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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 opened up by Riemann's work. He was also closely involved in academic politics, and the politics of the new Italian state. Works * E. Betti, ''Sopra gli spazi di un numero qualunque di dimensioni'', Ann. Mat. Pura Appl. 2 ... [...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 west and north 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, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galois Theory
In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between 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 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 ''solvable by radicals'' if its roots may be expressed by a formula involving only integers, 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 antiquity cannot be solved as they were stated ( doubling the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1892 Deaths
Year 189 ( CLXXXIX) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Silanus and Silanus (or, less frequently, year 942 ''Ab urbe condita''). The denomination 189 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * Plague (possibly smallpox) kills as many as 2,000 people per day in Rome. Farmers are unable to harvest their crops, and food shortages bring riots in the city. China * Liu Bian succeeds Emperor Ling, as Chinese emperor of the Han Dynasty. * Dong Zhuo has Liu Bian deposed, and installs Emperor Xian as emperor. * Two thousand eunuchs in the palace are slaughtered in a violent purge in Luoyang, the capital of Han. By topic Arts and sciences * Galen publishes his ''"Treatise on the various temperaments"'' (aka ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1823 Births
Eighteen or 18 may refer to: * 18 (number), the natural number following 17 and preceding 19 * one of the years 18 BC, AD 18, 1918, 2018 Film, television and entertainment * ''18'' (film), a 1993 Taiwanese experimental film based on the short story ''God's Dice'' * ''Eighteen'' (film), a 2005 Canadian dramatic feature film * 18 (British Board of Film Classification), a film rating in the United Kingdom, also used in Ireland by the Irish Film Classification Office * 18 (''Dragon Ball''), a character in the ''Dragon Ball'' franchise * "Eighteen", a 2006 episode of the animated television series ''12 oz. Mouse'' Music Albums * ''18'' (Moby album), 2002 * ''18'' (Nana Kitade album), 2005 * '' 18...'', 2009 debut album by G.E.M. Songs * "18" (5 Seconds of Summer song), from their 2014 eponymous debut album * "18" (One Direction song), from their 2014 studio album ''Four'' * "18", by Anarbor from their 2013 studio album '' Burnout'' * "I'm Eighteen", by Alice Cooper commonly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Betti Group
In mathematics, homology is a general way of associating a sequence of algebraic objects, such as abelian groups or modules, with other mathematical objects such as topological spaces. Homology groups were originally defined in algebraic topology. Similar constructions are available in a wide variety of other contexts, such as abstract algebra, groups, Lie algebras, Galois theory, and algebraic geometry. The original motivation for defining homology groups was the observation that two shapes can be distinguished by examining their holes. For instance, a circle is not a disk because the circle has a hole through it while the disk is solid, and the ordinary sphere is not a circle because the sphere encloses a two-dimensional hole while the circle encloses a one-dimensional hole. However, because a hole is "not there", it is not immediately obvious how to define a hole or how to distinguish different kinds of holes. Homology was originally a rigorous mathematical method for d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Betti Cohomology
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewed as a method of assigning richer algebraic invariants to a space than homology. Some versions of cohomology arise by dualizing the construction of homology. In other words, cochains are functions on the group of chains in homology theory. From its beginning in topology, this idea became a dominant method in the mathematics of the second half of the twentieth century. From the initial idea of homology as a method of constructing algebraic invariants of topological spaces, the range of applications of homology and cohomology theories has spread throughout geometry and algebra. The terminology tends to hide the fact that cohomology, a contravariant theory, is more natural than homology in many applications. At a basic level, this has to do ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemann
Georg Friedrich Bernhard Riemann (; 17 September 1826 – 20 July 1866) was a German mathematician who made 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. Biography Early years Riemann was born on 17 September 1826 in Breselenz, a village near Dannenber ... [...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 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 Einstein was concerned with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernhard Riemann
Georg Friedrich Bernhard Riemann (; 17 September 1826 – 20 July 1866) was a German mathematician who made 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. Biography Early years Riemann was born on 17 September 1826 in Breselenz, a village near ... [...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 behavior 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 a specialist work of writing (in contrast to reference works) or exhibition on a single subject or an aspect of a subjec ... [...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 in 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 in 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 mathe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carlo Matteucci
Carlo Matteucci (20 or 21 June 1811 – 25 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 b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
