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Электронное научное издание Альманах Пространство и Время Т. 15. Вып. 1 • 2017
STUDIA STUDIOSORUM: УСПЕХИ МОЛОДЫХ ИССЛЕДОВАТЕЛЕЙ
Тематический выпуск в рамках года подготовки и проведения XIX Всемирного фестиваля молодежи и студентов в России
Electronic Scientific Edition Almanac Space and Time volume 15, issue 1
STUDIA STUDIOSORUM: Achievements of Young Researchers
Thematic Issue in the run-up to the year of preparation and holding the 19th World Festival of Youth and Students in Russia Elektronische wissenschaftliche Auflage Almanach 'Raum und Zeit' Band 15, Ausgb. 1.
STUDIA STUDIOSORUM: Fortschritte der Nachwuchsforscher
Thematische Ausgabe im Rahmen des Jahres der Vorbereitung und Durchführung des XIX. Weltfestivals der Jugend und Studenten in Russland
v/il ^ . а . . Achievements in Natural Sciences /
Успехи в науках о природе Fortschritte in de r Natuw issenschafte n
Dolzhenko S.V. Kadysheva A.M.
**
S. V. Dolzhenko
A.M. Kadysheva
Study of the Influence of Sulfuric Acid Concentration Changes on the Course of Belousov-Zhabotinsky Reaction
Stepan V. Dolzhenko, Lyceum student in grade 10, Lyceum no. 1535 (Sechenov Lyceum), Moscow ORCID ID https://orcid.org/0000-0002-8946-8018
E-mail: stepan-v-dolzhenko@j-spacetime.com; stepan5dol@gmail.com
Alexandra M. Kadysheva, Lyceum student in grade 10, Lyceum no. 1535 (Sechenov Lyceum), Moscow ORCID ID https://orcid.org/0000-0002-8656-4338
E-mail: alexandra-m-kadysheva@j-spacetime.com; 1451sasha@gmail.com
Further research of the Belousov-Zhabotinsky reaction analogues gives impetus to developing such modern scientific directions as synergetics, theory of dynamic systems and deterministic chaos. We considered one of the numerous oscillatory reactions, in which the Ce3+ / Ce4+ ions and citric acid are used. The main goal of our research was to study the behavior of the autocatalytic oscillatory reaction system in dependence of the change in sulfuric acid concentration and the temperature of the reaction mixture. We confirmed that stability of the oscillatory system depends on the acidity of the reaction mixture. The increasing of sulfuric acid amount is the result of acceleration of Ce3+ ions oxidation, and as a consequence rate acceleration of the oscillatory reaction. The activation effect on the studied reaction is exerted by a temperature increasing, but observed effect can be partially replaced by a mechanical action. For living organisms, such sensitivity of the system to external changes means its inability to use one. However, this does not mean that Belousov-Zhabotinsky reaction analogues will behave accordingly. The data obtained can serve as a basis for comparing of the studied reaction and other types of oscillatory reactions.
Keywords: autocatalytic oscillatory reaction; Belousov-Zhabotinsky reaction; acidity of reaction medium; cerium ions catalyzed reactions; cellular clock.
It is known that the «cellular clocks» helps our cells to control the most important time-conjugated processes, e.g. meiosis and to coordinate different parts of metabolism. This process is qualitatively described in [Winfree 1984]. The name of this phenomenon comes from circadian rhythmicity as its main property. Scientists [Purves 2004] are interested in the unicellular organisms that live in circadian rhythms, e.g. Gonyaulax polyedra, which saves its rhythmic lifestyle without any changes even after
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Dolzhenko S.V., Kadysheva A.M. Study of the Influence of Sulfuric Acid Concentration Changes on the Course of
Belousov-Zhabotinsky Reaction
replacing it's culture under the constant light. Such studies help us to find out that undergoing processes are controlled mostly by intercellular 'clock' that is likely to be non-equilibrium thermodynamic (autocatalytic oscillatory) reaction. The most common reaction of such a type is the Belousov-Zhabotinsky reaction. The Belousov-Zhabotinsky reaction is a class of chemical reactions occurring in an oscillatory mode, in which certain reaction parameters (color, concentration of components, temperature, etc.) change periodically, forming a complex spatial-temporal structure of the reaction medium [Zhabotinsky 1964; Motoike, Adamatzky 2005; Sirimungkala et al. 1999].
