mathematics

Nikolay Krasovsky

Nikolay Krasovsky is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Nikolay Krasovsky rather than just read about it. In short: Nikolay Nikolayevich Krasovsky (Russian: Никола́й Никола́евич Красо́вский; 7 September 1924 – 4 April 2012, also transliterated Nikolai Krasovskii) was a Soviet and Russian mathematician who worked in the mathematical theory of control, the theory of dynamical systems, and the theory of differential games. He was the author of Krasovskii-LaSalle principle and the chief of the Ural scientific school in mathematical t…

Key takeaways

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Learn the definition first, then one example that makes the definition concrete.
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Reference excerpt

Nikolay Nikolayevich Krasovsky (Russian: Никола́й Никола́евич Красо́вский; 7 September 1924 – 4 April 2012, also transliterated Nikolai Krasovskii) was a Soviet and Russian mathematician who worked in the mathematical theory of control, the theory of dynamical systems, and the theory of differential games. He was the author of Krasovskii-LaSalle principle and the chief of the Ural scientific school in mathematical theory of control and the theory of differential games.

Biography Nikolay Krasovsky was born in Yekaterinburg (renamed later to Sverdlovsk that year) in the family of a doctor. In 1949, he graduated summa cum laude from the department of metallurgical science at the Ural State Technical University. In 1954, he presented his first thesis and received his Candidate of Sciences degree in mathematics. In 1957, he defended his second thesis for the degree of Doctor of Sciences and became a professor of mathematics. From 1949 to 1959, he worked at the Ural State Technical University. Since 1958, he worked at the Ural State University.

1949–1951 – assistant at the Ural State Technical University 1954–1955 – associate professor (docent) at the Ural State Technical University 1958–1959 – professor at the Ural State Technical University 1959–1960 – chief of the chair of theoretical mechanics at the Ural State University 1961–1963 – chief of the chair of computing mathematics at the Ural State University In 1963 Stanford University Press published a translation of his book Stability of Motion: applications of Lyapunov's second method to differential systems and equations with delay that had been prepared by Joel Lee Brenner.

1965–1970 – chief of the chair of applied mathematics at the Ural State University 1970–1977 – director the Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences 1971–1986 – professor at the chair of applied mathematics at the Ural State University since 1986 until his death – professor of the chair of theoretical mechanics at the Ural State University Advisor of the Ural branch of the Russian Academy of Sciences He died in Yekaterinburg aged 87, and was buried at the Shirokorechenskoye Cemetery.

Honours Order of the Red Banner of Labour (1961) Academician of the Academy of Sciences of the Soviet Union (1968) Hero of Socialist Labour (1974) Order of Lenin (1974) Lenin Prize (1976) - for his work in mathematical control theory USSR State Prize (1984) Order of the October Revolution (1984) Honorary foreign member of the Hungarian Academy of Sciences (1988) Lyapunov Gold Medal of the Russian Academy of Sciences (1992) Doctor Honoris Causa of the Ural State Technical University (1994) Professor Emeritus of the Ural State University (1996) Lomonosov Gold Medal of the Russian Academy of Sciences (1996) Demidov Prize (1996) Order "For Merit to the Fatherland", 3rd class (1999) Vonsovsky Gold Medal of the Ural Branch of the Russian Academy of Sciences (2003) IEEE Control Systems Award (2003) Order "For Merit to the Fatherland", 2nd class (2004) Laureate of the Science Support Foundation in the category "Outstanding Scientists" (2006) The Issacs Award (2006) Honorary citizen of Yekaterinburg

Sources

Information (and photo) at server of Russian Academy of Science (in Russian): http://www.ras.ru/win/db/show_per.asp?P=.id-68.ln-ru "Control under Lack of Information" - Book of Krasovsky and his son, translated to English: [1] List of publications (in English): https://web.archive.org/web/20060820152705/http://www.imm.uran.ru/PERSONS/BIOGRAPH/PUB/KRASOVSK.HTM Short biography (in Russian): http://www.eunnet.net/USUbio/?base=mag&id=0128

Illustrations

Worked examples

Example 1 — a first encounter with Nikolay Krasovsky

Start with the simplest possible case. Write down what Nikolay Krasovsky claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Nikolay Krasovsky before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Nikolay Krasovsky ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Nikolay Krasovsky

In research: Nikolay Krasovsky appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Nikolay Krasovsky in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Nikolay Krasovsky is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1924 births, 2012 deaths, 20th-century Russian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Nikolay Krasovsky outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Nikolay Krasovsky in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Nikolay Krasovsky means in your own words.
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Work through the three examples above with pen and paper.
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Frequently asked questions

What is Nikolay Krasovsky in simple terms?

Why does Nikolay Krasovsky matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Nikolay Krasovsky?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Nikolay Krasovsky.