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Sergey Bernstein
Sergei Natanovich Bernstein (, sometimes Romanized as ; 5 March 1880 – 26 October 1968) was a Ukrainian and Soviet mathematician of Jewish origin known for contributions to Partial differential equation, partial differential equations, differential geometry, probability theory, and approximation theory. Life Bernstein was born into the Jewish family of prominent Ukrainian physiologist Nathaniel Bernstein in Odessa. Sergei was brought up in Odessa but his father died on 4 February 1891 just before he was eleven years old. He graduated from high school in 1898. After this, following his mother's wishes, he went with his elder sister to Paris. Bernstein's sister studied biology in Paris and did not return to Ukraine but worked at the Pasteur Institute. After one year studying mathematics at the Sorbonne, Bernstein decided that he would rather become an engineer and entered the École supérieure d'électricité. However, he continued to be interested in mathematics and spent thr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Odessa
ODESSA is an American codename (from the German language, German: ''Organisation der ehemaligen SS-Angehörigen'', meaning: Organization of Former SS Members) coined in 1946 to cover Ratlines (World War II aftermath), Nazi underground escape-plans made at the end of World War II by a group of ''SS'' officers with the aim of facilitating secret escape routes, and any directly ensuing arrangements. The concept of the existence of an actual ODESSA organisation has circulated widely in fictional Spy fiction, spy novels and movies, including Frederick Forsyth's best-selling 1972 thriller ''The Odessa File''. The escape-routes have become known as "Ratlines (World War II), ratlines". Known goals of elements within the ''SS'' included allowing ''SS'' members to escape to Argentina or to the Middle East under false passports. Although an unknown number of wanted Nazis and war criminals escaped Germany and often Europe, most experts deny that an organisation called ODESSA ever existed. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernstein Polynomial
In the mathematics, mathematical field of numerical analysis, a Bernstein polynomial is a polynomial expressed as a linear combination of #Bernstein basis polynomials, Bernstein basis polynomials. The idea is named after mathematician Sergei Natanovich Bernstein. Polynomials in Bernstein form were first used by Bernstein in a constructive proof for the Stone–Weierstrass theorem, Weierstrass approximation theorem. With the advent of computer graphics, Bernstein polynomials, restricted to the interval [0, 1], became important in the form of Bézier curves. A numerical stability, numerically stable way to evaluate polynomials in Bernstein form is de Casteljau's algorithm. Definition Bernstein basis polynomials The \ n + 1\ Bernstein basis polynomials of degree \ n\ are defined as : \ b_(x)\ \equiv\ \binom\ x^ \left( 1 - x \right)^\ , ~~ for ~~ \nu = 0\ ,\ \ldots\ , n\ , where \ \tbinom\ is a binomial coefficient. So, for example, \ b_(x)\ =\ \tbinomx^2(1-x)^3\ =\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Borovoe
Burabay (, ''Burabai,'' , ''Borovoye'') is a prominent lake of the Kokshetau Lakes, a group of lakes in northern Kazakhstan, located in the Burabay District of Akmola Region, in the eastern part of the Kokshetau Hills. The name of the lake originates from the word ''bor'', which means "pine forest". The historical name is Auliekol, which means " holy lake". Geography The lake is separated from nearby lake Ulken Shabakty to the north by a narrow strip of land. Lake Kishi Shabakty lies to the NW and lake Shchuchye to the SW. The shores of the lake are overgrown with pine forest. The water in the lake is limpid and the bottom can be seen clearly. The water surface of the lake is almost open, only the western and northwestern shores are rushy; the southern shores are rocky, and the eastern shores are sandy. The bottom is flat. The lake has several capes. Near the northwestern cape, there is a rocky mushroom-shaped island, Jumbaqtas ("Sphinx"), reaching an elevation of abo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow University
Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, and six branches. Alumni of the university include past leaders of the Soviet Union and other governments. As of 2019, 13 Nobel laureates, six Fields Medal winners, and one Turing Award winner were affiliated with the university. History Imperial Moscow University Ivan Shuvalov and Mikhail Lomonosov promoted the idea of a university in Moscow, and Russian Empress Elizabeth decreed its establishment on . The first lectures were given on . Saint Petersburg State University and MSU each claim to be Russia's oldest university. Though Moscow State University was founded in 1755, St. Petersburg which has had a continuous existence as a "university" since 1819 sees itself as the successor of an academy established on in 1724, by a decree of Peter the Great ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
USSR Academy Of Sciences