The 'cellular clock' is a phenomenon, which gives a great field for researching in modern science. Although basic discoveries have already been done, it is necessary to conduct more researches in such area of science to make a «great leap forward» in this direction. Despite the fact that great attention was paid to oscillating reactions, the statistical basis for them is extremely small and needs to be enlarged in the nearest future.
Belousov-Zhabotinsky reaction has become one of the most famous chemical reactions in modern science, nowadays a lot of scientists do researches connected with it. Analogues of Belousov-Zhabotinsky reaction were found in different chemical systems, for example organic self-propagating high-temperature synthesis. Discovery of this reaction has given a push to developing such parts of science as synergetics, theories of dynamic systems and deterministic chaos.
In this article we consider only one of the numerous oscillatory reactions in which the Ce3+ / Ce4+ ions and citric acid are used. The aim of this research is to study the behavior of the autocatalytic oscillatory reaction system in dependence of the change in the sulfuric acid concentration and the temperature of the reaction mixture.
History of Belousov-Zhabotinsky reactions
The priority in the discovery of the reaction belongs to Boris Belousov [Belousov 1959]. He carried out investigations of Krebs cycle in attempt to find its non-organic analog. As a result, after one of the experiments held in 1951, B. Belousov found an interesting reaction: the oxidation of citric acid with potassium bromate in an acidic medium in the presence of a Ce+3 ion as catalyst, he was discovered self-oscillations [Belousov 1959]. Further development of the research of this reaction occurred, when Professor Simon Shnol offered his researcher, future Lenin Award laureate Anatoly Zhabotinsky, to investigate the reaction mechanism. The Zhabotinsky's group carried out detailed studies of the reaction, including its different variants, and also compiled the first mathematical model. The main results were outlined in Zhabotinsky's monograph Concentration Oscillations [Zhabotinsky 1974].
Fig. 1. Boris P. Belousov (1893—1970), chemist and biophysicist, who discovered the Belousov-Zhabotinsky reaction in the early 1950s. Photo ca. 1956—1958
Fig. 2. Anatol M. Zhabotinsky (1938—2008),
biophysicist, who created a theory of the chemical clock known as Belousov-Zhabotinsky reaction in the 1960s. Photo of 1983
Fig. 3. Simon E. Shnol (born 1930), biophysicist, historian of Soviet science. Photo of 1980
The discovery of the reaction actually gave impetus to the development of such sections of modern science as synergetics, the theory of dynamical systems and deterministic chaos. The solutions of this scientific work will give ground for many future studies in various fields of science, such as biology (organic analogues of the reaction used by many living organ-
Dolzhenko S.V., Kadysheva A.M. Study of the Influence of Sulfuric acid Concentration Changes on the course of
Belousov-Zhabotinsky Reaction
Electronic Scientific Edition Almanac Space and Time volume 15, issue 1 'STUPIA STUPIOSORUM: Achievements of Young Researchers'
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Dolzhenko S.V., Kadysheva A.M. Study of the Influence of Sulfuric Acid Concentration Changes on the Course of
Belousov-Zhabotinsky Reaction
isms), physics (physical understanding of the interaction of molecules), and chemistry (further study of oscillatory systems) [Goodwin 1979; From the history of the discovery ... 2001].
The Simplest Scheme of the Reaction Mechanism
The first model of observed processes was proposed by A. Zhabotinsky. The cycle of reaction considered by him consists of two stages. The first stage (I) is the oxidation of trivalent cerium with bromate anion:
Ce3+ (BrO3-) ^ Ce4+ (I)
The second stage (II) is the reduction of tetravalent cerium with malonic acid:
Ce4+ + CHBr(COOH)2 ^ Ce3+ + Br- + other products (II)
The bromate reduction products formed in stage (I) are being edited to malonic acid. The resulting brominated derivatives of malonic acid are destroyed with the release of bromide-anion, which is a strong inhibitor of the reaction.
The scheme of the self-oscillatory reaction can be qualitatively described in the following way: let there be Ce4+ ions in the system, they catalyze the formation of Br- (stage II). If the concentration of Br- is sufficiently large, reaction (I) is completely blocked. When the concentration of Ce4 + ions decreases as a result of reaction (II) to the threshold value, the concentration of Br - decreases, thereby unblocking the reaction (I). Thus, the rate of the reaction (I) increases and Ce4+concentration increases too. When the upper threshold value Ce4+ is reached, the Br- concentration also reaches high values, and this again leads to the blocking of the reaction (I). And so on (Fig. 4).
