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Section: Technology
Academician Khristianovich: Scientist, Engineer, Personality

Academician Khristianovich: Scientist, Engineer, Personality

November 9, 2008 was the centenary of the birth of S. A. Khristianovich, an outstanding Russian scientist

Khristianovich’s achievements were widely recognized during his lifetime: he was awarded with the highest awards of the Soviet Union, including the title of the Hero of Socialist Labor, six Orders of Lenin, three Stalin Prizes, three State Prizes, and Zhukovskii Prize. But the most valuable award for the scientist was the recognition of people whom he met and worked with during his long and fruitful life. His contemporaries called him a genius, a great engineer, and a legendary person. Today, his followers and the disciples of his disciples still call him that. The brief official record of service of Academician Sergey Alekseevich Khristianovich occupies quite a large space in the Large Soviet Encyclopedia. For a person who casts a glance at his biography, the scope of Khristianovich’s scientific views and the range of problems he solved seem to be incredible. The life of Academician Khristianovich, who achieved amazing results in all spheres of his activities, disproves the common opinion that there is no place for a universal genius in the era of science and technology.

The tribute paid to the great scientist is the books published by the Institute of Theoretical and Applied Mechanics, SB RAS (which was founded by S. A. Khristianovich in Novosibirsk), and by the Central Aerohydrodynamics Institute (TsAGI) in Moscow, where Khristianovich worked in supersonic aviation for more than 15 years. These collective memoirs comprise the reminiscences of many outstanding scientists, his former students and colleagues, and his relatives and friends. Each witness of those times has his own interpretation of events that happened many years ago, but the direct and emotional evidence of his contemporaries allows us to gain some historically correct idea about this person who has already become a legend. Owing to the tremendous efforts made by the authors and compilers of the anniversary books, we can get our readers acquainted with the life and creative activities of the scientist, using excerpts of the published reminiscences, comments, and autobiography of the “Greatest Mechanician of the 20th Century.”

About myself, science, and scientists*

He was extremely happy in his childhood: classical in-house education in a nobleman’s family in the Orel province, a loving household, his father a lawyer…

The further life of this typical representative of the Russian intelligentsia was clear: a classical school, university… The revolution of 1917 interfered in his brilliant future, as in the future of many people of the same age and social origin. It seemed there was no way back: the 12-year-old homeless orphan was selling cigarettes on the streets of the city of Rostov. However, as Khristianovich himself recalled, then he was offered a few fortunate opportunities: meeting his relatives and his future tutor, going to a Soviet school and then to the university at 16, and, finding himself, “by chance”, at the department of physics and mathematics. These chances, however, could not conceal an outstanding personality who constructed his life against adverse circumstances

…Actually, I did not get any systematic education before that. When we lived in the country, I had a teacher and a nursery governess. I studied French and German. I failed the exams to a classical school. After 1918, I took some lessons of Russian and arithmetic from a charming elderly lady…

…I do not remember whether it was a technical school or a naval academy… I studied there for only one autumn semester. I did not know anything. I do not even understand how I managed to enter that school. Then I received a letter from my aunt, who lived in Leningrad; she invited me to come for my holidays; being a student, I had the right to have a free ticket. I went there, got ill with malaria, and stayed in Leningrad…

In spring, I was enrolled in the fifth grade of Soviet school No. 16… I graduated from school rather quickly because I did two years in one. Late in autumn, when all the students had already been enrolled in the university, I was accepted as a student of the anthropology branch of the geology department, because there were no other vacancies. Soon, however, I exchanged the departments with one astronomer and became a student of the physics and mathematics department, mathematics branch.

I should say that it was a random choice. I was more interested in biology. If someone had suggested to me that I study a natural science (physics, chemistry, or biology), I would have never become a mathematician.

…The Hydrology Institute was responsible for a very important task: making an inventory of the water resources of the Soviet Union, the flow rates of rivers, and the underground waters; this was not only descriptive and geographical work. The institute employed outstanding chemists and biologists. I started to work in the hydraulic-mathematical department. There, too, were many gifted people who taught me to apply mathematics to vitally important problems.

…I was assigned the task of dealing with the project of the cascade of hydrological stations on the Volga River. Already at that time we were thinking about that and designing projects for these stations. We thought about what would happen to the sturgeons if dams were constructed and how the flow rate could be controlled to avoid any harm. This problem was associated with unsteady motion. If the dam gate is opened too wide or if the dam does not function for some reason, the huge mass of water previously sustained by the dam could flood the cities located further downstream.