The Academy of Sciences of the Soviet Union was the highest scientific institution of the Soviet Union from 1925 to 1991. It united the country's leading scientists and was subordinated directly to the Council of Ministers of the Soviet Union (until 1946 the Council of People's Commissars of the Soviet Union). In 1991, by the decree of the President of the Russian Soviet Federative Socialist Republic, the Russian Academy of Sciences was established on the basis of the Academy of Sciences of the Soviet Union. History Creation of the Academy of Sciences of the Soviet Union The Academy of Sciences of the Soviet Union was formed by a resolution of the Central Executive Committee and the Council of People's Commissars of the Soviet Union dated July 27, 1925, on the basis of the Russian Academy of Sciences (before the February Revolution – the Imperial Saint Petersburg Academy of Sciences). In the first years of Soviet Russia, the Institute of the Academy of Sciences was perceived ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kharkiv University
The V. N. Karazin Kharkiv National University (), also known as Kharkiv National University or Karazin University, is a public university in Kharkiv, Ukraine. It was founded in 1804 through the efforts of Vasily Karazin, becoming the second oldest university in modern-day Ukraine. During the Russian invasion of Ukraine, all buildings were partially or fully destroyed by attacks from Russian forces. History Russian Empire On , the Decree on the Opening of the Imperial University in Kharkov came into force. The university became the second university in the south of the Russian Empire. It was founded on the initiative of the local community with Vasily Karazin at the fore, whose idea was supported by the nobility and the local authorities. Count Seweryn Potocki was appointed the first supervisor of the university, the first rector being the philologist and philosopher . In 1811, the Philotechnical Society was founded, while the Mathematical Society of Kharkov, the Historica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
École Supérieure D'électricité
École or Ecole may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoie, a French commune * École-Valentin, a French commune in the Doubs département * Grandes écoles, higher education establishments in France * The École The École, formerly Ecole Internationale de New York, is an intimate and independent French-American school, which cultivates an internationally minded community of students from 2 to 14 years old in New York City’s vibrant Flatiron Distric ..., a French-American bilingual school in New York City * Ecole Software, a Japanese video-games developer/publisher {{disambiguation, geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Approximation Theory
In mathematics, approximation theory is concerned with how function (mathematics), functions can best be approximation, approximated with simpler functions, and with quantitative property, quantitatively characterization (mathematics), characterizing the approximation error, errors introduced thereby. What is meant by ''best'' and ''simpler'' will depend on the application. A closely related topic is the approximation of functions by generalized Fourier series, that is, approximations based upon summation of a series of terms based upon orthogonal polynomials. One problem of particular interest is that of approximating a function in a computer mathematical library, using operations that can be performed on the computer or calculator (e.g. addition and multiplication), such that the result is as close to the actual function as possible. This is typically done with polynomial or Rational function, rational (ratio of polynomials) approximations. The objective is to make the approxi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory or probability calculus 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 of probability, axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure (mathematics), 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 (probability theory), event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of determinism, non-deterministic or uncertain processes or measured Quantity, quantities that may either be single occurrences or evolve over time in a random fashion). Although it is no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometry
Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as classical antiquity, antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Nikolai Lobachevsky, Lobachevsky. The simplest examples of smooth spaces are the Differential geometry of curves, plane and space curves and Differential geometry of surfaces, surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equation
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to how is thought of as an unknown number solving, e.g., an algebraic equation like . However, it is usually impossible to write down explicit formulae for solutions of partial differential equations. There is correspondingly a vast amount of modern mathematical and scientific research on methods to numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such as existence, uniqueness, regularity and stability. Among the many open questions are the existence ... [...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, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); 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's theorem. The number of known mathematicians grew when Pythagoras of Samos () 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 math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