Fig 4. Simplest Scheme of auto-catalytic oxidation reaction (RBr is bromo derivative of a reducing agent).
-Br" RBr
The overall equation is:
3CH2(COOH)2 + 4BrO3- ^ 4Br- + 9CO2 + 6H2O
Removal of the carbon dioxide from the system allows us to understand that this exchange reaction will not last forever, so alive cell must maintain the level of all parts of it to maintain such kinds of systems.
Experimental Findings
The original reaction made by B. Belousov was a departure point for us in this experiment. We found a primary recipe in [Zhang et al. 1993] and used it as a standard, changing only molar concentration value of sulfuric acid and temperature of a reaction mixture. As an organic reducing agent we used citric acid (C6HsO7). Five experiments were carried out including the original one (Figs. 5—7).
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Elektronische wissenschaftliche Auflage Almanach 'Raum und Zeit Bd. 15., Ausgb. 1. 'STUPIA STUPIOSORUM: Fortschritte der Nachwuchsforscher'
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Dolzhenko S.V., Kadysheva A.M. Study of the Influence of Sulfuric Acid Concentration Changes on the Course of
Belousov-Zhabotinsky Reaction
Fig. 5. Sampling preparation: weighting of cerium (III) sulfate (A) and potassium bromate (B).
Photo © S. Dolzhenko, A. Kadysheva
Original Reaction Recipe
2.00 g of C6H8O7 0.16 g of Ce2(SO4)3 0.20 g of KBrO3
2.0 ml of H2SO4 (1:3 by volume)
Distilled water is up to 10.0 ml; heating on an alcohol burner.
Observations: the beginning of the reaction is about 30 s. The oscillation duration is more than 30 min. The period of one oscillation is equal to 2 s.
Recipe of Set no. 1
2.00 g of C6H8O7 0.16 g of Ce2(SO4)3 0.20 g of KBrO3
10.0 ml of H2SO4 (1:3 by volume)
1. Without heating.
Observations: the beginning of the reaction is 15 min. Without mechanical influence the oscillations are practically invisible. The oscillation duration is less than 5 minutes. The period of one oscillation is equal to 30 seconds.
2. Heating on an alcohol burner.
Observations: the beginning of the reaction is 30 s. The oscillation duration is no more than 20 min. The period of one oscillation is equal to 1 — 1.5 s.
Recipe of Set no. 2
2.00 g of C6H8O7
0.16 g of Ce2(SO4)3
0.20 g of KBrO3
1.0 ml of H2SO4 (1:3)
Distilled water is up to 10.0 ml.
Electronic Scientific Edition Almanac Space and Time volume 15, issue 1 'STUPIA STUPIOSORUM: Achievements of Young Researchers'
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Dolzhenko S.V., Kadysheva A.M. Study of the Influence of Sulfuric Acid Concentration Changes on the Course of
Belousov-Zhabotinsky Reaction
1. Without heating.
Observations: the reaction does not proceed.
2. Heating on an alcohol burner.
Observations: the reaction does not proceed.
Fig. 6. Dissolution of reagents in sulfuric acid using of magnetic stirrer. Photo © S. Dolzhenko, A. Kadysheva
Fig. 7. The course of the Belousov-Zhabotinsky reaction. Photo © S. Dolzhenko, A. Kadysheva
The mechanism of the studied reaction can described using the following chemical reactions in the simplest manner:
(I) Ce3+ + BrO3- + 6H+ ^ Ce4+ + Br" + 3H2O (colorless ^ yellow)
(II) (HOOCCH2)2C(OH)COOH + 2Ce4+ ^ (HOOCCH2)2C(O) + 2Ce3+ + CO2 + 2H+ (yellow ^ colorless)
(III) Br- + BrO3- + 2H+ ^ HBrO + HBrO2
(IV) Br- + HBrO + H+ ^ Br2 + H2O (colorless ^ yellow)
(V) 3H+ + 3Br- + HBrO2 ^ 2Br2 + 2H2O (colorless ^ yellow)
(VI) (HOOCCH2)2C(O) + 5Br2 ^ C(O)(CHBr2)(CBr3) + 5Br- + 2CO2 + 5H+ (yellow ^ colorless)
Conclusions
Stability of the oscillatory system depends on the acidity of the reaction mixture. The increasing of the sulfuric acid amount is the result of the acceleration of Ce3+ ions oxidation, and as a consequence the rate acceleration of the oscillatory reaction. However, simultaneously the amount of the oxidized insoluble bromo derivatives is increased too, which leads to an accelerated decrease in the bromate ions concentration value. Therefore, the oscillations of the system are rapidly decayed.