As I was a mathematician, I not only learned the engineering aspects but also started to develop calculation methods. I began with studying the problems related to the integration of hyperbolic nonlinear differential equations. I should say that at that time it was an entirely new problem which was considered by prominent scientists who studied wave propagation in gas and air motion at supersonic velocities. Mathematically, however, these problems turned out to be similar, and I managed to explore several issues…

“S. A. Khristianovich has published several papers on the hydraulics of open riverbeds, where he solved the most important engineering problems in this field. Discarding the old calculation procedures, which were mechanically borrowed from other fields of applied mathematics, he has constructed a new calculation technique and solved problems of long waves passing in one direction, of such waves being reflected from various interfaces, of waves generated by target destruction, of formation of the so-called strong discontinuities, or roll-up of waves, of waves in a tunnel, etc. 
A distinctive feature of his methods is simplicity and elegance, let alone their accuracy, which exceeds everything achieved previously. Owing to these advantages, his methods have been promptly accepted by the engineering community. It was his methods that were used for calculations when designing Neva III, Angara, Irtysh, Kuibyshev, Svir III, and other hydropower stations”. (S. Sobolev, Pravda, 29.08.1943) 
Cited from: Sergey Alekseevich Khristianovich. Outstanding Mechanician of the 20th Century, 2008

…Though I was fairly successful in Leningrad, i.e. I earned quite a lot and in fact was a promising scientist, I abandoned everything, moved to Moscow, and started to learn again. I combined learning with working at the Institute of Mathematics.

…The years I spent at the Institute of Mathematics were extremely fruitful. I managed to do quite a lot, more than I ever managed to do in such a short period in subsequent years. I studied the theory of plasticity, nonlinear filtration of underground waters, and then flight mechanics at high velocities. Therefore, in 1937, I joined the TsAGI seminar and worked there for two days a week studying the fundamentals of gas dynamics and aircraft aerodynamics.

In 1937, I completed my doctorate and defended two dissertations simultaneously… I felt, however, that I was not a real mathematician; though I had some ideas and some achievements, I was not a mathematically- minded person. I was enchanted by physical and engineering problems; I was happy to be involved in mechanical engineering and to perform experiments. I did not have enough memory or diligence for permanent training of the apparatus required from a mathematician; I did not like solitude as much as the mathematician does. That is why I did not become a mathematician.

In 1939, I was elected a corresponding member of the Academy of Sciences (Engineering Department), actually, for my works on hydrology, theoretical hydrology.” This is a simple explanation for quite a rare fact in the scientific community: he was elected a member of the Academy of Sciences at the age of 30. Many people would consider it the top of their career, while for Khristianovich it was only a small “station” at the beginning of a long way. By that time, S. A. Khristianovich, being both a doctor of mathematics and a doctor of technical sciences, had clearly understood that his true mission was not pure mathematics. He was attracted by experiments, by “live” facilities, which could be touched, and, last but not least, by the romance of high velocities… The war was at the door, and a lot of hopes were placed in aviation: the new, reformed TsAGI was waiting for the young corresponding member of the Academy of Sciences

…I was very young then. Yet, General I. F. Petrov, Head of TsAGI, offered me the position of leader and head of laboratory No. 6 at TsAGI, where a new wind tunnel was under construction. This was a high-velocity transonic wind tunnel with a variable-density flow, which was a unique facility not only in the Soviet Union but also in the whole world.

“It was he [S. A. Khristianovich] who proposed and took all responsibility for the perforation of the only wind tunnel in the country which could be used for aircraft testing. The perforation of the test-section walls in transonic tunnels made it possible to overcome the sonic barrier. Khristianovich’s authority allowed him to persuade Andrey Nikolaevich Tupolev, who had many objections to perforation at the beginning”. (Prof. G. Barenblatt, Berkley University, California, USA). 
Cited from: Sergey Alekseevich Khristianovich. Outstanding Mechanician of the 20th Century, 2008

…In 1940, I published my first paper in TsAGI proceedings. The work was based on the method developed by Sergey Alekseevich Chaplygin and offered a solution to the problem of the flow around an airfoil at high velocities approaching the velocity of sound. This was my first activity in aviation.

