herzfeld, N. N. Khudekov, S. A. Janczewski (Yanchevsky), the double Fourier series, n-dimensional ordered sets, the solution of complex Fredholm equations.
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- Odyniec W. P. О 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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Glavnauka, 1928, 280 p. - Janczewski S. Oscillation theorem for the differential boundary value problem of the fourth order, Ann. of Math., 29, 1927-1928, pp. 521-542.
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