If the amount of sulfuric acid is reducing, the acidity of the medium is not enough to oxidize a sufficient amount of Ce3+ ions. This is the reason of the decreasing of the bromate ions concentration level, which are the main autocatalysts of the studied reaction. The activation effect on the studied reaction is exerted by a temperature increasing, but observed effect can be partially replaced by a mechanical action.
Electronic Scientific Edition Almanac Space and Time volume 15, issue 1 'STUPIA STUPIOSORUM: Achievements of Young Researchers'
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Elektronische wissenschaftliche Auflage Almanach 'Raum und Zeit Bd.. 15., Ausgb. 1. 'STUPIA STUPIOSORUM: Fortschritte der Nachwuchsforscher'
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Dolzhenko S.V., Kadysheva A.M. Study of the Influence of Sulfuric Acid Concentration Changes on the Course of
Belousov-Zhabotinsky Reaction
For living organisms such sensitivity of the system to external changes means its inability to use one. However, this does not mean that Belousov-Zhabotinsky reaction analogues will behave accordingly. The data obtained can serve as a basis for comparing of the reaction studied and other oscillatory reactions.
Acknowledgements. We would like to thank our research advisors Prof. Anzhelika N. Fetisova, Dr.Sc. (Pharm), Sechenov First Moscow State Medicine University, and lyceum teacher Victor S. Malinsky, Ph.D. Without their help in course of our laboratory researches and work on the text, this article would not have been written.
References:
1. Belousov B.P. "Periodically Acting Reaction and Its Mechanism." Collected Abstracts on Radiation Medicine. Mos-
cow: Medgiz Publishre, 1958, pp. 145 — 147. (In Russian).
2. Field R.J., Foersterling H.D. "On the Oxybromine Chemistry Rate Constants with Cerium Ions in the Field —
Koeroes-Noyes Mechanism of the Belousov-Zhabotinskii Reaction: The Equilibrium HBrO2 + BrO3- + H+ 2BrO2* +H2O." The Journal of Physical Chemistry 90.21 (1986): 5400 —5407.
3. "From the History of Discovery and Study of Self-oscillatory Processes in Chemical Systems: The 50th Anniver-
sary of Discovery of Belousov-Zhabotinsky Reaction." Information Project InfoSci.Narod.Ru. N.p., 16 June 2001. Web. <http://infosci.narod.ru/chemistry/010616-1p.html>. (In Russian).
4. Goodwin B.C. Analytical Physiology of Cells and Developing Organisms. London, New York and San Francisco: Ac-
ademic Press, 1976. 249 p.
5. Lister T. Classic Chemistry Demonstrations. London: Education Division, Royal Society of Chemistry, 1995. 284 p.
6. Motoike I., Adamatzky A. "Three-Valued Logic Gates in Reaction - Diffusion Excitable Media." Chaos, Solitons &
Fractals 24 (2005): 107—114.
7. Palmer J. "Chemical Computer That Mimics Neurons To Be Created." BBC Science News. BBC, 11 Jan. 2010. Web.
<http://news.bbc.co.uk/ 2/hi/science/nature/8452196.stm>.
8. Purves D.E., Augustine G.J., Fitzpatrick D.E., Katz L.C. Neuroscience. Sunderland, MA: Sinauer Associates,
2004. 773 p.
9. Sirimungkala A., Forsterling H.-D., Dlask V., Field R. "Bromination Reactions Important in the Mechanism of the
Belousov-Zhabotinsky System". The Journal of Physical Chemistry A 103.8 (1999): 1038 — 1043.
10. Winfree A.T. "The Prehistory of the Belousov—Zhabotinsky Oscillator". Journal of Chemical Education 61.8 (1984):
661-663.
11. Zaikin A.N., Zhabotinsky A.M. "Concentration Wave Propagation in Two-dimensional Liquid-Phase Self-
oscillating System." Nature 225.5232 (1970): 535 — 537.