…By the beginning of World War II, we had created very good experimental facilities, which were not available in Germany… It was in these wind tunnels and in the Strength Laboratory that we actually finalized the development of our airplanes, thus arming our airforce.

Certainly, it was difficult to invent something completely new during the war: it takes time to go from scientific ideas, from the theory, from lab equipment to something real. …People worked day and night, but the basic material was already available. During the war, however, the researchers were developing ideas for new, jet-driven aviation…Some people thought it was strange and some called it a crime. Here, however, we should mention the keen insight of the government, who understood that they had to think about the time after the war. It was necessary to develop the scientific basis for jet-driven aviation, the aviation of sonic and supersonic velocities. It could seem that we were involved in the research that was not directly related to the military activities of those days. In any case, I mean the laboratory I headed.

“A large list of brilliant results obtained by S. A. Khristianovich refers to gas dynamics. He managed to solve extremely important fundamental problems in this field of science.The character of phenomena that occur in a gas flow around a certain body, for instance, a wing, an aircraft fuselage, or a propeller vane, depends on the velocity of the incoming flow with respect to the body. For velocities much smaller than the velocity of sound propagation in the gas, the flow is very similar to that of an incompressible fluid, e.g., water. The problem of such a flow can be considered to be solved. 
If the body has a relative velocity close to the speed of sound, the gas flow acquires a different character. If the relative velocity of the flow and the body is greater than the speed of sound, the phenomenon becomes drastically different. In the interval between the two cases, the flow occurs in the critical regime, with some part of the gas moving at a velocity greater than the speed of sound, and with the other part of the gas moving at a velocity smaller than the speed of sound. 
Researchers abroad followed the way of simplified interpretation of phenomena that occurred in a high-velocity gas flow around the body. Usually, their calculations ignored the thickness of the examined body, for instance, the thickness of the wing or the propeller vane. 
The first researcher who developed essentially new methods and started to study the phenomena without rough simplifications was S. A. Chaplygin, who created an outstanding theory of gas jets for subsonic velocities. Nevertheless, it was S. A. Khristianovich who was able to solve the global problem of the gas flow around a body at high subsonic velocities for the most important cases: the flow around a wing and around a body of revolution. 
As in hydraulics of open riverbeds, this substantial success was achieved by S. A. Khristianovich by using an elegant new mathematical apparatus that described the motion of such a gas. 
<…> The result of these activities was a method for calculating the drag force produced by the air flow on the wing, which determines the velocity that can be reached by a particular aircraft. Excellent agreement with experiments completely confirmed the validity of S. A. Khristianovich’s theory.”
(S. Sobolev, Pravda, 29.08.1943)

…In 1943, our large wind tunnel was put into full-time operation. When we started to test it, we found many unexpected phenomena that we had not even suspected to exist. A new theory had to be developed, and a lot had to be changed in the equipment in order to obtain the necessary results. Yet, this wind tunnel provided reliable results up to velocities approximately equal to 0.8 of the velocity of sound; the phenomena that happened closer to the velocity of sound were still a mystery.

There were many stories about this. There were rumors about the sound barrier where aircraft crashed… I think one of the most important achievements of TsAGI in those years was finding methods for creating a special wind tunnel for transonic tests, as they say now. It is worth noting that nobody in the world was able to do it.

…The wind tunnel was constructed, and we obtained the first large-scale test results in 1947. …Now, if we look at the sky, we will see airplanes of swept, triangular, and some other unusual shapes. These shapes are dictated by the laws of transonic and supersonic aerodynamics which were established owing to the creation of new facilities and to the upgrading of old equipment on the basis of this large-scale test. So it became possible to test aircraft models, even rather large models, at transonic velocities. Actually, these activities formed the basis for transonic aviation.

