 | In Russian | | NIKOLAI NIKOLAYEVICH YANENKO (1921-1984) - is an outstanding soviet mathematician and mechanical engineer, Hero of the Socialist Labor, three times the USSR State Prize laureate.
An academician Nikolai Nikolayevich Yanenko was a soviet scientist, who had made a great contribution to the development of mathematics, mechanics and also to the new trends of science, connected with computer engineering and its application. Besides, he was also a prominent organizer of soviet science, and it became quite apparent when he worked in Siberia and Ural, where creative collectives, able to solve complicated practical problems were formed. They are called now "academician Yanenko School". |
Yanenko's name and scientific progress of his school are well known in our country and abroad; many of his scientific works obtained world recognition. Lastly he was all round educated charming person, the real communist and a patriot of the soviet science and our homeland. He was a native Siberian and a patriot of his region.
 | N.N.Yanenko was born on May 22, 1921 in Siberian town Kainsk (now it's called Kuibyshev). In 1939 after finishing secondary school in Novosibirsk he entered the physico-mathematical department of Tomsk State University, which graduated with honours in 1942. From November 1942 till May 1945 he took part in the Great Patriotic War fronts (Volhovsky, Leningradsky, the 2nd and 3rd Baltic fronts). In December 1945 he was demobilized and in February 1946 he entered the post-graduate course of Tomsk State University physico-mathematical department. In 1949 he was awarded Ph. D. for a thesis, in 1954 - the doctoral thesis. In 1966 he was elected a Corresponding Member of USSR Academy of Sciences; in 1970 - a full member of USSR Academy of Sciences at the department of mechanics and control processes. |
N.N.Yanenko is the mathematician who has started his way up with differential topology and finished, unfortunately, prematurely, with daring developments in computational mathematics and mathematical physics. As a geometrician he has been formed under indubitable influence of his teacher Petr K. Rashevsky, a well-known soviet pedagogue and a great specialist in the field of differential geometry. Rashevsky taught Yanenko while Nikolai studied at Tomsk University (a part of Moscow State University professorship was evacuated to Tomsk). In 1946 after traversing the battle path from Leningrad to Canonsburg and getting demobilized as a lieutenant Nikolai entered the post-graduate course. Here Rashevsky taught him. It was the classical problem of differential geometry - the problem of surface bending that was the subject of his research.
 | The results of this research, stated in Yanenko's Ph. D. thesis (1949) and doctoral thesis (1954), after basis works of Kartan, Thomas and Allendorfer, had allowed to derive the fundamental theory about the features of bending, what, per se, had completed the development of this area of differential geometry. |
In 1948 in the Yanenko's scientific biography an important event took place: Nikolai Nikolayevich began to work in the academician A.N.Tihonov's group, which was solving important applied problems. This event was the first step on Yanenko's path towards great scientific achievements. Let's dwell upon this determinative moment.
 | At that time, legendary, as we suppose now, scientists, who started their work in the field of computer engineering, found themselves in rather peculiar situation. Each of them, one could say, was equivalent to today's laboratory: they could combine target setting, mathematical model choosing, searching method of its realization on calculating devices, which were rather primitive at that time, settled the task for those who worked with that devices, - in short, he was a worker operating a number of machines simultaneously. Besides he had to provide for control methods for the results as everything depended on calculations. |
This work was to be done in a limited period of time. Only skilled professionals possessing outstanding personal qualities could operate with such a system. On the other hand, this system itself influenced the researcher, built him up as a scientist and as a person. Nikolai Nikolayevich was indeed that sort of a specialist. He could skillfully combine the adherence to basis theoretical research with the attempt to approximate it as much as possible to the large-scale domestic task solution. Such kind of universalism characterized Yanenko as a scientist and citizen. These ideas were inseparable for him in the work and his private life. It is necessary to note that Nikolai Nikolayevich combined successfully the breadth of scientific views with the depth of theoretical and applied inventions; that is why it is difficult to characterize the whole range of his activity. But we'd like to underline one characteristic property in his creative work: search and availability of his elaborations, complexity of those problems that seemed simple at first glance.
