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Erik Albert Holmgren
Erik Albert Holmgren (7 July 1872 – 18 March 1943) was a Swedish mathematician known for contributions to partial differential equations. Holmgren's uniqueness theorem is named after him. Torsten Carleman Torsten Carleman (8 July 1892, Visseltofta, Osby Municipality – 11 January 1949, Stockholm), born Tage Gillis Torsten Carleman, was a Swedish mathematician, known for his results in classical analysis and its applications. As the director of ... was one of his students. His father was the mathematician Hjalmar Holmgren (1822 – 1885). Notes External links * Swedish mathematicians PDE theorists 1943 deaths 1872 births {{Sweden-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sweden
Sweden, ; fi, Ruotsi; fit, Ruotti; se, Ruoŧŧa; smj, Svierik; sje, Sverji; sju, Sverje; sma, Sveerje or ; yi, שוועדן, Shvedn; rmu, Svedikko; rmf, Sveittiko. formally the Kingdom of Sweden, is a Nordic countries, Nordic country located on the Scandinavian Peninsula in Northern Europe. It borders Norway to the west and north, and Finland to the east. At , Sweden is the largest Nordic country and the List of European countries by area, fifth-largest country in Europe. The Capital city, capital and largest city is Stockholm. Sweden has a population of 10.5 million, and a low population density of ; around 87% of Swedes reside in urban areas in the central and southern half of the country. Sweden’s urban areas together cover 1.5% of its land area. Because the country is so long, ranging from 55th parallel north, 55°N to 69th parallel north, 69°N, the climate of Sweden is diverse. Sweden has been inhabited since Prehistoric Sweden, prehistoric times, . T ... [...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 were Thales of Miletus (c. 624–c.546 BC); 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' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagoreans, 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 mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equations
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to how is thought of as an unknown number to be solved for in an algebraic equation like . However, it is usually impossible to write down explicit formulas 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 e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Holmgren's Uniqueness Theorem
In the theory of partial differential equations, Holmgren's uniqueness theorem, or simply Holmgren's theorem, named after the Swedish mathematician Erik Albert Holmgren (1873–1943), is a uniqueness result for linear partial differential equations with real analytic coefficients. Simple form of Holmgren's theorem We will use the multi-index notation: Let \alpha=\\in \N_0^n,, with \N_0 standing for the nonnegative integers; denote , \alpha, =\alpha_1+\cdots+\alpha_n and : \partial_x^\alpha = \left(\frac\right)^ \cdots \left(\frac\right)^. Holmgren's theorem in its simpler form could be stated as follows: :Assume that ''P'' = ∑, ''α'', ≤''m'' ''A''''α''(x)∂ is an elliptic partial differential operator with real-analytic coefficients. If ''Pu'' is real-analytic in a connected open neighborhood ''Ω'' ⊂ R''n'', then ''u'' is also real-analytic. This statement, with "analytic" replaced by "smooth", is Hermann Weyl' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torsten Carleman
Torsten Carleman (8 July 1892, Visseltofta, Osby Municipality – 11 January 1949, Stockholm), born Tage Gillis Torsten Carleman, was a Swedish mathematician, known for his results in classical analysis and its applications. As the director of the Mittag-Leffler Institute for more than two decades, Carleman was the most influential mathematician in Sweden. Work The dissertation of Carleman under Erik Albert Holmgren, as well as his work in the early 1920s, was devoted to singular integral equations. He developed the spectral theory of integral operators with ''Carleman kernels'', that is, kernels ''K''(''x'', ''y'') such that ''K''(''y'', ''x'') = for almost every (''x'', ''y''), and : \int , K(x, y) , ^2 dy < \infty for almost every ''x''. In the mid-1920s, Carleman developed the theory of quasi-analytic functions. He proved ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Swedish Mathematicians
Swedish or ' may refer to: Anything from or related to Sweden, a country in Northern Europe. Or, specifically: * Swedish language, a North Germanic language spoken primarily in Sweden and Finland ** Swedish alphabet, the official alphabet used by the Swedish language * Swedish people or Swedes, persons with a Swedish ancestral or ethnic identity ** A national or citizen of Sweden, see demographics of Sweden The demography of Sweden is monitored by the ''Statistiska centralbyrån'' (Statistics Sweden). Sweden's population was 10,481,937 (May 2022), making it the 15th-most populous country in Europe after Czech Republic, the 10th-most populous m ... ** Culture of Sweden * Swedish cuisine See also * * Swedish Church (other) * Swedish Institute (other) * Swedish invasion (other) * Swedish Open (other) {{disambig Language and nationality disambiguation pages ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1943 Deaths
Events Below, the events of World War II have the "WWII" prefix. January * January 1 – WWII: The Soviet Union announces that 22 German divisions have been encircled at Stalingrad, with 175,000 killed and 137,650 captured. * January 4 – WWII: Greek-Polish athlete and saboteur Jerzy Iwanow-Szajnowicz is executed by the Germans at Kaisariani. * January 11 ** The United States and United Kingdom revise previously unequal treaty relationships with the Republic of China. ** Italian-American anarchist Carlo Tresca is assassinated in New York City. * January 13 – Anti- Nazi protests in Sofia result in 200 arrests and 36 executions. * January 14 – 24 – WWII: Casablanca Conference: Franklin D. Roosevelt, President of the United States; Winston Churchill, Prime Minister of the United Kingdom; and Generals Charles de Gaulle and Henri Giraud of the Free French forces meet secretly at the Anfa Hotel in Casablanca, Morocco, to plan the Allied European strategy for t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