“Sergey Alekseevich was not a very sociable person, but he had some friends, though business relations were not readily converted into friendships. Most often, his friends were people possessing the same features he had: creativity and a sense of humor.
It happened so that S. A. Khristianovich and two of his friends, Sergey L’vovich Sobolev, who had been his friend since the time they were students, and Mikhail Alekseevich Lavrent’ev, with whom he had worked together at the Institute of Mathematics, were awarded with country houses (dachas) in the village of Mozzhinka in the 1950s. …The dachas were being constructed by captive Germans, who worked honestly… When the Germans saw Sergey Alekseevich going along the street, they called him “Fuhrer” – his gait, his eyes, everything about him betrayed a strong will”. (T. Atkarskaya)
“…The task for S. A. Khristianovich, the first deputy of the chairman of the Presidium of the Siberian Branch of the Russian Academy of Sciences, was extremely important and difficult. He had to supervise the construction of Academgorodok. The challenge was to quickly construct a town from scratch, for 35—40 thousand people, with good living and working conditions. The work had to be of good quality, and the environment preserved to the maximum possible extent.
… Being an active and committed person, Sergey Alekseevich Khristianovich started to do the task with responsibility and enthusiasm”. (A. P. Filatov, First Secretary of the Committee of the Communist Party
of the Novosibirsk Oblast in 1966—1973).
Cited from: Sergey Alekseevich Khristianovich. Outstanding Mechanician of the 20th Century, 2008

…I am grateful to my destiny. I have always been lucky to work in excellent teams. TsAGI … was an exceptional institution. There were outstanding people and interesting problems there. I learned a lot there. I was not an engineer before that, actually; I became an engineer at TsAGI. I learned many things in the field of design and construction, I participated in real missions, and I learned to apply academic knowledge to solving problems important for practice and to reaching the final product at the end.

A new stage in his life started when he was invited to take the position of Academic Secretary of the Engineering Department of the Academy of Sciences.

This nomination was not a sinecure, but his active and well-organized intellect of a thinker and engineer could not but wish such a task. Somehow, by an exceptional intuition, he managed to find the most important aspects and problems, whether in the theory of fracture of a gas reservoir or in gas-dynamic problems of a nuclear explosion. Wider horizons required a new (nation-wide) measure of responsibility… There is war again, though this time it is cold war. S. A. Khristianovich participated in all tests of Soviet nuclear weapons, and nobody understood the destructive capability and the large scale of action of the new weapons better than he did…The idea to spread Russia’s research potential over the vast and rich lands to the east of the Urals was, for S. A. Khristianovich, a typical engineering solution, precise, simple, and elegant

…There were not many people in the Presidium at that time. We were only thirteen. There was a lot of work to do: we had to work at the Academy of Sciences proper and to establish relations between the Academy of Sciences and industry. In the course of construction and in learning to use the new equipment, we encountered numerous problems which had to be properly solved. It was the Academy of Sciences that was to deal with all the questions.

“He was a talented scientist who quickly caught the essence of things even if the field of science was not familiar to him. It took him a short time to evaluate a new idea and to understand the essence. As he understood the problem profoundly, he was able to see all details and aspects, and he always tried to obtain a guaranteed result”. (Prof. V. K. Baev, SB RAS).
Cited from: Sergey Alekseevich Khristianovich. Outstanding Mechanician of the 20th Century, 2008

…I established relations with different branches of industry; I met a lot of people and got acquainted with methods and ideas developed in the fields new to me.

In 1957, it became obvious that it was necessary to develop our eastern regions, i.e. to conquer the rich lands of Siberia. The main academic forces were focused in Moscow, Leningrad, and Kiev.

There were no scientists in the depth of the country. Siberia and the Urals were little known areas of Russia, with vast resources and only a few teams of researchers.

“He was a person with an extremely powerful charisma. He was always surrounded by young people. He was a poor lecturer, but, if you knewthe subject, you were delighted to communicate with him. He was a fountain of ideas.” (Chief researcher A. F. Latypov, the ITAM, SB RAS).
Cited from: Sergey Alekseevich Khristianovich. Outstanding Mechanician of the 20th Century, 2008

…It was decided to start with academic science as a basis. Mikhail Alekseevich Lavrent’ev and I published an article in the Pravda newspaper and proposed an idea of creating the Siberian Branch of the USSR Academy of Sciences. Even before this publication, however, the global principles of creating a large new research center had been discussed and established. As the Siberian Branch of the USSR Academy of Sciences was created, I moved to Novosibirsk. From 1957 till 1962, I was the first deputy of the chairman of the Siberian Branch.

My responsibilities included commissioning the design and construction of Academgorodok. I was also the Director of the Institute of Theoretical and Applied Mechanics (ITAM), which was under construction at that time. It is a well-equipped institute, which continues working at present.