| Let's now turn to the subject of Yanenko's research. We have already touched upon the Yanenko's works in the field of geometry. These works were connected with the study of the systems of nonlinear differential equations in the partial derivatives describing the behavior of geometric objects. N.N.Yanenko was engaged in studying and solving nonlinear equations later. However, the application sphere of the research had changed; it had become close to the needs of mechanics, physics and contemporary engineering. Nikolai Nikolayevich has published more than 50 works on nonlinear equations in partial derivatives; three monographs including. Moor of his works are devoted to numerical methods for solving nonlinear differential equations. |  |
In the monograph called "Sistemy kvazilineynykh uravneniy i ikh prilozheniya k gazovoy dinamike" [Systems of quasilinear equations and their applications to gas dynamics] (which was written together with B.L.Rozhdestvensky) longstanding investigations of soviet and foreign scientists in the theory of a system of quasilinear differential hyperbolic equations are summed up. The monograph concerns the progress in the study both classical and generalized solving quasilinear conservation laws systems. This work is well known to specialists and widely used by mathematicians, operators and physicists. In 1985 the second publication of this monograph (1978) was awarded the USSR State Prize.
 | Much attention Yanenko paid to the theory of differential equations to the problems connected with needs of computational mathematics (the problems of realization of mathematical models by numerical methods). Being able not only to set a problem, but to realize it (to come to the very end), Nikolai Nikolayevich had made his contribution to solving these problems. For instance, in solving the Navier-Stokes equations there was the problem of approximation of these equations. These equations don't belong to the Koshi-Kovalevskaya system, and this fact makes it difficult to solve many problems. In 1965 Yanenko thought out the idea of approximation of Navier-Stokes equations for incompressible liquid with small parameter equations system, which described the movement of weakly compressible liquid. Obtained system was evolutionary; that's why proved numerical methods could be applied to it. Such approach appeared to be productive, it is investigated now by many Russian and foreign scientists. |
It is known when examining the averaged characteristics of turbulent liquid or gas flow there are different flow regions where the "turbulent" (averaged) viscosity can be negative. This fact had drawn Yanenko's attention, and he began a detailed study of nonlinear differential variable type equations and their solution characteristics with his students. The monograph "Nelineynye uravneniya peremennogo tipa" [Nonlinear variable equations], written by Yanenko together with N.A.Larkin and V.A.Novikov, sums up their investigations.
While becoming familiar with new branches of mechanics, physics and computation mathematics Nikolai Nikolayevich didn't forget his geometric education. With great success he used geometric ideas and methods in solving different problems in the other fields of mathematics. The differential binding method that allows to get exact solutions of difficult differential equations is a brilliant example of it. These solutions are efficient in our days, when achieved level of computational mathematics seems to give the opportunity to find solutions of many problems numerically. Obtaining the exact solution is so-called "moment of the truth" in the process of investigation. This solution allows before the realization of numerical algorithm (that, by the way, is a difficult task) to check the adequacy of the given model and situation, to evaluate the influence of a number of parameters, to describe the phenomenon and notice the possible calculation difficulties. In a word, the exact solution gives important information to an investigator, not saying, it can a kind of a test for the program debugging.
Using the differential binding method Yanenko and his students had solved a number of interesting problems of one-dimensional and multidimensional gas dynamics, which his monograph "Metod differencialnykh svyazey i ego prilozheniya v gazovoy dinamike" [The differential binding method and its application to gas dynamics](together with A.F.Sidorov and V.P.Shapeev) is devoted to. This work was published in 1984 after Yanenko's death.
As I have already mentioned, researches in the field of numerical methods for mathematical physics took the central place in Yanenko's works. Computational mathematics had become his constant research subject since 1949. More than 150 works are devoted to this topic.
Yanenko's great achievement in the field of computational mathematics is the creation of "the method of fractional steps"that allowed to cut down the IBM multidimensional problems solving by splitting up this problem into number of one-dimensional. This method was developed and specified in 1957-1963, and in 1967 Yanenko's monograph "Fractional step method for solving multidimensional computational physics problems" was published and soon it was translated into German, French and English. That was the recognition of the soviet scientist achievements.
| Yanenko's activity in making and developing new science discipline (which he called mathematical technology), packet subjects including, is the striking example of his constant urge towards new fundamental inventions. Nikolai Nikolayevich began to work at this problem in the 60s-70s, and one could say, it more and more provoked his interest, he did his best to achieve a success. Yanenko's achievements in this field are undoubted. He has worked out the basis principles of modular analysis of mathematical physics and continuum mechanics; he has given the first definitions of module and application programs packet, carried out its classification. Yanenko was one of the first to understand the importance of threading calculations in working out the ways of increasing IBM productivity, the importance of creation of IBM with extreme productivity. He has revealed the correlation between the continuum mechanics task solution algorithm and the true computer structure, and has produced different ways of identification of such structures. This fact plays an important role in system and applied software mathematical support developments. |  |
From the very outset of his scientific work in the academician A. N. Tihonov's group N.N.Yanenko faced problems that required exceptional abilities of a physicist. He had to construct the equation of fluid state, taking into account the role of electronic multiplier. But there was a problem: he had to solve strongly nonlinear integrodifferential equation. N.N.Yanenko has showed his worth not only as a mathematician, but also as a specialist who understood the problems of physics greatly. He has got the asymptotic formula for the fluid state equation. Here he also used the geometrical ideas and methods. He has retained his interest to the research of substance characteristics at a later time. These works have been continued as long as Nikolai Nikolayevich with his students constructed the equation for star shell state (Pulsar, White Dwarf). The main feature of this system is the potent magnetic field. This field determinates the turn of the abnormal characteristics; in particular, chance to exit a blast rarefaction waves.
