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Evgeny Yakovlevich Remez
Evgeny Yakovlevich Remez (sometimes spelled as Evgenii Yakovlevich Remez, russian: Евге́ний Я́ковлевич Ре́мез; (born 1895 in Mstislavl, now Belarus; died 1975 in Kyiv, now Ukraine) was a Soviet mathematician. He is known for his work in the constructive function theory, in particular, for the Remez algorithm and the Remez inequality. His doctoral students include Boris Korenblum. References *V K Dzyadyk, Yu A Mitropol'skii and A M Samoilenko, Evgenii Yakovlevich Remez (on the centenary of his birth) (Ukrainian), Ukrain. Mat. Zh. 48 (2) (1996), 285-286. *Yu A Mitropol'skii, V K Dzyadyk and V T Gavrilyuk, Evgenii Yakovlevich Remez (on the occasion of the ninetieth anniversary of his birth) (Russian), Ukrain. Mat. Zh. 38 (4) (1986), 539-540. *Yu A Mitropol'skii, V K Dzjadyk and V T Gavriljuk, Evgenii Yakovlevich Remez (on the occasion of his eightieth birthday) (Russian), Ukrain. Mat. Z. 28 (5) (1976), 711. External links *Remez at MacTutor Sovi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mstislavl
Mstislaw or Mstislavl ( be, Мсціслаў, [], russian: Мстиславль [msʲtʲɪˈslavlʲ], pl, Mścisław, lt, Mstislavlis) is a town in the Mogilev Region, Eastern Belarus. It serves as the administrative center of Mstsislaw District. As of 2009, its population was 10,804. History Mstislavl was first mentioned in the Ipatiev Chronicle in 1156. It was initially a part of the Principality of Smolensk, but had become the capital of the Principality of Mstislavl by 1180. In the Middle Ages, it was the family seat of Princes Mstislavsky. Pyotr Mstislavets is believed to have been born in Mstislavl. In 1377, it was conquered by the Grand Duchy of Lithuania. The first Lithuanian duke of Mstislavl was Karigaila, brother of Jogaila. The town remained part of the Polish–Lithuanian Commonwealth under the Mścisław Voivodship until the Partitions of Poland in 1772. Buildings of historic interest include the Carmelite church (1637, renovated 1746–50) and the Jesuit c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Belarus
Belarus,, , ; alternatively and formerly known as Byelorussia (from Russian ). officially the Republic of Belarus,; rus, Республика Беларусь, Respublika Belarus. is a landlocked country in Eastern Europe. It is bordered by Russia to the east and northeast, Ukraine to the south, Poland to the west, and Lithuania and Latvia to the northwest. Covering an area of and with a population of 9.4 million, Belarus is the List of European countries by area, 13th-largest and the List of European countries by population, 20th-most populous country in Europe. The country has a hemiboreal climate and is administratively divided into Regions of Belarus, seven regions. Minsk is the capital and List of cities and largest towns in Belarus, largest city. Until the 20th century, different states at various times controlled the lands of modern-day Belarus, including Kievan Rus', the Principality of Polotsk, the Grand Duchy of Lithuania, the Polish–Lithuanian Commonwealth, and t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kyiv
Kyiv, also spelled Kiev, is the capital and most populous city of Ukraine. It is in north-central Ukraine along the Dnieper, Dnieper River. As of 1 January 2021, its population was 2,962,180, making Kyiv the List of European cities by population within city limits, seventh-most populous city in Europe. Kyiv is an important industrial, scientific, educational, and cultural center in Eastern Europe. It is home to many High tech, high-tech industries, higher education institutions, and historical landmarks. The city has an extensive system of Transport in Kyiv, public transport and infrastructure, including the Kyiv Metro. The city's name is said to derive from the name of Kyi, one of its four legendary founders. During History of Kyiv, its history, Kyiv, one of the oldest cities in Eastern Europe, passed through several stages of prominence and obscurity. The city probably existed as a commercial center as early as the 5th century. A Slavs, Slavic settlement on the great trade ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ukraine
Ukraine ( uk, Україна, Ukraïna, ) is a country in Eastern Europe. It is the second-largest European country after Russia, which it borders to the east and northeast. Ukraine covers approximately . Prior to the ongoing Russian invasion, it was the eighth-most populous country in Europe, with a population of around 41 million people. It is also bordered by Belarus to the north; by Poland, Slovakia, and Hungary to the west; and by Romania and Moldova to the southwest; with a coastline along the Black Sea and the Sea of Azov to the south and southeast. Kyiv is the nation's capital and largest city. Ukraine's state language is Ukrainian; Russian is also widely spoken, especially in the east and south. During the Middle Ages, Ukraine was the site of early Slavic expansion and the area later became a key centre of East Slavic culture under the state of Kievan Rus', which emerged in the 9th century. The state eventually disintegrated into rival regional po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soviet Union
