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Enrico Betti
Enrico Betti Glaoui (21 October 1823 – 11 August 1892) was an Italian mathematician, now remembered mostly for his 1871 paper on topology that led to the later naming after him of the Betti numbers. He worked also on the theory of equations, giving early expositions of Galois theory. He also discovered Betti's theorem, a result in the theory of elasticity. Biography Betti was born in Pistoia, Tuscany. He graduated from the University of Pisa in 1846 under (1792–1857). In Pisa, he was also a student of Ottaviano-Fabrizio Mossotti and Carlo Matteucci. After a time teaching, he held an appointment there from 1857. In 1858 he toured Europe with Francesco Brioschi and Felice Casorati, meeting Bernhard Riemann. Later he worked in the area of theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pistoia
Pistoia (; ) is a city and ''comune'' in the Italian region of Tuscany, the capital of a province of the same name, located about north-west of Florence and is crossed by the Ombrone Pistoiese, a tributary of the River Arno. It is a typical Italian medieval city, and it attracts many tourists, especially in the summer. The city is famous throughout Europe for its plant nurseries. History ''Pistoria'' (in Latin other possible forms are ''Pistorium'' or ''Pistoriae'') was a centre of Gallic, Ligurian and Etruscan settlements before becoming a Roman colony in the 6th century BC, along the important road Via Cassia: in 62 BC the demagogue Catiline and his fellow conspirators were slain nearby. From the 5th century the city was a bishopric, and during the Lombardic kingdom it was a royal city and had several privileges. Pistoia's most splendid age began in 1177 when it proclaimed itself a free commune: in the following years it became an important political centre, ere ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galois Theory
In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field (mathematics), field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to group theory, which makes them simpler and easier to understand. Galois introduced the subject for studying root of a function, roots of polynomials. This allowed him to characterize the polynomial equations that are solvable by radicals in terms of properties of the permutation group of their roots—an equation is by definition ''solvable by radicals'' if its roots may be expressed by a formula involving only integers, nth root, th roots, and the four basic arithmetic operations. This widely generalizes the Abel–Ruffini theorem, which asserts that a general polynomial of degree at least five cannot be solved by radicals. Galois theory has been used to solve classic problems including showing that two problems of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1892 Deaths
In Samoa, this was the only leap year spanned to 367 days as July 4 repeated. This means that the International Date Line was drawn from the east of the country to go west. Events January * January 1 – Ellis Island begins processing Immigration to the United States, immigrants to the United States. February * February 27 – Rudolf Diesel applies for a patent, on his compression ignition engine (the Diesel engine). * February 29 – St. Petersburg, Florida is incorporated as a town. March * March 1 – Theodoros Deligiannis ends his term as Prime Minister of Greece and Konstantinos Konstantopoulos takes office. * March 6–March 8, 8 – "Exclusive Agreement": Rulers of the Trucial States (Abu Dhabi, Dubai, Sharjah, Ajman, Ras al-Khaimah and Umm al-Quwain) sign an agreement, by which they become ''de facto'' British protectorates. * March 11 – The first basketball game is played in public, between students and faculty at the Springfield YMCA before 200 spectators. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1823 Births
Events January–March * January 22 – By secret treaty signed at the Congress of Verona#Spanish Question, Congress of Verona, the Quintuple Alliance gives France a mandate to invade Spain for the purpose of restoring Ferdinand VII of Spain, Ferdinand VII (who has been captured by armed revolutionary liberals) as absolute monarch of the country. * January 23 – In Paviland Cave on the Gower Peninsula of Wales, William Buckland inspects the "Red Lady of Paviland", the first identification of a prehistoric (male) human burial (although Buckland dates it as Roman). * February 3 ** Jackson Male Academy, precursor of Union University, opens in Tennessee. ** Gioachino Rossini's opera ''Semiramide'' is first performed, at ''La Fenice'' in Venice. * February 10 – The first worldwide carnival parade takes place in Cologne, Kingdom of Prussia, Prussia. * February 11 – Carnival tragedy of 1823: About 110 boys are killed during a stampede at the Franciscan Church of St Mary of Je ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Betti Group
In mathematics, the term homology, originally introduced in algebraic topology, has three primary, closely-related usages. The most direct usage of the term is to take the ''homology of a chain complex'', resulting in a sequence of abelian groups called ''homology groups.'' This operation, in turn, allows one to associate various named ''homologies'' or ''homology theories'' to various other types of mathematical objects. Lastly, since there are many homology theories for topological spaces that produce the same answer, one also often speaks of the ''homology of a topological space''. (This latter notion of homology admits more intuitive descriptions for 1- or 2-dimensional topological spaces, and is sometimes referenced in popular mathematics.) There is also a related notion of the cohomology of a cochain complex, giving rise to various cohomology theories, in addition to the notion of the cohomology of a topological space. Homology of chain complexes To take the homology of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Betti Cohomology
