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Yuri Petunin
Yuri Ivanovich Petunin () was a Soviet and Ukrainian mathematician. Petunin was born in the city of Michurinsk (USSR) on September 30, 1937. After graduating from the Tambov State Pedagogical Institute he began his studies at Voronezh State University under the supervision of S.G Krein. He completed his postgraduate studies in 1962, and in 1968 he received his Doctor of Science Degree, the highest scientific degree awarded in the Soviet Union. In 1970 he joined the faculty of the computational mathematics department at Kyiv State University. Yuri Petunin is highly regarded for his results in functional analysis. He developed the theory of Scales in Banach spaces,S G Krein and Yu I Petunin, Scales of Banach spaces, 1966 Russ. Math. Surv. 21, 85–129 the theory of characteristics of linear manifolds in conjugate Banach spaces,Yu. I. Petunin and A. N. Plichko, The Theory of the Characteristics of Subspaces and Its Applications n Russian Vishcha Shkola, Kyiv (1980) and with S.G. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tambov Oblast
Tambov Oblast (russian: Тамбо́вская о́бласть, ''Tambovskaya oblast'') is a federal subject of Russia (an oblast). Its administrative center is the city of Tambov. As of the 2010 Census, its population was 1,091,994. Geography Tambov Oblast is situated in forest steppe. It borders on the Ryazan, Penza, Saratov, Voronezh and Lipetsk Oblasts. History The oldest known population of the Tambov region, the Mordovians-Moksha, formed as a nation of local ethnic groups from the 6th century BC. The first Russian settlers arrived in the pre-Mongol period, but the final settlement occurred in the 17th century. To protect the southern borders of Russia from the raids of the Tatars, and to further develop the Black Soil region, the Russian government built the walled cities of Kozlov (1635) and Tambov (1636). The cities protected the main path of nomad raids on Russian land and paved the way for a quick settlement of the region. Kozlovsky Uyezd originally exis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Banach Space
In mathematics, more specifically in functional analysis, a Banach space (pronounced ) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is complete in the sense that a Cauchy sequence of vectors always converges to a well-defined limit that is within the space. Banach spaces are named after the Polish mathematician Stefan Banach, who introduced this concept and studied it systematically in 1920–1922 along with Hans Hahn and Eduard Helly. Maurice René Fréchet was the first to use the term "Banach space" and Banach in turn then coined the term " Fréchet space." Banach spaces originally grew out of the study of function spaces by Hilbert, Fréchet, and Riesz earlier in the century. Banach spaces play a central role in functional analysis. In other areas of analysis, the spaces under study are often Banach spaces. Definition A Banach space is a com ... [...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 that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2011 Deaths
This is a list of deaths of notable people, organised by year. New deaths articles are added to their respective month (e.g., Deaths in ) and then linked here. 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991 1990 1989 1988 1987 See also * Lists of deaths by day * Deaths by year {{DEFAULTSORT:deaths by year ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1937 Births
Events January * January 1 – Anastasio Somoza García becomes President of Nicaragua. * January 5 – Water levels begin to rise in the Ohio River in the United States, leading to the Ohio River flood of 1937, which continues into February, leaving 1 million people homeless and 385 people dead. * January 15 – Spanish Civil War: Second Battle of the Corunna Road ends inconclusively. * January 20 – Second inauguration of Franklin D. Roosevelt: Franklin D. Roosevelt is sworn in for a second term as President of the United States. This is the first time that the United States presidential inauguration occurs on this date; the change is due to the ratification in 1933 of the Twentieth Amendment to the United States Constitution. * January 23 – Moscow Trials: Trial of the Anti-Soviet Trotskyist Center – In the Soviet Union 17 leading Communists go on trial, accused of participating in a plot led by Leon Trotsky to overthrow Joseph Stalin's regime, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics (particularly proof theory). Hilbert adopted and defended Georg Cantor's set theory and transfinite numbers. In 1900, he presented a collection of problems that set the course for much of the mathematical research of the 20th century. Hilbert and his students contributed significantly to establishing rigor and developed important tools used in modern mathematical physics. Hilbert is known as one of the founders of proof theory and mathematical logic. Life Early life and ed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauss
Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes referred to as the ''Princeps mathematicorum'' () and "the greatest mathematician since antiquity", Gauss had an exceptional influence in many fields of mathematics and science, and he is ranked among history's most influential mathematicians. Also available at Retrieved 23 February 2014. Comprehensive biographical article. Biography Early years Johann Carl Friedrich Gauss was born on 30 April 1777 in Brunswick (Braunschweig), in the Duchy of Brunswick-Wolfenbüttel (now part of Lower Saxony, Germany), to poor, working-class parents. His mother was illiterate and never recorded the date of his birth, remembering only that he had been born on a Wednesday, eight days before the Feast of the Ascension (which occurs 39 days after Easter). Gau ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unimodal
In mathematics, unimodality means possessing a unique mode. More generally, unimodality means there is only a single highest value, somehow defined, of some mathematical object. Unimodal probability distribution In statistics, a unimodal probability distribution or unimodal distribution is a probability distribution which has a single peak. The term "mode" in this context refers to any peak of the distribution, not just to the strict definition of mode which is usual in statistics. If there is a single mode, the distribution function is called "unimodal". If it has more modes it is "bimodal" (2), "trimodal" (3), etc., or in general, "multimodal". Figure 1 illustrates normal distributions, which are unimodal. Other examples of unimodal distributions include Cauchy distribution, Student's ''t''-distribution, chi-squared distribution and exponential distribution. Among discrete distributions, the binomial distribution and Poisson distribution can be seen as unimodal, though ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vysochanskij–Petunin Inequality
In probability theory, the Vysochanskij– Petunin inequality gives a lower bound for the probability that a random variable with finite variance lies within a certain number of standard deviations of the variable's mean, or equivalently an upper bound for the probability that it lies further away. The sole restrictions on the distribution are that it be unimodal and have finite variance. (This implies that it is a continuous probability distribution except at the mode, which may have a non-zero probability.) Theorem Let X be a random variable with unimodal distribution, and \alpha\in \mathbb R. If we define \rho=\sqrt then for any r>0, :\begin \operatorname(, X-\alpha, \ge r)\le \begin \frac&r\ge \sqrt\rho \\ \frac-\frac&r\le \sqrt\rho \\ \end. \end Relation to Gauss's inequality Taking \alpha equal to a mode of X yields the first case of Gauss's inequality. Tightness of Bound Without loss of generality, assume \alpha=0 and \rho=1. * If r. * If 1\le r\le \sqrt, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Statistics
Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory. Introduction Statistical data collection is concerned with the planning of studies, especially with the design of randomized experiments and with the planning of surveys using random sampling. The initial analysis of the data often follows the study protocol specified prior to the study being conducted. The data from a study can also be analyzed to consider secondary hypotheses inspired by the initial results, or to suggest new studies. A secondary analysis of the data from a planned study uses tools from data analysis, and the process of doing this is mathematical statistics. Data analysis is divided into: * descriptive statistics - the pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pattern Recognition
Pattern recognition is the automated recognition of patterns and regularities in data. It has applications in statistical data analysis, signal processing, image analysis, information retrieval, bioinformatics, data compression, computer graphics and machine learning. Pattern recognition has its origins in statistics and engineering; some modern approaches to pattern recognition include the use of machine learning, due to the increased availability of big data and a new abundance of processing power. These activities can be viewed as two facets of the same field of application, and they have undergone substantial development over the past few decades. Pattern recognition systems are commonly trained from labeled "training" data. When no labeled data are available, other algorithms can be used to discover previously unknown patterns. KDD and data mining have a larger focus on unsupervised methods and stronger connection to business use. Pattern recognition focuses more on the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
