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Leonida Tonelli
Leonida Tonelli (19 April 1885 – 12 March 1946) was an Italian mathematician, noted for creating Tonelli's theorem, a variation of Fubini's theorem, and for introducing semicontinuity methods as a common tool for the direct method in the calculus of variations. Education Tonelli graduated from the University of Bologna in 1907; his Ph.D. thesis was written under the direction of Cesare Arzelà. Work Selected publications * , 1900 * . Zanichelli, Bologna, vol. 1: 1922, vol. 2: 1923 * * . Zanichelli, Bologna 1928 See also * Calculus of variations * Fourier series *Lebesgue integral *Mathematical analysis Notes References Biographical and general references *. The "''Yearbook''" of the renowned Italian scientific institution, including an historical sketch of its history, the list of all past and present members as well as a wealth of information about its academic and scientific activities. *, available from thBiblioteca Digitale Italiana di Matematica *. "''The work o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gallipoli, Apulia
Gallipoli (; scn, label= Salentino, Caḍḍìpuli ; ) is a southern Italian town and ''comune'' in the province of Lecce, in Apulia. In 2014, it had a population of 31,862 and is one of the towns where the Greek dialect Griko is spoken. Geography The town is located by the Ionian Sea, on the west coast of the Salento Peninsula. The town of Gallipoli is divided into two parts, the modern and the old city. The new town includes all the newest buildings including a skyscraper. The old town is located on a limestone island, linked to the mainland by a bridge built in the 16th century. The municipality borders with Alezio, Galatone, Matino, Sannicola and Taviano. It counts the hamlets (''frazioni'') of Baia Verde, Lido Conchiglie, Lido San Giovanni, Rivabella and Torre del Pizzo. History According to a legend, the city was founded in ancient times by Idomeneus of Crete. Pliny the Elder attributes the foundation to the Senones Gauls, while more likely it was a Messapic settle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semicontinuity
In mathematical analysis, semicontinuity (or semi-continuity) is a property of extended real-valued functions that is weaker than continuity. An extended real-valued function f is upper (respectively, lower) semicontinuous at a point x_0 if, roughly speaking, the function values for arguments near x_0 are not much higher (respectively, lower) than f\left(x_0\right). A function is continuous if and only if it is both upper and lower semicontinuous. If we take a continuous function and increase its value at a certain point x_0 to f\left(x_0\right) + c for some c>0, then the result is upper semicontinuous; if we decrease its value to f\left(x_0\right) - c then the result is lower semicontinuous. The notion of upper and lower semicontinuous function was first introduced and studied by René Baire in his thesis in 1899. Definitions Assume throughout that X is a topological space and f:X\to\overline is a function with values in the extended real numbers \overline=\R \cup \ = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modena
Modena (, , ; egl, label=Emilian language#Dialects, Modenese, Mòdna ; ett, Mutna; la, Mutina) is a city and ''comune'' (municipality) on the south side of the Po Valley, in the Province of Modena in the Emilia-Romagna region of northern Italy. A town, and seat of an archbishop, it is known for its car industry since the factories of the famous Italian upper-class sports car makers Ferrari, De Tomaso, Lamborghini, Pagani (automobile), Pagani and Maserati are, or were, located here and all, except Lamborghini, have headquarters in the city or nearby. One of Ferrari's cars, the Ferrari 360, 360 Modena, was named after the town itself. Ferrari's production plant and Formula One team Scuderia Ferrari are based in Maranello south of the city. The University of Modena, founded in 1175 and expanded by Francesco II d'Este in 1686, focuses on economics, medicine and law, and is the second oldest :wikt:athenaeum, athenaeum in Italy. Italian military officers are trained at the Milit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rome
, established_title = Founded , established_date = 753 BC , founder = King Romulus (legendary) , image_map = Map of comune of Rome (metropolitan city of Capital Rome, region Lazio, Italy).svg , map_caption = The territory of the ''comune'' (''Roma Capitale'', in red) inside the Metropolitan City of Rome (''Città Metropolitana di Roma'', in yellow). The white spot in the centre is Vatican City. , pushpin_map = Italy#Europe , pushpin_map_caption = Location within Italy##Location within Europe , pushpin_relief = yes , coordinates = , coor_pinpoint = , subdivision_type = Country , subdivision_name = Italy , subdivision_type2 = Region , subdivision_name2 = Lazio , subdivision_type3 = Metropolitan city , subdivision_name3 = Rome Capital , government_footnotes= , government_type = Strong Mayor–Council , leader_title2 = Legislature , leader_name2 = Capitoline Assemb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Accademia Nazionale Dei Lincei
