|
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 fonctions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tula, Russia
Tula ( rus, Тула, p=ˈtulə) 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, a tributary of the Oka. At the 2010 census, Tula had a population of 501,169, an increase from 481,216 in 2002, making it the 32nd largest city in Russia by population. A primarily industrial city, Tula was a fortress at the border of the Principality of Ryazan. The city was seized by Ivan Bolotnikov, and withstood a four-month siege by the Tsar's army. Historically, Tula was a major centre for the manufacture of 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 air base, Tula State University, Tula Kremlin, The Tula State Museum of Weapons and Kazanskaya embankment of the Upa River (). Tula has a historical association ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laguerre Polynomials
In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834–1886), are solutions of Laguerre's equation: xy'' + (1 - x)y' + ny = 0 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 Gaussian quadrature to numerically compute integrals of the form \int_0^\infty f(x) e^ \, dx. These polynomials, usually denoted , , …, are a polynomial sequence which may be defined by the Rodrigues formula, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Analysts
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Warsaw Faculty
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase ''universitas magistrorum et scholarium'', 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 Church 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 ''universitas'' (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, notarial law.Hunt Janin: "The university in medieval life, 1179–1499", McFarland, 2008, , p. 55f.de Ridder-Symoens, Hilde''A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Warsaw Alumni
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the designation is reserved for colleges that have a graduate school. The word ''university'' is derived from the Latin ''universitas magistrorum et scholarium'', which roughly means "community of teachers and scholars". The first universities were created in Europe by Catholic Church monks. The University of Bologna (''Università di Bologna''), founded in 1088, is the first university in the sense of: *Being a high degree-awarding institute. *Having independence from the ecclesiastic schools, although conducted by both clergy and non-clergy. *Using the word ''universitas'' (which was coined at its foundation). *Issuing secular and non-secular degrees: grammar, rhetoric, logic, theology, canon law, notarial law.Hunt Janin: "The university ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow State University Alumni
Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million residents within the city limits, over 17 million residents in the urban area, and over 21.5 million residents in the 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 largest cities; being the most populous city entirely in Europe, the largest urban and metropolitan area in Europe, and the largest city by land area on the European continent. First documented in 1147, Moscow grew to become a prosperous and powerful city that served as the capital of the Grand Duchy that bears its name. When the Grand Duchy of Moscow evolved into the Tsardom of Russia, Moscow remained the political and economic center for most of the Tsardom's history. When th ... [...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'' is sunk off Lyme Regis, Dorset, England, by an Imperial German Navy U-boat, with the loss of 547 crew. ** Battle of Broken Hill: A train ambush near Broken Hill, New South Wales, Australia, is carried out by two men (claiming to be in support of the Ottoman Empire) who are killed, together with 4 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'' premières in the United States, starring Theda Bara as a ''femme fatale''; she quickly becomes one o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1849 Births
Events January–March * January 1 – France begins issue of the 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. The Hungarian government and parliament flee to Debrecen. * January 8 – Hungarian Revolution of 1848: Romanian armed groups massacre 600 unarmed Hungarian civilians, at 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: Battle of Nagyszeben – The Hungarian army in Transylvania, led by Josef Bem, is defeated by the Austrians, led by Anton Puchner. * January 23 – Elizabeth Blackwell is awarded her M.D. by the Medi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Russian Language
Russian (russian: русский язык, russkij jazyk, link=no, ) is an East Slavic languages, East Slavic language mainly spoken in Russia. It is the First language, native language of the Russians, and belongs to the Indo-European languages, Indo-European language family. It is one of four living East Slavic languages, and is also a part of the larger Balto-Slavic languages. Besides Russia itself, Russian is an official language in Belarus, Kazakhstan, and Kyrgyzstan, and is used widely as a lingua franca throughout Ukraine, the Caucasus, Central Asia, and to some extent in the Baltic states. It was the De facto#National languages, ''de facto'' 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 and continues to be used in public life with varying proficiency in all of the post-Soviet states. Russian has over 258 million total speakers worldwide. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French Language
French ( or ) is a Romance language of the Indo-European family. It descended from the Vulgar Latin of the Roman Empire, as did all Romance languages. French evolved from Gallo-Romance, the Latin spoken in Gaul, and more specifically 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) largely supplanted. French was also influenced by native Celtic languages of Northern Roman Gaul like Gallia Belgica and by the ( Germanic) Frankish language of the post-Roman Frankish invaders. Today, owing to France's past overseas expansion, there are numerous French-based creole languages, most notably Haitian Creole. A French-speaking person or nation may be referred to as Francophone in both English and French. French is an official language in 29 countries across multiple continents, most of which are members of the ''Organisation internationale de la Francophonie'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrey Markov
Andrey Andreyevich Markov, first name also spelled "Andrei", in older works also spelled Markoff) (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. Markov and his younger brother Vladimir Andreevich 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 University). Among his t ... [...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, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. 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. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
_-_09.JPG "Click for more on -> University Of Warsaw Faculty")
