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Rodion Kuzmin
Rodion Osievich Kuzmin (russian: Родион Осиевич Кузьмин, 9 November 1891, Riabye village in the Haradok district – 24 March 1949, Leningrad) was a Soviet mathematician, known for his works in number theory and analysis. His name is sometimes transliterated as Kusmin. He was an Invited Speaker of the ICM in 1928 in Bologna. Selected results * In 1928, Kuzmin solved the following problem due to Gauss (see Gauss–Kuzmin distribution): if ''x'' is a random number chosen uniformly in (0, 1), and :: x = \frac :is its continued fraction expansion, find a bound for :: \Delta_n(s) = \mathbb \left\ - \log_2(1+s), :where :: x_n = \frac . :Gauss showed that ''Δ''''n'' tends to zero as ''n'' goes to infinity, however, he was unable to give an explicit bound. Kuzmin showed that :: , \Delta_n(s), \leq C e^~, :where ''C'',''α'' > 0 are numerical constants. In 1929, the bound was improved to ''C'' 0.7''n'' by Paul Lévy. * In 19 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Haradok
Haradok ( be, Гарадок, - russian: Городок, Gorodok, pl, Horodek) is a town in the Vitebsk Region of Belarus with the population of 34,700 people. Approximately 14,000 people reside in the town itself around 30,000 people reside within the district. Haradok district is one of the largest in the country. The town is located on the north-east of Belarus and occupies around 3,000 square kilometers. It is situated 30 kilometers away from Vitebsk, the major city of one of the six provinces in the Republic of Belarus. History Within the Grand Duchy of Lithuania, Haradok was part of Vitebsk Voivodeship. Haradok was acquired by the Russian Empire in 1772, in the course of the First Partition of Poland. In 1939, 1,584 Jews lived in the town, making up 21.7% of the population. During World War II, Haradok was under German occupation from 10 July 1941 until 24 December 1943. In the first half of August 1941, between 120 and 200 Jews were shot by the Germans near the villa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Lévy (mathematician)
Paul Pierre Lévy (15 September 1886 – 15 December 1971) was a French mathematician who was active especially in probability theory, introducing fundamental concepts such as local time, stable distributions and characteristic functions. Lévy processes, Lévy flights, Lévy measures, Lévy's constant, the Lévy distribution, the Lévy area, the Lévy arcsine law, and the fractal Lévy C curve are named after him. Biography Lévy was born in Paris to a Jewish family which already included several mathematicians. His father Lucien Lévy was an examiner at the École Polytechnique. Lévy attended the École Polytechnique and published his first paper in 1905, at the age of nineteen, while still an undergraduate, in which he introduced the Lévy–Steinitz theorem. His teacher and advisor was Jacques Hadamard. After graduation, he spent a year in military service and then studied for three years at the École des Mines, where he became a professor in 1913. During Worl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theorists
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."German original: "Die Mathematik ist die Königin der Wissenschaften, und die Arithmetik ist die Königin der Mathematik." Number theorists study prime numbers as well as the properties of mathematical objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory are often best understood through the study of analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes or other number-theoretic objects in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soviet Mathematicians
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen national republics; in practice, both its government and its economy were highly centralized until its final years. It was a one-party state governed by the Communist Party of the Soviet Union, with the city of Moscow serving as its capital as well as that of its largest and most populous republic: the Russian SFSR. Other major cities included Leningrad (Russian SFSR), Kiev (Ukrainian SSR), Minsk (Byelorussian SSR), Tashkent (Uzbek SSR), Alma-Ata (Kazakh SSR), and Novosibirsk (Russian SFSR). It was the largest country in the world, covering over and spanning eleven time zones. The country's roots lay in the October Revolution of 1917, when the Bolsheviks, under the leadership of Vladimir Lenin, overthrew the Russian Provisional Government tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
People From Gorodoksky Uyezd
A person ( : people) is a being that has certain capacities or attributes such as reason, morality, consciousness or self-consciousness, and being a part of a culturally established form of social relations such as kinship, ownership of property, or legal responsibility. The defining features of personhood and, consequently, what makes a person count as a person, differ widely among cultures and contexts. In addition to the question of personhood, of what makes a being count as a person to begin with, there are further questions about personal identity and self: both about what makes any particular person that particular person instead of another, and about what makes a person at one time the same person as they were or will be at another time despite any intervening changes. The plural form "people" is often used to refer to an entire nation or ethnic group (as in "a people"), and this was the original meaning of the word; it subsequently acquired its use as a plural form of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1949 Deaths
