A. A. Lyapunov (on his 60th birthday)

Ao A .

LYAPUNOV*

(ON H I S 6 0 T H

BIRTHDAY)

October 8, 1971 m a r k e d the sixtieth birthday of the renowned Soviet scientist, Corresponding Member of the Academy of Sciences of the USSR Aleksei Andreevich Lyapunov. A . A . Lyapunov was born in 1911 in the city of Moscow. He r e c e i v e d his s e c o n d a r y education at the 42rid Moscow School (under the G r e a t e r Dep a r t m e n t of Public Education) founded by P r o f . Martyn Fedorovich Berg. An advanced level of p r e p a r a t i o n in the exact and natural s c i e n c e s for that t i m e , a spirit of scientific inquiry, and a r e m a r k a b l e o r g a n i z a tion of scientific r e s e a r c h in s e m i n a r g r o u p s were c h a r a c t e r i s t i c features of this school. The a c a d e m i c staff of the school included in its m e m b e r s h i p Academician A. Yu. Ishlinskii, C o r responding Member of the Academy of Sciences V. V. Sokolovskii, P r o f s . A. A~ and Yu. A. Strepikhov (brothers), P r o f . Bo Yu. Levin, P r o f s . B, G. and M. G. Ravich (brothers), and this list is far f r o m complete. It was on this campus that the young L y a p u n o v ' s i n t e r e s t in m a t h e m a t i c s and science was nurtured. It was his love of the natural s c i e n c e s and biology in p a r t i c u l a r that subsequently encouraged him to conceive and develop his many significant r e s e a r c h e s ia the field of mathematical biology and c y b e r n e t i c s . Aleksei A n d r e e v i c h ' s scientific c a r e e r began in 1929 when he was h i r e d as a l a b o r a t o r y technician at the State G e o p h y s i c s Institute. He was g r e a t l y i n A c a d e m i c i a n s P , T. L a z a r e v , G. A. G a m b u r t s e v , N. N. Luzin, and

A. A. Lyapunov influenced in that p e r i o d by P. S. Novikov.

At the same time Lyapunov worked hard to improve his own teaching skills, serving as an assistant to Academician M. A. L a v r e n t ' e v , In 1934 Lyapunov moved to the V. A. Steklov Mathematical Institute, where he s e r v e d as a staff m e m ber for many y e a r s . In 1939 he s u c c e s s f u l l y defended his Candidate's d i s s e r t a t i o n in the field of set theory. Whatever designs and plans he had for his future were cut short by the war. Aleksei Andreevich s e r v e d at the front'. Even t h e r e , however, in between battles he continued to jot down in field notebooks many thoughts that l a t e r f o r m e d the foundation for a number of his investigations. In 1944 Lyapunov b e c a m e a Communist. He was awarded the O r d e r of the Red Star and s e v e r a l m e d als for his w a r t i m e s e r v i c e to the fatherland. At the w a r ' s end Lyapunov left the battlefield to teach at the Artillery Academy. It was there, and later at Moscow State University (MGU), that his pedagogical talent began to flourish. His personal c h a r m and his ability to p r e s e n t his m a t e r i a l lucidly, comprehensibly, and ,get concisely, captivated his audience. At this time he also developed and organized r a d i c a l l y new c o u r s e s in s e v e r a l m a t h e m a t i c a l disciplines. After demobilization Lyapunov r e t u r n e d to his home base at the Mathematical Institute. T h e r e he worked his way up as a junior scientist, senior s c i e n t i s t , candidate for the doctoral d e g r e e , and Doctor *Corresponding Member of the Academy of Sciences of the USSR. T r a n s l a t e d f r o m Kibernetika, No. 5, pp. 149-150, S e p t e m b e r - O c t o b e r , 1 9 7 1 .