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constructive Function Theory
In mathematical analysis, constructive function theory is a field which studies the connection between the smoothness of a function and its degree of approximation. It is closely related to approximation theory. The term was coined by Sergei Bernstein. Example Let ''f'' be a 2''π''-periodic function. Then ''f'' is ''α''- Hölder for some 0 < ''α'' < 1 if and only if for every natural ''n'' there exists a ''Pn'' of degree ''n'' such that : where ''C''(''f'') is a positive number depending on ''f''. The "only if" is due to , see |
Remez Algorithm
The Remez algorithm or Remez exchange algorithm, published by Evgeny Yakovlevich Remez in 1934, is an iterative algorithm used to find simple approximations to functions, specifically, approximations by functions in a Chebyshev space that are the best in the uniform norm ''L''∞ sense. It is sometimes referred to as Remes algorithm or Reme algorithm. A typical example of a Chebyshev space is the subspace of Chebyshev polynomials of order ''n'' in the space of real continuous functions on an interval, ''C'' 'a'', ''b'' The polynomial of best approximation within a given subspace is defined to be the one that minimizes the maximum absolute difference between the polynomial and the function. In this case, the form of the solution is precised by the equioscillation theorem. Procedure The Remez algorithm starts with the function f to be approximated and a set X of n + 2 sample points x_1, x_2, ...,x_ in the approximation interval, usually the extrema of Chebyshev polynomial linear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Remez Inequality
In mathematics, the Remez inequality, discovered by the Soviet mathematician Evgeny Yakovlevich Remez , gives a bound on the sup norms of certain polynomials, the bound being attained by the Chebyshev polynomials. The inequality Let ''σ'' be an arbitrary fixed positive number. Define the class of polynomials π''n''(''σ'') to be those polynomials ''p'' of the ''n''th degree for which :, p(x), \le 1 on some set of measure ≥ 2 contained in the closed interval 1, 1+''σ'' Then the Remez inequality states that :\sup_ \left\, p\right\, _\infty = \left\, T_n\right\, _\infty where ''T''''n''(''x'') is the Chebyshev polynomial of degree ''n'', and the supremum norm is taken over the interval 1, 1+''σ'' Observe that ''T''''n'' is increasing on , +\infty/math>, hence : \, T_n\, _\infty = T_n(1+\sigma). The R.i., combined with an estimate on Chebyshev polynomials, implies the following corollary: If ''J'' ⊂ R is a finite interval, and ''E'' ⊂&nb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boris Korenblum
Boris Isaac Korenblum (Борис Исаакович Коренблюм, 12 August 1923, Odessa, now Ukraine – 15 December 2011, Slingerlands, New York) was a Soviet-Israeli-American mathematician, specializing in mathematical analysis. Boris Korenblum was a child prodigy in music, languages, and mathematics. He started as a violinist at the famous School of Stolyarsky in Odessa. After he won a young mathematicians competition, the family was given an apartment in Kiev, an extraordinary event. Boris was given a mentor, a local mathematics professor, who would peremptorily supervise his course of self study. To the great chagrin of his mother, Boris decided against pursuing a music career. In June 1941, when the war began, he volunteered, not yet having reached the draft age, for the Soviet Army. Because of his fluency in German, he served in a reconnaissance unit. Some of his tasks was going to the enemy lines to capture a prisoner for interrogation. He was also the one to inter ... [...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] |
Approximation Theorists
An approximation is anything that is intentionally similar but not exactly equal to something else. Etymology and usage The word ''approximation'' is derived from Latin ''approximatus'', from ''proximus'' meaning ''very near'' and the prefix ''ad-'' (''ad-'' before ''p'' becomes ap- by assimilation) meaning ''to''. Words like ''approximate'', ''approximately'' and ''approximation'' are used especially in technical or scientific contexts. In everyday English, words such as ''roughly'' or ''around'' are used with a similar meaning. It is often found abbreviated as ''approx.'' The term can be applied to various properties (e.g., value, quantity, image, description) that are nearly, but not exactly correct; similar, but not exactly the same (e.g., the approximate time was 10 o'clock). Although approximation is most often applied to numbers, it is also frequently applied to such things as mathematical functions, shapes, and physical laws. In science, approximation can refer t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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