Events January * January 1 – A United Nations-sponsored ceasefire brings an end to the Indo-Pakistani War of 1947. The war results in a stalemate and the division of Kashmir, which still continues as of 2022. * January 2 – Luis Muñoz Marín becomes the first democratically elected Governor of Puerto Rico. * January 11 – The first "networked" television broadcasts take place, as KDKA-TV in Pittsburgh, Pennsylvania goes on the air, connecting east coast and mid-west programming in the United States. * January 16 – Şemsettin Günaltay forms the new government of Turkey. It is the 18th government, last single party government of the Republican People's Party. * January 17 – The first VW Type 1 to arrive in the United States, a 1948 model, is brought to New York by Dutch businessman Ben Pon. Unable to interest dealers or importers in the Volkswagen, Pon sells the sample car to pay his travel expenses. Only two 1949 models are sold in America tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1891 Births
Events January–March * January 1 ** Paying of old age pensions begins in Germany. ** A strike of 500 Hungarian steel workers occurs; 3,000 men are out of work as a consequence. **Germany takes formal possession of its new African territories. * January 2 – A. L. Drummond of New York is appointed Chief of the Treasury Secret Service. * January 4 – The Earl of Zetland issues a declaration regarding the famine in the western counties of Ireland. * January 5 **The Australian shearers' strike, that leads indirectly to the foundation of the Australian Labor Party, begins. **A fight between the United States and Indians breaks out near Pine Ridge agency. ** Henry B. Brown, of Michigan, is sworn in as an Associate Justice of the Supreme Court. **A fight between railway strikers and police breaks out at Motherwell, Scotland. * January 6 – Encounters continue, between strikers and the authorities at Glasgow. * January 7 ** General Miles' force ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nearest Integer Function
Rounding means replacing a number with an approximate value that has a shorter, simpler, or more explicit representation. For example, replacing $ with $, the fraction 312/937 with 1/3, or the expression with . Rounding is often done to obtain a value that is easier to report and communicate than the original. Rounding can also be important to avoid misleadingly precise reporting of a computed number, measurement, or estimate; for example, a quantity that was computed as but is known to be accurate only to within a few hundred units is usually better stated as "about ". On the other hand, rounding of exact numbers will introduce some round-off error in the reported result. Rounding is almost unavoidable when reporting many computations – especially when dividing two numbers in integer or fixed-point arithmetic; when computing mathematical functions such as square roots, logarithms, and sines; or when using a floating-point representation with a fixed number of significant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gelfond–Schneider Theorem
In mathematics, the Gelfond–Schneider theorem establishes the transcendence of a large class of numbers. History It was originally proved independently in 1934 by Aleksandr Gelfond and Theodor Schneider. Statement : If ''a'' and ''b'' are complex algebraic numbers with ''a'' ≠ 0, 1, and ''b'' not rational, then any value of ''ab'' is a transcendental number. Comments * The values of ''a'' and ''b'' are not restricted to real numbers; complex numbers are allowed (here complex numbers are not regarded as rational when they have an imaginary part not equal to 0, even if both the real and imaginary parts are rational). * In general, is multivalued, where ln stands for the natural logarithm. This accounts for the phrase "any value of" in the theorem's statement. * An equivalent formulation of the theorem is the following: if ''α'' and ''γ'' are nonzero algebraic numbers, and we take any non-zero logarithm of ''α'', then is either rational or transcendental. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gelfond–Schneider Constant
The Gelfond–Schneider constant or Hilbert number is two to the power of the square root of two: :2 = ... which was proved to be a transcendental number by Rodion Kuzmin in 1930. In 1934, Aleksandr Gelfond and Theodor Schneider independently proved the more general ''Gelfond–Schneider theorem'', which solved the part of Hilbert's seventh problem described below. Properties The square root of the Gelfond–Schneider constant is the transcendental number :\sqrt=\sqrt^= .... This same constant can be used to prove that "an irrational elevated to an irrational power may be rational", even without first proving its transcendence. The proof proceeds as follows: either \sqrt^\sqrt is rational, which proves the theorem, or it is irrational (as it turns out to be), and then :\left(\sqrt^\right)^=\sqrt^=\sqrt^2=2 is an irrational to an irrational power that is rational, which proves the theorem. The proof is not constructive, as it does not say which of the two cases is true, but it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transcendental Number
In mathematics, a transcendental number is a number that is not algebraic—that is, not the root of a non-zero polynomial of finite degree with rational coefficients. The best known transcendental numbers are and . Though only a few classes of transcendental numbers are known—partly because it can be extremely difficult to show that a given number is transcendental—transcendental numbers are not rare. Indeed, almost all real and complex numbers are transcendental, since the algebraic numbers comprise a countable set, while the set of real numbers and the set of complex numbers are both uncountable sets, and therefore larger than any countable set. All transcendental real numbers (also known as real transcendental numbers or transcendental irrational numbers) are irrational numbers, since all rational numbers are algebraic. The converse is not true: not all irrational numbers are transcendental. Hence, the set of real numbers consists of non-overlapping rational, algebrai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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