mathematics

Rafail Krichevskii

Rafail Krichevskii 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 Rafail Krichevskii rather than just read about it. In short: Rafail Evseevich Krichevskii (Рафаил Евсеевич Кричевский, sometimes transliterated as "Krichevskiy" or "Krichevsky", 12 October 1936 – 27 November 2025) was a Russian mathematician and information theorist. He had lived in the United States since 1996.

Key takeaways

Rafail Krichevskii belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Rafail Krichevskii to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Rafail Krichevskii from memory before moving on to harder problems.

Reference excerpt

Rafail Evseevich Krichevskii (Рафаил Евсеевич Кричевский, sometimes transliterated as "Krichevskiy" or "Krichevsky", 12 October 1936 – 27 November 2025) was a Russian mathematician and information theorist. He had lived in the United States since 1996. He graduated from Moscow State University in 1958. He received his PhD degree in Theoretical Cybernetics in 1963. His PhD advisor was Sergey Yablonsky. Further, Krichevskii became a Doctor of Physical and mathematical sciences (1988) and professor (1991), specializing in the field of mathematical cybernetics and information theory. From 1962 to 1996, he worked at the Sobolev Institute of Mathematics. In the late 90s, he worked in University of California, Riverside, US. His main publications are in the fields of universal source coding, optimal hashing, combinatorial retrieval and error-correcting codes. Krichevsky–Trofimov estimator is widely used in source coding and bioinformatics. He supervised five doctoral (Russian candidate degree) students and two higher doctoral (habilitation) students. He was the author of about 80 scientific papers. In 1986, Krichevskii was an Invited Speaker with talk Retrieval and data compression complexity at the ICM in Berkeley, California. Krichevskii died on 27 November 2025, at the age of 89.

Selected publications With V.K.Trofimov: "The Performance of Universal Encoding." IEEE Trans. Inform. Theory, V.27:2, (1981) 199–207. doi:10.1109/TIT.1981.1056331 With B. Ya Ryabko and A. Yu Haritonov: "Optimal key for taxons ordered in accordance with their frequencies." Discrete Applied Mathematics 3, no. 1 (1981): 67–72. doi:10.1016/0166-218X(81)90029-9 "Optimal hashing." Information and Control, V. 62:1, (1984) 64–92. doi:10.1016/S0019-9958(84)80010-8 "Laplace's law of succession and universal encoding." IEEE Trans. Inform. Theory, V. 44:1, (1998) 296–303. doi:10.1109/18.651051 "Universal Compression and Retrieval." Kluwer Academic Publishers (1994), 219 p.https://www.springer.com/br/book/9780792326724

References

External links Rafail Evseevich Krichevskii at the Mathematics Genealogy Project Mathnet.ru

Illustrations

Worked examples

Example 1 — a first encounter with Rafail Krichevskii

Start with the simplest possible case. Write down what Rafail Krichevskii 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 Rafail Krichevskii 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 Rafail Krichevskii 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 Rafail Krichevskii

In research: Rafail Krichevskii 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 Rafail Krichevskii 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: Rafail Krichevskii is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1936 births, 2025 deaths, 20th-century Russian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Rafail Krichevskii 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 Rafail Krichevskii in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Rafail Krichevskii means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Rafail Krichevskii out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Rafail Krichevskii in simple terms?

Why does Rafail Krichevskii 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 Rafail Krichevskii?

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 Rafail Krichevskii.