Betti may refer to: People * Betti (given name) * Betti (surname) Other uses * Betti number in topology, named for Enrico Betti * Betti's theorem in engineering theory, named for Enrico Betti * Betti reaction, a chemical addition reaction See also * Beti (other) * Betty (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemann
Georg Friedrich Bernhard Riemann (; ; 17September 182620July 1866) was a German mathematician who made profound contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rigorous formulation of the integral, the Riemann integral, and his work on Fourier series. His contributions to complex analysis include most notably the introduction of Riemann surfaces, breaking new ground in a natural, geometric treatment of complex analysis. His 1859 paper on the prime-counting function, containing the original statement of the Riemann hypothesis, is regarded as a foundational paper of analytic number theory. Through his pioneering contributions to differential geometry, Riemann laid the foundations of the mathematics of general relativity. He is considered by many to be one of the greatest mathematicians of all time. Early years Riemann was born on 17 September 1826 in Breselenz, a village near Dannenberg in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena. The advancement of science generally depends on the interplay between experimental studies and theory. In some cases, theoretical physics adheres to standards of mathematical rigour while giving little weight to experiments and observations.There is some debate as to whether or not theoretical physics uses mathematics to build intuition and illustrativeness to extract physical insight (especially when normal experience fails), rather than as a tool in formalizing theories. This links to the question of it using mathematics in a less formally rigorous, and more intuitive or heuristic way than, say, mathematical physics. For example, while developing special relativity, Albert E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernhard Riemann
Georg Friedrich Bernhard Riemann (; ; 17September 182620July 1866) was a German mathematician who made profound contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rigorous formulation of the integral, the Riemann integral, and his work on Fourier series. His contributions to complex analysis include most notably the introduction of Riemann surfaces, breaking new ground in a natural, geometric treatment of complex analysis. His 1859 paper on the prime-counting function, containing the original statement of the Riemann hypothesis, is regarded as a foundational paper of analytic number theory. Through his pioneering contributions to differential geometry, Riemann laid the foundations of the mathematics of general relativity. He is considered by many to be one of the greatest mathematicians of all time. Early years Riemann was born on 17 September 1826 in Breselenz, a village near Danne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Felice Casorati (mathematician)
Felice Casorati (17 December 1835 – 11 September 1890) was an Italian mathematician who studied at the University of Pavia. He was born in Pavia and died in Casteggio. He is best known for the Casorati–Weierstrass theorem in complex analysis. The theorem, named for Casorati and Karl Theodor Wilhelm Weierstrass, describes the remarkable behaviour of holomorphic functions near essential singularities, which is that every holomorphic function gets values from any complex neighbourhood, in any neighbourhood of the singularity. The Casorati matrix is useful in the study of linear difference equations, just as the Wronskian is useful with linear differential equations. It is calculated based on n functions of the single input variable. Works * , available at Gallica (also aGDZ. Freely available copies of volume 1 of his best-known monograph A monograph is generally a long-form work on one (usually scholarly) subject, or one aspect of a subject, typically created by a sin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Francesco Brioschi
Francesco Brioschi (22 December 1824 – 13 December 1897) was an Italian mathematician. Biography Brioschi was born in Milan in 1824. He graduated from the Collegio Borromeo in 1847. From 1850 he taught analytical mechanics at the University of Pavia. After the Italian unification in 1861, he was elected to the Chamber of Deputies and then appointed twice secretary of the Italian Education Ministry. In 1863 he founded the Polytechnic University of Milan, where he worked until his death, lecturing in hydraulics, analytical mechanics and construction engineering. In 1865 he entered the Senate of the Kingdom. In 1870 he became a member of the Accademia dei lincei and in 1884 he succeeded Quintino Sella as president of the National Academy of the Lincei. He directed the ''Il Politecnico'' (''The Polytechnic'') review and, between 1867 and 1877, the ''Annali di Matematica Pura ed Applicata'' (''Annals of pure and applied mathematics''). He died in Milan in 1897. As a mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carlo Matteucci
Carlo Matteucci (20 June 1811 – 24 June 1868) was an Italian physicist and neurophysiologist who was a pioneer in the study of bioelectricity. Biography Carlo Matteucci was born at Forlì, in the province of Romagna, to Vincenzo Matteucci, a physician, and Chiara Folfi. He studied mathematics at the University of Bologna from 1825 to 1828, receiving his doctorate in 1829. From 1829 to 1831, he studied at the École Polytechnique in Paris, France. Upon returning to Italy, Matteucci studied at Bologna (1832), Florence, Ravenna (1837) and Pisa. He established himself as the head of the laboratory of the Hospital of Ravenna and became a professor of physics at the local college. In 1840, by recommendation of François Arago (1786–1853), his teacher at the École Polytechnique, to the Grand-Duke of Tuscany, Matteucci accepted a post of professor of physics at the University of Pisa. Instigated by the work of Luigi Galvani (1737–1798) on bioelectricity, Matteucci began in 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
