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Leonida Tonelli
Leonida Tonelli (19 April 1885 – 12 March 1946) was an Italian people, Italian mathematician, noted for proving Fubini's theorem#Tonelli's theorem for non-negative measurable functions, Tonelli's theorem, a variation of Fubini's theorem, and for introducing Semicontinuity, 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 includes a historical sketch of its history, the list of all past and present members as well as a wealth of information about its academic an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gallipoli, Apulia
Gallipoli (; ; ) is a Southern Italy, southern Italy, 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, 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 (''Frazione, 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, Senone Gauls, while more likely it was a Messap ... [...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). Briefly, a function on a domain X is lower semi-continuous if its epigraph \ is closed in X\times\R, and upper semi-continuous if -f is lower semi-continuous. 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. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modena
Modena (, ; ; ; ; ) 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. It has 184,739 inhabitants as of 2025. 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 Automobili, Pagani and Maserati are, or were, located there and all, except Lamborghini, (having their factory in Sant'Agata Bolognese), 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rome
Rome (Italian language, Italian and , ) is the capital city and most populated (municipality) of Italy. It is also the administrative centre of the Lazio Regions of Italy, region and of the Metropolitan City of Rome. A special named with 2,746,984 residents in , Rome is the list of cities in the European Union by population within city limits, third most populous city in the European Union by population within city limits. The Metropolitan City of Rome Capital, with a population of 4,223,885 residents, is the most populous metropolitan cities of Italy, metropolitan city in Italy. Rome metropolitan area, Its metropolitan area is the third-most populous within Italy. Rome is located in the central-western portion of the Italian Peninsula, within Lazio (Latium), along the shores of the Tiber Valley. Vatican City (the smallest country in the world and headquarters of the worldwide Catholic Church under the governance of the Holy See) is an independent country inside the city boun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Accademia Nazionale Dei Lincei
The (; literally the "Academy of the Lynx-Eyed"), 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 Papal States and later in the nation of Italy. Thus the Pontifical Academy of Sciences, established in 1936, claims this heritage as the ''Accademia Pontificia dei Nuovi Lincei (''"Pontifical Academy of the New Lynxes"'')'', founded in 1847, descending from the first two incarnations of t ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lebesgue Integral
In mathematics, the integral of a non-negative Function (mathematics), function of a single variable can be regarded, in the simplest case, as the area between the Graph of a function, graph of that function and the axis. The Lebesgue integral, named after france, French mathematician Henri Lebesgue, is one way to make this concept rigorous and to extend it to more general functions. The Lebesgue integral is more general than the Riemann integral, which it largely replaced in mathematical analysis since the first half of the 20th century. It can accommodate functions with discontinuities arising in many applications that are pathological from the perspective of the Riemann integral. The Lebesgue integral also has generally better analytical properties. For instance, under mild conditions, it is possible to exchange limits and Lebesgue integration, while the conditions for doing this with a Riemann integral are comparatively baroque. Furthermore, the Lebesgue integral can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Series
A Fourier series () is an Series expansion, expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood. For example, Fourier series were first used by Joseph Fourier to find solutions to the heat equation. This application is possible because the derivatives of trigonometric functions fall into simple patterns. Fourier series cannot be used to approximate arbitrary functions, because most functions have infinitely many terms in their Fourier series, and the series do not always Convergent series, converge. Well-behaved functions, for example Smoothness, smooth functions, have Fourier series that converge to the original function. The coefficients of the Fourier series are determined by integrals of the function multiplied by trigonometric func ... [...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 Function (mathematics), functions and functional (mathematics), functionals, to find maxima and minima of functionals: Map (mathematics), mappings from a set of Function (mathematics), 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: li ... [...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 publica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