The Accademia dei Lincei (; literally the "Academy of the Lynx-Eyed", but anglicised as the Lincean Academy) is one of the oldest and most prestigious European scientific institutions, located at the Palazzo Corsini on the Via della Lungara in Rome, Italy. Founded in the Papal States in 1603 by Federico Cesi, the academy was named after the lynx, an animal whose sharp vision symbolizes the observational prowess that science requires. Galileo Galilei was the intellectual centre of the academy and adopted "Galileo Galilei Linceo" as his signature. "The Lincei did not long survive the death in 1630 of Cesi, its founder and patron", and "disappeared in 1651". During the nineteenth century, it was revived, first in the Vatican and later in the nation of Italy. Thus the Pontifical Academy of Science, founded in 1847, claims this heritage as the ''Accademia Pontificia dei Nuovi Lincei ("Pontifical Academy of the New Lynxes")'', descending from the first two incarnations of the Academy. S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (mathematics), series, and analytic functions. These theories are usually studied in the context of Real number, real and Complex number, complex numbers and Function (mathematics), functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any Space (mathematics), space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space). History Ancient Mathematical analysis formally developed in the 17th century during the Scientific Revolution, but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lebesgue Integral
In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that function and the -axis. The Lebesgue integral, named after French mathematician Henri Lebesgue, extends the integral to a larger class of functions. It also extends the domains on which these functions can be defined. Long before the 20th century, mathematicians already understood that for non-negative functions with a smooth enough graph—such as continuous functions on closed bounded intervals—the ''area under the curve'' could be defined as the integral, and computed using approximation techniques on the region by polygons. However, as the need to consider more irregular functions arose—e.g., as a result of the limiting processes of mathematical analysis and the mathematical theory of probability—it became clear that more careful approximation techniques were needed to define a suitable integral. Also, one might ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Series
A Fourier series () is a summation of harmonically related sinusoidal functions, also known as components or harmonics. The result of the summation is a periodic function whose functional form is determined by the choices of cycle length (or ''period''), the number of components, and their amplitudes and phase parameters. With appropriate choices, one cycle (or ''period'') of the summation can be made to approximate an arbitrary function in that interval (or the entire function if it too is periodic). The number of components is theoretically infinite, in which case the other parameters can be chosen to cause the series to converge to almost any ''well behaved'' periodic function (see Pathological and Dirichlet–Jordan test). The components of a particular function are determined by ''analysis'' techniques described in this article. Sometimes the components are known first, and the unknown function is ''synthesized'' by a Fourier series. Such is the case of a discrete-ti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus Of Variations
The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to lie on a surface in space, then the solution is less obvious, and possibly many solutions may exist. Such solutions are known as ''geodesics''. A related problem is posed by Fermat's principle: light follows the path of shortest optical length connecting two points, which depends up ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laurence Chisholm Young
Laurence Chisholm Young (14 July 1905 – 24 December 2000) was a British mathematician known for his contributions to measure theory, the calculus of variations, optimal control theory, and potential theory. He was the son of William Henry Young and Grace Chisholm Young, both prominent mathematicians. He moved to the US in 1949 but never sought American citizenship. The concept of Young measure is named after him: he also introduced the concept of the generalized curve and a concept of generalized surface which later evolved in the concept of varifold. The Young integral also is named after him and has now been generalised in the theory of rough paths. Life and academic career Laurence Chisholm Young was born in Göttingen,. the fifth of the six children of William Henry Young and Grace Chisholm Young.. He held positions of Professor at the University of Cape Town, South Africa, and at the University of Wisconsin-Madison. He was also a chess grandmaster. Selected publicat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
