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Nikolay Yakovlevich Sonin
Nikolay Yakovlevich Sonin (Russian: Никола́й Я́ковлевич Со́нин, February 22, 1849 – February 27, 1915) was a Russian mathematician. Biography He was born in Tula and attended Lomonosov University, studying mathematics and physics there from 1865 to 1869. His advisor was Nikolai Bugaev. He obtained a master's degree with a thesis submitted in 1871, then he taught at the University of Warsaw where he obtained a doctorate in 1874. He was appointed to a chair in the University of Warsaw in 1876. In 1894, Sonin moved to St. Petersburg, where he taught at the University for Women. Sonin worked on special functions, in particular cylindrical functions. For instance, the Sonine formula is a formula given by Sonin for the integral of the product of three Bessel functions. He is furthermore credited with the introduction of the associated Laguerre polynomials.Sonine, N. Y. (1880): "Recherches sur les fonctions cylindriques et le développement des fonctio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tula, Russia
Tula (, ) is the largest city and the administrative center of Tula Oblast in Russia, located south of Moscow. Tula is located in the northern Central Russian Upland on the banks of the Upa (river), Upa River, a tributary of the Oka (river), Oka. At the Russian Census (2010), 2010 census, Tula had a population of 501,169, an increase from 481,216 in 2002, making it the List of cities and towns in Russia by population, 32nd-largest city in Russia by population.A primarily industrial types of inhabited localities in Russia, city, Tula was a fortress at the border of the Principality of Ryazan. The city was seized by Ivan Bolotnikov in 1606 during the Time of Troubles and withstood a four-month siege by the Tsar's army. Historically, Tula has been a major centre for the manufacture of Weapon, armaments. The Demidov family built the first armament factory in Russia in the city, in what would become the Tula Arms Plant, which still operates to this day. Tula is home to the Klokovo (a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laguerre Polynomials
In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834–1886), are nontrivial solutions of Laguerre's differential equation: xy'' + (1 - x)y' + ny = 0,\ y = y(x) which is a second-order linear differential equation. This equation has nonsingular solutions only if is a non-negative integer. Sometimes the name Laguerre polynomials is used for solutions of xy'' + (\alpha + 1 - x)y' + ny = 0~. where is still a non-negative integer. Then they are also named generalized Laguerre polynomials, as will be done here (alternatively associated Laguerre polynomials or, rarely, Sonine polynomials, after their inventor Nikolay Yakovlevich Sonin). More generally, a Laguerre function is a solution when is not necessarily a non-negative integer. The Laguerre polynomials are also used for Gauss–Laguerre quadrature to numerically compute integrals of the form \int_0^\infty f(x) e^ \, dx. These polynomials, usually denoted , , ..., are a polynomial sequ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Analysts
Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of abstract objects that consist of either abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to prove properties of objects, a ''proof'' consisting of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstracti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academic Staff Of The University Of Warsaw
An academy (Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of tertiary education. The name traces back to Plato's school of philosophy, founded approximately 386 BC at Akademia, a sanctuary of Athena, the goddess of wisdom and Skills, skill, north of Ancient Athens, Athens, Greece. The Royal Spanish Academy defines academy as scientific, literary or artistic society established with public authority and as a teaching establishment, public or private, of a professional, artistic, technical or simply practical nature. Etymology The word comes from the ''Academy'' in ancient Greece, which derives from the Athenian hero, ''Akademos''. Outside the city walls of Athens, the Gymnasium (ancient Greece), gymnasium was made famous by Plato as a center of learning. The sacred space, dedicated to the goddess of wisdom, Athena, had formerly been an olive Grove (nature), grove, hence the expression "the groves of Academe". In these gardens, the philos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Warsaw Alumni
A university () is an institution of tertiary education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase , which roughly means "community of teachers and scholars". Universities typically offer both undergraduate and postgraduate programs. The first universities in Europe were established by Catholic monks. The University of Bologna (), Italy, which was founded in 1088, is the first university in the sense of: *being a high degree-awarding institute. *using the word (which was coined at its foundation). *having independence from the ecclesiastic schools and issuing secular as well as non-secular degrees (with teaching conducted by both clergy and non-clergy): grammar, rhetoric, logic, theology, canon law and notarial law.Hunt Janin: "The university in medieval life, 1179–1499", McFarland, 2008, , p. 55f.de Ridder-Symoens, Hilde''A History of the University in Europe: Volume 1, Universities in the Midd ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow State University Alumni
Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents within the city limits, over 19.1 million residents in the urban area, and over 21.5 million residents in Moscow metropolitan area, its metropolitan area. The city covers an area of , while the urban area covers , and the metropolitan area covers over . Moscow is among the world's List of largest cities, largest cities, being the List of European cities by population within city limits, most populous city entirely in Europe, the largest List of urban areas in Europe, urban and List of metropolitan areas in Europe, metropolitan area in Europe, and the largest city by land area on the European continent. First documented in 1147, Moscow became the capital of the Grand Principality of Moscow, which led the unification of the Russian lan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1915 Deaths