12. Zhang D., Gyorgyi L., Peltier W.R. "Deterministic Chaos in the Belousov-Zhabotinsky Reaction: Experiments and
Simulations." Chaos: An Interdisciplinary Journal of Nonlinear Science 3.4 (1993): 723—745.
13. Zhabotinsky A.M. "Periodical Process of Oxidation of Malonic Acid Solution." Biophysics 9.3 (1964): 306—311. (In
Russian).
14. Zhabotinsky A.M. Self-oscillations by Concentration. Moscow: Nauka Publisher, 1974. 179 p. (In Russian).
Cite MLA 7:
Dolzhenko, S. V., and A. M. Kadysheva. "Study of the Influence of Sulfuric Acid Concentration Changes on the Course of Belousov-Zhabotinsky Reaction." Electronic Scientific Edition Almanac Space and Time 15.1 (Studia Studiosorum: Achievements of Young Researchers) (2017). Web. <2227-9490e-aprovr_e-ast15-1.2017.16>.
Dolzhenko S.V., Kadysheva A.M. Study of the Influence of Sulfuric acid Concentration Changes on the course of
Belousov-Zhabotinsky Reaction
Electronic Scientific Edition Almanac Space and Time volume 15, issue 1 'STUPIA STUPIOSORUM: Achievements of Young Researchers'
Achievements in Natural Sciences
Elektronische wissenschaftliche Auflage Almanach 'Raum und Zeit Bd. 15., Ausgb. 1 'STUPIA STUPIOSORUM: Fortschritte der Nachwuchsforscher'
Fortschritte in der Naturwissenschaften
Dolzhenko S.V., Kadysheva A.M. Study of the Influence of Sulfuric Acid Concentration Changes on the Course of
Belousov-Zhabotinsky Reaction
УДК 544.431.8
ИЗУЧЕНИЕ ВЛИЯНИЯ ИЗМЕНЕНИЯ КОНЦЕНТРАЦИИ СЕРНОЙ КИСЛОТЫ НА ХОД РЕАКЦИИ БЕЛОУСОВА-ЖАБОТИНСКОГО
Долженко Степан Владимирович, ученик 10 класса лицея № 1535 им. И.М. Сеченова (Сеченовский Лицей), Москва
ORCID ID https://orcid.org/0000-0002-8946-8018
E-mail: stepan-v-dolzhenko@j-spacetime.com; stepan5dol@gmail.com
Кадышева Александра Михайловна, ученица 10 класса лицея № 1535 им. И.М. Сеченова (Сеченовский Лицей), Москва
ORCID ID https://orcid.org/0000-0002-8656-4338
E-mail: alexandra-m-kadysheva@j-spacetime.com; 1451sasha@gmail.com
Исследование аналогов реакций Белоусова -Жаботинского дает импульс развитию таких направлений современной науки, как синергетика, теория динамических систем и детерминированного хаоса. В данной работе нами изучена одна из многочисленных колебательных реакций, для проведения которой используют ионы Ce3+ / Ce4+ и лимонную кислоту. Основной целью исследования было изучение поведения автокаталитической колебательной реакционной системы в зависимости от изменения концентрации серной кислоты и температуры реакционной смеси. В ходе эксперимента мы подтвердили, что устойчивость колебательной системы зависит от кислотности реакционной смеси. Увеличение количества серной кислоты является результатом ускорения окисления ионов Ce3+ и, как следствие, ускорения скорости колебательной реакции. Активирующий эффект на изученную реакцию оказывает повышение температуры, однако наблюдаемый эффект может быть частично заменен механическим воздействием на реакционную систему. Для живых организмов такая чувствительность системы к внешним изменениям означает неспособность ее использования. Однако это не означает, что аналоги реакции Белоусова-Жаботинского будут вести себя соответствующим образом. Полученные данные могут служить основой для сравнения исследуемой реакции и других видов колебательных реакций.
Ключевые слова: автокаталитическая колебательная реакция; реакция Белоусова-Жаботинского; кислотность реакционной среды; церий-катализируемые реакции; клеточные часы.
ЛИТЕРАТУРА
1. Белоусов Б.П. Периодически действующая реакция и её механизм // Сборник рефератов по радиоизо-
топной медицине. М.: Медгиз, 1958. С. 145—147.
2. Гудвин Б. Аналитическая физиология клеток и развивающихся организмов / Под ред. А.М. Жаботинского.