After 1962, I was no longer the deputy chairman of the Siberian Branch. I worked as the ITAM Director until 1965, when I had to leave Novosibirsk because of my health. The Siberian climate was absolutely unbearable for me, strange as it may seem. Though I liked living there, I was running a fever 24 hours a day, and the doctors advised me to leave Siberia.

Again, nothing unnecessary, nothing personal, only: “The Siberian climate was absolutely unbearable for me…” The main reason, however, was a conflict with his long-standing friend and colleague rather than the acute condition of tuberculosis. As evidenced by his wife, however, Khristianovich never said anything bad about M. A. Lavrent’ev or V. V. Struminskii (Khristianovich’s successor), who canceled several research topics of the institute and dismantled the working test facilities whose construction had required a lot of efforts. Thus, Moscow was waiting for him to come back. He was leaving behind the white buildings of Siberian institutes and the ITAM, which had become a home for him; Novosibirsk University, which was modeled after the Moscow Institute of Physics and Technology, where Khristianovich had been the first rector; the sand beaches of the Ob Lake raised on Khristianovich’s initiative for recreation of scientists and workers… What did he feel when he left his favorite brainchild? The work he had done here would be more than enough for several outstanding people. His career continued for another 35 years stuffed with new ideas and projects

…I started working at the large and very interesting Institute of the Committee of Standards, located close to Moscow, in the village of Mendeleevo. It was called the Institute of Physicotechnical and Radiotechnical Measurements. Its task was to create standards and standard instruments… At the time when I moved to Moscow in 1965, the institute was rather small; prominent people had left it. But I recall my work among those lively and interesting people with great pleasure. I was engaged in various issues of measurement instrumentation and physical problems.

“Undoubtedly, “talent” is an alarming and binding word, let alone the word “genius,” which implies the highest degree of talent and natural gifts. In the conference hall of the Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences, the portrait of its founder, Sergey Alekseevich Khristianovich, occupies a well-deserved place among the portraits of great mechanical engineers: M. V. Lomonosov, O. Reynolds, N. E. Zhukovskii, S. A. Chaplygin, T. Karman, and L. Prandtl. In many other research centers where Academician Khristianovich worked, he is still called a genius. Usually, the appraisal of even most prominent scientists becomes less intense, and enthusiastic words become more restrained. This does not happen to Khristianovich’s reputation. People still admire the scale of his personality, the depth of his mind, his scientific insight, and his national commitment of a true patriot.
Those who were lucky to learn and understand Khristianovich’s achievements in science and engineering will agree that he and his ideas can be considered part of a worldwide heritage for many years. Being a universal scientist, mechanical engineer, mathematician, hydrologist, specialist in power engineering, metrologist, and ecologist, he considered his engineering talent to be the most valuable advantage and reached extremely important results in each aspect of his activities: in high-velocity aviation and rocket engineering, in the developing and testing of nuclear weapons, in the theory of plasticity and theory of filtration, in mining, extraction and transportation of coal, oil and gas, in protection against floods and the problem of water resources, in developing high-efficiency power engineering, in upgrading the methods of physical and mathematical modeling of natural, hydrophysical, and atmospheric phenomena, in improving the metrological level of scientific research and engineering projects, and in providing the high quality of domestic production.
Being a volunteer to accept personal responsibility for many extremely important projects, recommendations, and decisions, which were often taken at the governmental level, Sergey Alekseevich was a generator of revolutionary scientific ideas, further developed by his numerous disciples and successors. At the same time, he was able to support the most promising ideas proposed by other people.
<…> Sergey Alekseevich Khristianovich was a constructor both in the literal and figurative sense of this word. He constructed the best laboratories, institutes, and research centers of the country. He actively participated in the forming and developing of the educational system of the Moscow Institute of Physics and Technology, which is now famous all over the world. Being a brilliant teacher and tutor, he made his best students and best production engineers head the most important and promising directions in mechanics and its engineering applications.
<…> Khristianovich was not only a legendary person, but also an openhearted, strict but amiable, reliable and kind man. He grew up and was formed as a scientist among the most outstanding people of his time, but he never put on airs. He retained the ability and talent to feel and understand any person. Those were the features of his character that originated, to a large extent, from his orphanage.”
(Doctor of technical sciences G. N. Amir’yants, TsAGI, Moscow) **

…I was asked to perform some voluntary activities as the chairman of the Interdepartmental Quality Control Board … This board within the Committee of Standards examined the products as well as controlled the implementation of new methods into the quality control system.