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of P h y s i c o m a t h e m a t i c a l Sciences. Then in 1953 and until 1961 Aleksei Andreevich s e r v e d as chief s c i entist in the Department of Applied Mathematics. In 1956 he was awarded the O r d e r of the Red Banner of Labor for his scientific and pedagogical work. Since 1961 Lyapunov has worked as a m e m b e r of the Novosibirsk Science Center. In 1950 the academic title of p r o f e s s o r was conferred upon Aleksei Andreevich, and in 1964 he was elected as a Corresponding Member of the Academy of Sciences of the USSR. A. A. Lyapunov has worked in the followingprincipal a r e a s during the span of his almost f o r t y - y e a r scientific c a r e e r : The g r e a t e s t number of his published works in the field of p a r e m a t h e m a t i c s p e r t a i n s to set t h e o r y . Many of his p a p e r s on analytic and Borel sets were published evet~ in the p r e w a r y e a r s . His fundamental r e s u l t s in set t h e o r y were p r e s e n t e d in his doctoral d i s s e r t a t i o n , ~R-Sets, ~ which was published in book f o r m as p a r t of the t r a n s a c t i o n s (Trudy, Vol. 40) of the V. A. Steklov Mathematical Institute, as well as in p a p e r s preceding and succeeding it. Lyapunov is also r e s p o n s i b l e for some important p a p e r s in probability and m a t h e m a t i c a l s t a t i s t i c s . Of considerable i n t e r e s t is his paper on selection f r o m a finite number of distribution functions, which b e a r s on the work of W. yon Neumann and E. P e a r s o n on selection between simple hypotheses. This work was extensively developed in the ensuing y e a r s . Lyapunov's p a p e r , non completely additive vector functions, ~ which r e l a t e s to vector distribution functions, has also been frequently cited and elaborated. He has published s e v e r a l interesting p a p e r s on the applications of m a t h e m a t i c s in g e o p h y s i c s , topography, a r t i l l e r y , and other fields. Lyapunov was one of the f i r s t scientists in the Soviet Union to r e c o g n i z e the e n o r m o u s potential of the newly emerging electronic c o m p u t e r s , quickly t r a n s f e r r i n g his scientific i n t e r e s t s to the new fields that they opened up. His work in this a r e a g r e a t l y encouraged the vigorous development and timely recognition of the m a j o r b r a n c h e s Of science of g r e a t fundamental t h e o r e t i c a l and p r a c t i c a l significance, and p r o m o t e d the consolidation and unification of powerful scientific r e s o u r c e s , including both mathematicians and eng i n e e r s , m i l i t a r y specialists, biologists, linguists, and o t h e r s . Lyapunov's enthusiasm, energy, brilliant m a s t e r y of his subject, scientific erudition, and personal c h a r m played an extremely vital part in the popularization and development of these b r a n c h e s of science. A. A. Lyapunov's most important p a p e r s and achievements in the field of c y b e r n e t i c s include the following: In 1953 he devised the operational method in p r o g r a m m i n g . This method paved the way for many subsequent studies in p r o g r a m m i n g theory by the students of Lyapunov (Podlovchenko, Kulagina, Yanov, and Kriuitskii) and r e s e a r c h in automatic p r o g r a m m i n g . Lyapunov's operational method is widely used by computer centers throughout the Soviet Union. Essentially comprising the t r a n s f o r m a t i o n o~ a l g o r i t h m i c p r o g r a m m i n g languages, it is g e n e r a l l y the b a s i s of all methodological textbooks on p r o g r a m m i n g o A n u m b e r of important r e s u l t s in machine t r a n s l a t i o n and mathematical linguistics have been obtained by Lyapunov and his students. Indeed, A. A. Lyapunov is the sponsor of the most important and p r o found investigations in this a r e a in the Soviet Union. Lyapunov is responsible for s e v e r a l incisive r e s u l t s in mathematical biology. P a r t i c u l a r l y n o t e worthy in this discipline is his work in genetics, in the mathematical theory of evolution, and especially in the c y b e r n e t i c approach to the description of life p r o c e s s e s . In fact, the latter field was c r e a t e d by Lyapunov. Of considerable importance are his studies in the formalization of biological concepts and the introduction of exact methods of investigation into biology. It is especially important to note that Lyapunov explained the h i e r a r c h i c principle of the s t r u c t u r e of control s y s t e m s and control p r o c e s s e s . In cybernetics this principle is fundamental, being comparable in significance with the central notion of c y b e r n e t i c s , namely the feedback concept, which can be fully analyzed only within the context of the h i e r a r c h i c principle. Lyapunov's g r e a t contribution was in e l u c i dating the full significance of the principle and in devoting e n o r m o u s effort to make its role widely r e c o g nized.

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L y a p u n o v ' s work is welt-known outside the Soviet Union. His published works have been t r a n s l a t e d many t i m e s into English, F r e n c h , and G e r m a n . His works on p r o g r a m m i n g and mathematical biology have r e c e i v e d international a c c l a i m . Lyapunov is editor of one of the m o s t popular collective publications on c y b e r n e t i c s , " P r o b l e m y K i b e r n e t i k a ' (Problems of Cybernetics). He also s e r v e s as editor of the r e g u l a r s e r i e s of t r a n s l a t i o n s , "Kiberneticheskii Sbornik" (Cybernetics Collection). Ao A. Lyapunov is a member of the National Council of the Committee on Operations Research, serving as Chariman of the Section of Methodological Problems in Operations Research. He has been awarded the Memorial Medal of the French Senate~ Lyapunov devotes considerable time and energy to improving the level of.mathematical education in the secondary school and the specialized school. The AkademgorodokSchool in the city of Novosibirsk, in whose founding and educational program Lyapunov has had a vital part, has been widely acclaimed. In 1968 A. A. Lyapunov was awarded the Order of the Red Banner of Labor, and in 1970 the Anniversary Medal, for his tremendous contribution to the Science Center founded in Novosibirsk. The editorial staff of Kibernetika warmly toasts Aleksei Andreevich on his sixtieth birthday and wishes him many years of good health and productive labor in honor of Soviet science and of the fatherland~

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