М.: Мир, 1979. 287 с.
3. Жаботинский А.М. Концентрационные автоколебания. М.: Наука, 1974. 179 с.
4. Жаботинский А.М. Периодический ход окисления малоновой кислоты в растворе (исследование кинети-
ки реакции Белоусова) / / Биофизика. 1964. Т. 9. Вып. 3. С. 306 — 311.
5. Из истории открытия и изучения автоколебательных процессов в химических системах: к 50-летию откры-
тия реакции Белоусова-Жаботинского [Электронный ресурс] / / InfoSci.Narod.Ru. Информационный
проект. 2001. 16 июня. Режим доступа: http://infosci.narod.ru/ chemistry/010616-1p.html.
6. Field R.J., Foersterling H.D. "On the Oxybromine Chemistry Rate Constants with Cerium Ions in the Field —
Koeroes-Noyes Mechanism of the Belousov-Zhabotinskii Reaction: The Equilibrium HBrO2 + BrO3- + H+
2BrO2* +H2O." The Journal of Physical Chemistry 90.21 (1986): 5400 —5407.
7. Goodwin B.C. Analytical Physiology of Cells and Developing Organisms. London, New York and San Francisco: Ac-
ademic Press, 1976. 249 p.
8. Lister T. Classic Chemistry Demonstrations. London: Education Division, Royal Society of Chemistry, 1995. 284 p.
Dolzhenko S.V., Kadysheva A.M. Study of the Influence of Sulfuric Acid Concentration Changes on the Course of
Belousov-Zhabotinsky Reaction
Electronic Scientific Edition Almanac Space and Time volume 15, issue 1 'STUPIA STUPIOSORUM: Achievements of Young Researchers'
Achievements in Natural Sciences
Elektronische wissenschaftliche Auflage Almanach 'Raum und Zeit Bd.. 15., Ausgb. 1. 'STUPIA STUPIOSORUM: Fortschritte der Nachwuchsforscher'
Fortschritte in der Naturwissenschaften
Dolzhenko S.V., Kadysheva A.M. Study of the Influence of Sulfuric Acid Concentration Changes on the Course of
Belousov-Zhabotinsky Reaction
9. Motoike I., Adamatzky A. "Three-Valued Logic Gates in Reaction - Diffusion Excitable Media." Chaos, Solitons &
Fractals 24 (2005): 107-114.
10. Palmer J. "Chemical Computer That Mimics Neurons To Be Created." BBC Science News. BBC, 11 Jan. 2010. Web.
<http://news.bbc.co.uk/ 2/hi/science/nature/8452196.stm>.
11. Purves D.E., Augustine G.J., Fitzpatrick D.E., Katz L.C. Neuroscience. Sunderland, MA: Sinauer Associates,
2004. 773 p.
12. Sirimungkala A., Försterling H.-D., Dlask V., Field R. "Bromination Reactions Important in the Mechanism of the
Belousov-Zhabotinsky System". The Journal of Physical Chemistry A 103.8 (1999): 1038 — 1043.
13. Winfree A.T. "The Prehistory of the Belousov—Zhabotinsky Oscillator". Journal of Chemical Education 61.8 (1984):
661-663.
14. Zaikin A.N., Zhabotinsky A.M. "Concentration Wave Propagation in Two-dimensional Liquid-Phase Self-
oscillating System." Nature 225.5232 (1970): 535 — 537.
15. Zhang D., Györgyi L., Peltier W.R. "Deterministic Chaos in the Belousov-Zhabotinsky Reaction: Experiments and
Simulations." Chaos: An Interdisciplinary Journal of Nonlinear Science 3.4 (1993): 723—745.
Цитирование по ГОСТ Р 7.0.11—2011:
Dolzhenko, S. V., Kadysheva, А. М. Study of the Influence of Sulfuric Acid Concentration Changes on the Course of Belousov-Zhabotinsky Reaction [= Изучение влияния изменения концентрации серной кислоты на ход реакции Бело-усова-Жаботинского] [Электронный ресурс] / С.В. Долженко, А.М. Кадышева // Электронное научное издание Альманах Пространство и Время. — 2017. — Т. 15. — Вып. 1: Studia studiosorum: успехи молодых исследователей. — Стационарный сетевой адрес: 2227-9490e-aprovr_e-ast15-1.2017.16.
