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Sergey Bobkov
Sergey Bobkov (Russian: Cергей Германович Бобков; born March 15, 1961) is a mathematician. Currently Bobkov is a professor at the University of Minnesota, Twin Cities. He was born in Vorkuta ( Komi Republic, Russia) and graduated from the Department of Mathematics and Mechanics in Leningrad State University. In 1988 he earned PhD in Mathematics and Physics (under direction of Vladimir N. Sudakov, Steklov Institute of Mathematics) and in 1997 earned his Doctor of Science. During 1998–2000 Bobkov held positions at Syktyvkar State University, Russia. From 1995 to 1996 he was an Alexander von Humboldt Fellow at Bielefeld University, Germany. He spent the summers of 2001 and 2002 as an EPSRC Fellow at Imperial College London, UK. Bobkov was awarded a Simons Fellowship (2012) and Humboldt Research Award (2014). Bobkov is known for research in mathematics on the border of probability theory, analysis, convex geometry and information theory Informati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analysis (mathematics)
Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions. These theories are usually studied in the context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space). History Ancient Mathematical analysis formally developed in the 17th century during the Scientific Revolution, but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were implicitly present in the early days of ancient Greek mathematics. For instance, an infinite geometric sum is implicit in Zeno's paradox of the dichotomy. (St ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1961 Births
Events January * January 3 ** United States President Dwight D. Eisenhower announces that the United States has severed diplomatic and consular relations with Cuba ( Cuba–United States relations are restored in 2015). ** Aero Flight 311 (Koivulahti air disaster): Douglas DC-3C OH-LCC of Finnish airline Aero crashes near Kvevlax (Koivulahti), on approach to Vaasa Airport in Finland, killing all 25 on board, due to pilot error: an investigation finds that the captain and first officer were both exhausted for lack of sleep, and had consumed excessive amounts of alcohol at the time of the crash. It remains the deadliest air disaster to occur in the country. * January 5 ** Italian sculptor Alfredo Fioravanti marches into the U.S. Consulate in Rome, and confesses that he was part of the team that forged the Etruscan terracotta warriors in the Metropolitan Museum of Art. ** After the 1960 military coup, General Cemal Gürsel forms the new government of Turkey (25th gove ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
People From Vorkuta
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 per ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Related categories * :Year of birth missing (living people) / :Year of birth unknown * :Date of birth missing (living people) / :Date of birth unknown * :Place of birth missing (living people) / :Place of birth unknown * :Year of death missing / :Year of death unknown * :Date of death missing / :Date of death unknown * :Place of death missing / :Place of death unknown * :Missing middle or first names See also * :Dead people * :Template:L, which generates this category or death years, and birth year and sort keys. : {{DEFAULTSORT:Living people 21st-century people People by status ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bobkov's Inequality
In probability theory, Bobkov's inequality is a functional isoperimetric inequality for the canonical Gaussian measure. It generalizes the Gaussian isoperimetric inequality. The equation was proven in 1997 by the Russian mathematician Sergey Bobkov. Bobkov's inequality Notation: Let *\gamma^n(dx)=(2\pi)^e^d^nx be the canonical Gaussian measure on \R^n with respect to the Lebesgue measure In measure theory, a branch of mathematics, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of ''n''-dimensional Euclidean space. For ''n'' = 1, 2, or 3, it coincides wit ..., *\phi(x)=(2\pi)^e^ be the one dimensional canonical Gaussian density *\Phi(t)=\gamma^1 \infty,t/math> the cumulative distribution function *I(t):=\phi(\Phi^(t)) be a function I(t): ,1to ,1/math> that vanishes at the end points \lim\limits_ I(t)=\lim\limits_ I(t)=0. Statement For every locally Lipschitz continuous (or smooth) function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concentration Of Measure
In mathematics, concentration of measure (about a median) is a principle that is applied in measure theory, probability and combinatorics, and has consequences for other fields such as Banach space theory. Informally, it states that "A random variable that depends in a Lipschitz way on many independent variables (but not too much on any of them) is essentially constant". The concentration of measure phenomenon was put forth in the early 1970s by Vitali Milman in his works on the local theory of Banach spaces, extending an idea going back to the work of Paul Lévy. It was further developed in the works of Milman and Gromov, Maurey, Pisier, Schechtman, Talagrand, Ledoux, and others. The general setting Let (X, d) be a metric space with a measure \mu on the Borel sets with \mu(X) = 1. Let :\alpha(\epsilon) = \sup \left\, where :A_\epsilon = \left\ is the \epsilon-''extension'' (also called \epsilon-fattening in the context of the Hausdorff distance) of a set A. The funct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isoperimetric Problems
In mathematics, the isoperimetric inequality is a geometric inequality involving the perimeter of a set and its volume. In n-dimensional space \R^n the inequality lower bounds the surface area or perimeter \operatorname(S) of a set S\subset\R^n by its volume \operatorname(S), :\operatorname(S)\geq n \operatorname(S)^ \, \operatorname(B_1)^, where B_1\subset\R^n is a unit sphere. The equality holds only when S is a sphere in \R^n. On a plane, i.e. when n=2, the isoperimetric inequality relates the square of the circumference of a closed curve and the area of a plane region it encloses. '' Isoperimetric'' literally means "having the same perimeter". Specifically in \R ^2, the isoperimetric inequality states, for the length ''L'' of a closed curve and the area ''A'' of the planar region that it encloses, that : L^2 \ge 4\pi A, and that equality holds if and only if the curve is a circle. The isoperimetric problem is to determine a plane figure of the largest possible area ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information Theory
Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. The field is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering (field), information engineering, and electrical engineering. A key measure in information theory is information entropy, entropy. Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. For example, identifying the outcome of a fair coin flip (with two equally likely outcomes) provides less information (lower entropy) than specifying the outcome from a roll of a dice, die (with six equally likely outcomes). Some other important measures in information theory are mutual informat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Geometry
In mathematics, convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space. Convex sets occur naturally in many areas: computational geometry, convex analysis, discrete geometry, functional analysis, geometry of numbers, integral geometry, linear programming, probability theory, game theory, etc. Classification According to the Mathematics Subject Classification MSC2010, the mathematical discipline ''Convex and Discrete Geometry'' includes three major branches: * general convexity * polytopes and polyhedra * discrete geometry (though only portions of the latter two are included in convex geometry). General convexity is further subdivided as follows: *axiomatic and generalized convexity *convex sets without dimension restrictions *convex sets in topological vector spaces *convex sets in 2 dimensions (including convex curves) *convex sets in 3 dimensions (including convex surfaces) *convex sets in ''n'' dimensions (including convex hy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion). Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vorkuta
Vorkuta (russian: Воркута́; kv, Вӧркута, ''Vörkuta''; Nenets for "the abundance of bears", "bear corner") is a coal-mining town in the Komi Republic, Russia, situated just north of the Arctic Circle in the Pechora coal basin at the river Vorkuta. In 2010 its population was 70,548, down from 84,917 in 2002. Vorkuta is the fourth largest city north of the Arctic Circle and the easternmost town in Europe. It is also the coldest city in all of Europe, boasting a record cold temperature of −52 °C (−61 °F). Vorkuta's population has dropped steadily since the fall of the Soviet Union, when mines were privatized and many people began moving farther south. Many of the mines have been abandoned and by September 2020, the city's estimated population was only about 50,000. A report in March 2021 described the villages in the area as "ghost towns" with many "abandoned structures". History In 1930 the geologist Georgy Chernov (1906–2009) discovered subst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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