We all know how important the quality of products is and, hence, their competitiveness at the international market. When we buy shoes, we hope they are good shoes. For a turbine to operate properly, all its elements should be at the top level. Industrial engineering is an interrelated branch in today’s world. Each object produced is the result of tremendous efforts of predecessors.

…It was different thirty years ago. At that time, it seemed that the best manufacturers were talented handicraftsmen. Ladies preferred to order shoes from a good shoemaker. The same was true of clothes. Later on, customers started to prefer buying ready-made things. They were more reliable, especially various machines. A special field, industrial engineering, became necessary in order to improve the product quality and to replace some products with newer and better ones.

Naturally, many of these issues were raised by military aviation, where rapid introduction of new airplanes and new equipment was of vital importance. Therefore, aviation was the first branch of industry to develop the principles of such a system: organization of production, testing, and interaction between science and design (or chains with feedback). This happened in the first turn in the Soviet Union and in the United States.

…When I worked at TsAGI, I learned to create such industrial chains. I understood the system very well, I knew how to use it, and I became so much used to this system that I was surprised to learn that it was not applied in other branches of industry.

…The times were severe, and I had to sign papers concerning the maiden flights of all new airplanes. Yet, my hand never trembled. I was always sure that the airplane would fly and nothing would happen to it, because usually the process of designing was monitored, then there were tests, calculations, and norms to follow.

…The evolution of models progressed step by step; owing to the system developed, we actually overcame the sound barrier almost without human victims or catastrophes, we can not say this about aviation in other countries, whose development cost many human lives and more time.

…I regret so much that I am old enough and can not apply all my efforts to this cause which I believe to be the most important in our country.

He had a happy life. It was happy from the viewpoint of an ordinary Soviet citizen: he got a good education despite his orphanage; he was not imprisoned in the notorious 1937, like many of his colleagues; he was admired by ladies (he was married four times), though his name had never been dragged through the mud; he lived a long life having high ranks, money, and awards… But people like Khristianovich have different measures of happiness. And we can say that he lived up to his high standards. Being a prominent scientist, an engineer by the grace of God, a government-scale constructor and founder of scientific schools, he could rightfully say at the end of his life that he had constructed a House, planted a Tree, and brought up Disciples. Sergey Alekseevich Khristianovich passed away on April 28, 2000. The obituary notice at the Institute for Problems in Mechanics of the Russian Academy of Sciences (which was the last place of his work) started with the words, “A genius has died” and ended with, “He will stay in our hearts forever.”

In 2005, the Institute of Theoretical and Applied Mechanics, SB RAS, was awarded the name of its founder. Professor G. Barenblatt, a famous scientist and a former student of Khristianovich, commented on this: “God is with us. Finally we see the real appraisal of Sergey Alekseevich Khristianovich, and I am happy that I have lived to see this day. I was lucky to know him closely, and I was happy to see the flight of his imagination, to absorb his creative impetus, and to feel the influence of his brilliant personality… Sergey Alekseevich is now in the realm of Great Russian Mecanicians forever… God bless his memory!”

The Editorial Board is grateful to A. M. Kharitonov, doctor of technical sciences, Executive Director of the International Center of Aerophysical Research (Novosibirsk), G. A. Amir’yants, doctor of technical sciences, chief researcher, TsAGI (Moscow), K. Yu. Kosminkov, editor, TsAGI (Moscow), and O. E. Podoinitsyna, press secretary of the Presidium of the Siberian Branch of the Russian Academy of Sciences, for their assistance in preparing the publication

The publication uses photographs and illustrations from the books “Sergey Alekseevich Khristianovich. Outstanding Mechanician of the 20th Century” (Nauka, Moscow, 2008) and “Academician S. A. Khristianovich” (Geo Academic Publishing House, Novosibirsk, 2008), and also from the archive of the Presidium of the Siberian Branch of the Russian Academy of Sciences

* Cited from: Sergey Alekseevich Khristianovich. Outstanding Mechanician of the 20th Century, 2008, pp. 19—39.

** Cited from: Academician S. A. Khristianovich, 2008, pp. 8—9

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