Events Below, the events of World War I have the "WWI" prefix. January *January – British physicist Sir Joseph Larmor publishes his observations on "The Influence of Local Atmospheric Cooling on Astronomical Refraction". *January 1 ** WWI: British Royal Navy battleship HMS Formidable (1898), HMS ''Formidable'' is sunk off Lyme Regis, Dorset, England, by an Imperial German Navy U-boat, with the loss of 547 crew. **WWI: Battle of Broken Hill: A train ambush near Broken Hill, Australia, is carried out by two men (claiming to be in support of the Ottoman Empire) who are killed, together with four civilians. * January 5 – Joseph E. Carberry sets an altitude record of , carrying Capt. Benjamin Delahauf Foulois as a passenger, in a fixed-wing aircraft. * January 12 ** The United States House of Representatives rejects a proposal to give women the right to vote. ** ''A Fool There Was (1915 film), A Fool There Was'' premières in the United States, starring Theda Bara as a '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1849 Births
Events January–March * January 1 – France begins issue of the Ceres series (France), Ceres series, the nation's first postage stamps. * January 5 – Hungarian Revolution of 1848: The Austrian army, led by Alfred I, Prince of Windisch-Grätz, enters in the Hungarian capitals, Buda and Pest, Hungary, Pest. The Hungarian government and parliament flee to Debrecen. * January 8 – Hungarian Revolution of 1848: Romanian armed groups massacre 600 unarmed Hungarian civilians, at Aiud, Nagyenyed.Hungarian HistoryJanuary 8, 1849 And the Genocide of the Hungarians of Nagyenyed/ref> * January 13 ** Second Anglo-Sikh War – Battle of Tooele: British forces retreat from the Sikhs. ** The Colony of Vancouver Island is established. * January 21 ** General elections are held in the Papal States. ** Hungarian Revolution of 1848: At Sibiu, Nagyszeben (now Sibiu in Romania)– The Hungarian army in Transylvania, led by Josef Bem, is defeated by the Austrians, led by Anton Puchner. * Ja ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Russian Language
Russian is an East Slavic languages, East Slavic language belonging to the Balto-Slavic languages, Balto-Slavic branch of the Indo-European languages, Indo-European language family. It is one of the four extant East Slavic languages, and is the native language of the Russians. It was the ''de facto'' and ''de jure'' De facto#National languages, official language of the former Soviet Union.1977 Soviet Constitution, Constitution and Fundamental Law of the Union of Soviet Socialist Republics, 1977: Section II, Chapter 6, Article 36 Russian has remained an official language of the Russia, Russian Federation, Belarus, Kazakhstan, Kyrgyzstan, and Tajikistan, and is still commonly used as a lingua franca in Ukraine, Moldova, the Caucasus, Central Asia, and to a lesser extent in the Baltic states and Russian language in Israel, Israel. Russian has over 253 million total speakers worldwide. It is the List of languages by number of speakers in Europe, most spoken native language in Eur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French Language
French ( or ) is a Romance languages, Romance language of the Indo-European languages, Indo-European family. Like all other Romance languages, it descended from the Vulgar Latin of the Roman Empire. French evolved from Northern Old Gallo-Romance, a descendant of the Latin spoken in Northern Gaul. Its closest relatives are the other langues d'oïl—languages historically spoken in northern France and in southern Belgium, which French (Francien language, Francien) largely supplanted. It was also substratum (linguistics), influenced by native Celtic languages of Northern Roman Gaul and by the Germanic languages, Germanic Frankish language of the post-Roman Franks, Frankish invaders. As a result of French and Belgian colonialism from the 16th century onward, it was introduced to new territories in the Americas, Africa, and Asia, and numerous French-based creole languages, most notably Haitian Creole, were established. A French-speaking person or nation may be referred to as Fra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrey Markov
Andrey Andreyevich Markov (14 June 1856 – 20 July 1922) was a Russian mathematician best known for his work on stochastic processes. A primary subject of his research later became known as the Markov chain. He was also a strong, close to master-level, chess player. Markov and his younger brother Vladimir Markov (mathematician), Vladimir Andreyevich Markov (1871–1897) proved the Markov brothers' inequality. His son, another Andrey Markov (Soviet mathematician), Andrey Andreyevich Markov (1903–1979), was also a notable mathematician, making contributions to constructive mathematics and Recursion#Functional recursion, recursive function theory. Biography Andrey Markov was born on 14 June 1856 in Russia. He attended the St. Petersburg Grammar School, where some teachers saw him as a rebellious student. In his academics he performed poorly in most subjects other than mathematics. Later in life he attended Saint Petersburg Imperial University (now Saint Petersburg State Uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Integration
In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for "numerical integration", especially as applied to one-dimensional integrals. Some authors refer to numerical integration over more than one dimension as cubature; others take "quadrature" to include higher-dimensional integration. The basic problem in numerical integration is to compute an approximate solution to a definite integral :\int_a^b f(x) \, dx to a given degree of accuracy. If is a smooth function integrated over a small number of dimensions, and the domain of integration is bounded, there are many methods for approximating the integral to the desired precision. Numerical integration has roots in the geometrical problem of finding a square with the same area as a given plane figure ('' quadrature'' or ''squaring''), as in the quadrature of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