N.N.Yanenko paid much attention to mechanics of continuum. A great number of his works is devoted to problems of transportation, change of phase, examination of different modifications of state equations. These works have awoken specialist's interest and got high appraisal.
| A real scientist can't manage without thinking about the role of his special investigations in the common system of human knowledge. It is important not only to solve the tasks in the context of his science, but to answer: what for am I doing that? What will change after that? What result will my investigations lead to? Yanenko's philosophical works, which are summarized in the monograph "Methodological Problems of Mathematical Physics", should be examined from the scientific point of view. What is typical here? Yanenko analyses structure and development of mathematics as the instrument of real world perception. Making conclusions and inference concerning specific mathematical objects and directions of his investigations, he gets characteristics of the cognition process in general. All this is done not for showing his great knowledge or building up speculative structures. The main goal is to popularize the progressive scientific-organizational ideas; their realization allows toincrease scientist's labour productivity greatly. Civil, patriotic Yanenko's position - position of a soviet man and a real intellectual - comes to light here. |  |
Much attention should be paid to Yanenko's educational activity. It was also many-sided. He lectured not only in Moscow, Ural, Novosibirsk universities (there are about 20 Doctors of Science and 50 candidates among his direct followers). Very important in his activity was to set up and lead six All-Union seminars.
Not elaborating these seminars, I would like to say a few words about Yanenko's typical features as an educator, teacher of young scientists. Like other outstanding representatives of the soviet science Yanenko was a very democratic person, he possessed foresight, great erudition, ability to pose problems with a prospect, reply softly, - softly and in time, not binding but developing the initiative. But it is very important to underline his personal example that Yanenko set by his activity and life to younger colleagues (and not only younger). He evoked love and respect, and it, perhaps, has done more for the young people to become real science researchers, than some special complex of pedagogical measures. He did possessed these qualities, and he managed to arouse in other people the aspiration to "bring up" such qualities in them.
 | Setting up and regular functioning of six All-Union seminars are the examples of self-return, doing everything in his power to create the high level scientific manpower. All seminars conducted by Yanenko were marked off the atmosphere of collective creative work. A high level of presented works conveys the popularity and prestige of Yanenko's seminars. |
Nikolai Nikolayevich took part in the development of international contacts, popularization of the soviet science abroad. His activity on elaboration and realization the joint scientific programs with CMEA countries should be marked specially. He has done much for strengthening business and friendly contacts with scientists from different countries, for organization of important international arrangements, was the representative of the soviet science in different international organizations, scientific magazines, organizational committees of conferences and symposia. Many foreign scientists know Yanenko by his scientific works and their joint undertakings.
 | Yanenko's prominent services to the State were highly marked in Russia. He is three times the USSR State Prize laureate, was awarded three Orders of the Red Banner of Labour and the Order of the October Revolution. On May 22, 1981, at the day of his 60-th anniversary, he was given the rank of the Hero of the Socialist Labour. He was the true worker, and his creative biography might be the brilliant confirmation of the fact, that a person develops and gains himself by labour. During his life he faced difficult problems, and Nikolai Nikolayevich didn't get away from them: in the process of solving the problems he learned and got new great results that allowed to open new field of research. |
On the next stage there were new problems and success. Going up, he saw father ahead, broader and clearer. Not the aspiration to his personal success was the chief factor but the unquenchable interest of a researcher and the exalted sense of responsibility for his work. Just from this point of view Yanenko's personality should be appreciated. Sometimes because of being concentrated and deep in thought he seemed to be rough. But in fact he was kind, sympathetic and one couldn't but feel it in the process of communication. True will and rare perspicacity hid behind the modesty, gentleness in communication and his unwillingness to be in sight. These qualities helped him to find right solutions in hard moments of his life.
Personal qualities helped him to be a scientist, scientific abilities - to be a person.
G.I.Marchuk.
 | In Russian | (From the book «Nikolaj Nikolaevich Yanenko: Ocherki.
Stat'i. Vospominaniya». - Novosibirsk: Nauka, 1988. - P.9-17). |
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